CN100447688C - Electronic cam control method and servo motor control system - Google Patents

Abstract

The present invention provides an electronic cam control method in which displacement points, accelerations, and the like can be smoothly connected between a synchronous control section and an asynchronous control section, without vibration. This is a control method of an electronic cam using a servo motor. There is a synchronous control section in which the control object is moved at a constant speed, and an asynchronous control in which the control object is moved from the end position of the synchronous control section to the start position of the next synchronous control section interval, the control in the asynchronous control interval uses a quintic function for the position control of the electronic cam, uses a quartic function for the speed control of the electronic cam, and uses a cubic function for the acceleration control of the electronic cam, so that the control makes the asynchronous The operation of the electronic cam near the change point of switching between the control interval and the synchronous control interval is smooth.

Description

Electronic cam control method and servo motor control system

technical field

The invention relates to a control method of an electronic cam and a servo motor control system.

Background technique

Various industrial machines such as packaging machines use speed-controllable motors such as servo motors as drive sources. The packaging machine includes: a film supply unit that continuously draws out a strip-shaped packaging film and supplies it to the packaging machine body; a packaged object supply unit that supplies the packaged objects to the packaging machine body at predetermined intervals; and the packaging machine body. The main body of the packaging machine is properly processed (for example, tubular bag making, bag forming) into a form that can wrap the packaged object with the supplied packaging film, and at the same time store the packaged object in the processed packaging film. Then, the object to be packaged is transported in a state housed in the packaging film, and during the transportation, the packaging film is sealed and cut at an appropriate position to manufacture individual packages.

The sealing process for conventional packaging films is carried out for the side edges of the film in the direction of travel (longitudinal seal, central seal) and in the direction perpendicular to the direction of travel (transverse seal, end seal). Each sealing position is sealed with different types of sealing devices.

Moreover, in the case of a packaging machine, for example, as a process of continuously drawing out a strip-shaped film in a film supply part, or a process of feeding a packaged object to the packaging machine body while being conveyed by a packaged object supply part, or a packaging machine The drive source of each closing device in the drive source respectively uses servomotor or other electric machinery.

The end closure device used to seal the packaging film in the direction perpendicular to the traveling direction includes a pair of upper and lower end closures (built-in heaters), which move the end closures in a prescribed trajectory, and the front end of the end closures The packaging film is clamped from top to bottom with a specified pressure between the sealing surfaces of the packaging film, so that the contact parts of the packaging film are melted and heat-sealed. If the moving track of the closing surface of the end closure is roughly different, there are two types of circular and non-circular represented by a roughly rectangular shape. The former circular trajectory is called a rotary type, and end closures are installed on the upper and lower pairs of rotating shafts. Furthermore, when the rotary shaft is rotated in a certain direction, the end closure also rotates and moves. At this time, the closing surface of the end closure is formed in an arc shape, and the radius of curvature of the arc is substantially consistent with the radius of curvature of the circular track. As a result, line contact is made slowly from the side in the advancing direction of the closure surface, and as a result, a terminal closure portion corresponding to the width of the closure surface is formed.

There are box motion type and crank motion type of the end closure device adopting a non-circular locus such as a substantially rectangular shape. Both methods move horizontally in a state where the film is clamped by the upper and lower pair of end sealers, so that the time for the sealing surface to be in contact with the end sealing portion of the packaging film is prolonged. Since this method can prolong the heating time for the film, it is suitable for the case where the packaging film is difficult to melt and soften, and it is difficult to heat seal the film material.

In addition, in the end closure device, a cutter is built in the sealing surface of the end closure, and the packaging film containing the packaged objects is separated one by one from the front end of the packaging film by closing and cutting the packaging film toward the lateral end. manufacture.

Furthermore, the end closing device seals a predetermined portion of the packaging film (film portion between front and rear packaged objects) in the lateral direction every time the end sealer moves (one revolution). Therefore, it is necessary to perform control so that the pair of end sealers sandwich the packaging film in accordance with the timing at which a predetermined portion for performing end closure of the packaging film reaches the position where the end closure device is installed. In other words, when the packaging film is controlled to be transported at a certain speed, when the same product is packaged, since the packaging distance (the distance between the end sealing parts of the packaging film) is also equal, it takes a certain amount of time (transportation time) between the end closures. Speed x packaging pitch) to clamp the film at intervals.

On the other hand, it is necessary to make the conveying speed of the packaging film equal to the moving speed of the sealing surface of the end closure while the packaging film is clamped by the end closure. Moreover, in many cases, when the moving speed of the sealing surface of the end closure is constant during one rotation (one revolution) of the end closure, the required end sealing position cannot be clamped by a pair of end closures. .

Therefore, usually the closing surface of the end closure is clamped between the packaging film and controlled so that the closing surface of the end closure is synchronized with the conveying speed of the packaging film and moves at the same speed as the conveying speed. When the sealing surface leaves the packaging film, the appropriate The speed of movement of the sealing surfaces is controlled, and then when the packaging film is clamped between the sealing surfaces, it is in contact with the correct end closure location in the packaging film and can be heat-sealed.

Recently, a servo motor is used as a drive source for the end sealer, and the end sealer is operated as described above (speed change) by electronic cam control using the servo motor. Here, the period in synchronization with the conveyance speed of the film is called a synchronous control period, and the period out of synchronization with the conveyance speed of the film is called an asynchronous control period. In the synchronous control section, the electronic cam control is uniquely specified according to the conveying speed of the film. Specifically, in the case of the rotary type, the rotational speed of the servo motor is constant, and in the case of the square motion type or the crank motion type, the rotational speed of the servo motor is controlled to increase or decrease according to a predetermined pattern.

As mentioned above, the rotation speed of the servo motor in the synchronous control section is uniquely specified according to the conveying speed of the packaging film, and the time of one synchronous control section is determined according to the packaging distance (packing interval) for performing end sealing and the conveying speed of the packaging film. The times of the asynchronous control intervals of and once are uniquely solved, respectively. Therefore, as a simple consideration, by dividing the distance (rotation angle of the motor) to be moved by the end sealer in the asynchronous control section by the time allocated to the asynchronous control section, it can be obtained by making the non-synchronous control section constant speed Movement so that the closing surface of the end closure is at the start position of the next synchronous control interval at the required timing.

As electronic cam control using this servo motor, the technology disclosed in Patent Document 1 is conventional. The control method disclosed in this Patent Document 1 is an example of electronic cam control using a servomotor for a rotary cutting device that cuts a film laterally or a sealing device that seals a film laterally. The control is smooth around the transition point from the asynchronous control interval to the synchronous control interval.

Specifically, since the technology disclosed in Patent Document 1 is applied to a rotary type, the speed of the electronic cam is controlled to be a straight line (constant speed) in the synchronous control section and a cubic curve in the asynchronous control section.

[Patent Document 1] JP-A-2000-198094

In the invention disclosed in Patent Document 1, the acceleration of the electronic cam cannot be smoothed in the vicinity of the change point from the asynchronous control section to the synchronous control section. In this way, if the acceleration waveform is discontinuous between the asynchronous control section and the synchronous control section, vibration may be generated there. In particular, as the number of products produced per unit time increases, the demand for high-speed operation increases, and vibration tends to occur near the change point from the asynchronous control section to the synchronous control section, which becomes an obstacle to high-speed control.

Furthermore, in the method of generating a cam table for electronic cam control offline, the synchronization start position, synchronization range, and synchronization ratio of the synchronization curve in offline are changed, or specific points are passed in order to prevent mechanical interference, etc. It is impossible to generate and carry out the asynchronous cam curve in real time, and the cam table needs to be regenerated, which reduces the efficiency.

Contents of the invention

The object of the present invention is to provide a control method of an electronic cam and a servo motor control system, in which the acceleration of the electronic cam can be smoothly connected at the displacement point between the synchronous control section and the non-synchronous control section without vibration.

The control method of the electronic cam of the present invention is a control method of the electronic cam using a servo motor, and has: a synchronous control section for controlling the object to be controlled to move to the same position at the same time with respect to the position of the main shaft; and performing An asynchronous control section used for control of moving the control object from the end position of the synchronous control section to the start position of the next synchronous control section. Also, the control in the asynchronous control interval, by

Use the quintic function for the position control of the electronic cam,

Use the quartic function for the speed control of the electronic cam,

By using a cubic function for the acceleration control of the electronic cam, it is possible to smoothly control the operation of the electronic cam near the change point where the asynchronous control section and the synchronous control section are switched.

In addition, it is preferable that the values of the main shaft position, cam position, cam speed, and cam acceleration as the end position information of the asynchronous control section can be accepted as input parameters of each function at any time.

Furthermore, preferably as the start position information of the asynchronous control section, for each control cycle, the values of the main shaft position, cam position, cam speed, and cam acceleration obtained in the previous control cycle are used as input parameters of each function .

Furthermore, it is preferable to obtain the quintic function so that it passes through the cam position with respect to the main shaft position set as a specified passing point on the way of the asynchronous control section, and obtain the cubic function so that the specified passing point on the way The cam acceleration is 0.

On the other hand, the servo motor control system of the present invention has a synchronous control section for controlling the object to be controlled to move to the same position at the same timing with respect to the spindle position, and a synchronous control section for moving the object to be controlled from The servo motor control system of the asynchronous control interval of the control of the control of the end position of the synchronous control interval moving to the start position of the next synchronous control interval includes: a critical point condition setting part, which is set for the start position of the asynchronous control interval and The main shaft position, cam position, cam speed, and cam acceleration of the end position; the judging part, based on the obtained main shaft position, judges whether it is in the synchronous control interval or the asynchronous control interval; the control curve generation part, the judgment result of the judging part is In the case of a synchronous control section, based on the cam position, cam speed, and cam acceleration at the start position and end position of the asynchronous control section, an asynchronous curve of the cam position with respect to the main shaft position, which is composed of a quintic function, is obtained. An asynchronous curve of the cam speed with respect to the position of the main shaft constituted by a secondary function, an asynchronous curve of the acceleration with respect to the position of the main shaft by a cubic function; Position, a component that generates and outputs output information for operating the servo motor.

Furthermore, it is preferable that even in the asynchronous control interval, the values of the spindle position, cam position, cam speed, and cam acceleration at the end position of the asynchronous control interval can be input, and the control curve generating means sequentially generates the values based on the input values. The various asynchronous curves.

The control curve generating part preferably includes, for each control cycle in the asynchronous control interval, using the main shaft position, cam position, cam speed, and cam acceleration of the previous cycle as the starting position of the asynchronous curve to generate this control cycle Functions for asynchronous curves in .

Furthermore, it is preferable to include means for setting a specific passing point on the way of the asynchronous control section, and the control curve generation means calculates the quintic function when generating an asynchronous curve in the asynchronous control section, and makes it pass through the The process of calculating the cam position of the main shaft position of the specified passing point on the way as described above, and calculating the cubic function so that the cam acceleration of the specified passing point on the way is 0.

Furthermore, the control curve generation means may include a function of generating a synchronization curve set based on a square motion curve or a crank motion curve in the synchronization control section.

According to the present invention, by using the quintic curve for the characteristics of the cam position with respect to the main shaft position in the asynchronous curve, it is possible to smoothly connect the acceleration and the like between the asynchronous control section and the synchronous control section. In addition, in the asynchronous control section, the asynchronous curve is calculated sequentially in the control cycle, so that it can cope even if the target position changes. In addition, by setting each value obtained in the previous control cycle as the information on the start position of the asynchronous control section of the next control cycle, even if the target value changes, smooth correspondence can also be achieved.

[definition of terms]

Here, the main axis refers to an axis for obtaining a time reference of the entire system. For example, the position of the main shaft (spindle position) can be obtained by attaching an encoder to the shaft to acquire the signal of the main shaft. In addition, since it is used to obtain the time reference, the internal timer of the controller of the control system can be used as the main axis. In addition, the slave axis is an axis that operates by some kind of function, variable, coefficient, or constant with respect to the operation of the main axis.

Synchronous control refers to the control of a specific designated part of the mechanism of the driven shaft at the same time and at the same position for the part (work) connected to the main shaft. Therefore, a function that necessarily specifies the relationship between the master axis and the slave axis during synchronous control is determined. Represented by this function is a synchronization curve.

In addition, the cam position represents the positional relationship between the master axis and the slave axis. For example, in the embodiment, the angle θ is the position of the driven shaft, and x is the position of the main shaft, so the position of the cam can be expressed as

θ = f(x).

Therefore, when the above formula is differentiated by x, it becomes the cam speed (d θ/dx). Specifically, become

dθ/dx=df(x)/dx.

Furthermore, differentiating the above formula by x yields the cam acceleration (d ² θ/dx ² ).

d ² θ/dx ² ＝d ² f(x)/dx ²

Asynchronous control is control in a section in which the aforementioned synchronous control is not performed. In other words, after the end of the synchronous control and before the start of the next synchronous control, the cam position, the cam speed, and the cam acceleration are controlled. (connect without disconnection) to control the cam speed and cam acceleration.

In the present invention, the acceleration and the like can be smoothly connected at the displacement point between the synchronous control section and the asynchronous control section, and no vibration or the like occurs.

Description of drawings

FIG. 1 is a diagram showing an example of a packaging system to which a preferred embodiment of the present invention is applied.

FIG. 2 is a diagram showing an embodiment of the control system of the present invention.

FIG. 3 is a flowchart showing the functions of the motion control unit.

Fig. 4 is a diagram showing an asynchronous curve (phase-position characteristic) in an asynchronous control section.

Fig. 5 is a diagram showing an asynchronous curve (phase-velocity characteristic) in an asynchronous control section.

Fig. 6 is a diagram showing an asynchronous curve (phase-acceleration characteristic) in an asynchronous control section.

7 is a diagram showing an asynchronous curve (phase-position characteristic) when the target value in the asynchronous control section is changed.

FIG. 8 is a diagram showing an asynchronous curve (phase-velocity characteristic) when the target value in the asynchronous control section is changed.

9 is a diagram showing an asynchronous curve (phase-acceleration characteristic) when the target value in the asynchronous control section is changed.

Fig. 10 is a diagram showing an asynchronous curve (phase-position characteristic) when a specific point to pass within the asynchronous control section is specified.

FIG. 11 is a diagram showing an asynchronous curve (phase-velocity characteristic) when a specific point to be passed within the asynchronous control section is designated.

FIG. 12 is a diagram showing an asynchronous curve (phase-acceleration characteristic) when a specific point to pass within the asynchronous control section is specified.

Fig. 13 is a schematic diagram showing an example of a square movement type end closure device.

Fig. 14 is a diagram showing the relationship between the electronic cam and the packaging film by abstracting the mechanism of the square movement.

FIG. 15 is a diagram showing a synchronization curve (phase-position characteristic) in a synchronization control interval of a square motion method.

Fig. 16 is a diagram showing a synchronization curve (phase-velocity characteristic) in a synchronization control section of a square motion method.

FIG. 17 is a diagram showing a synchronization curve (phase-acceleration characteristic) in a synchronization control section of a square motion method.

Fig. 18 is a diagram showing a synchronous curve and an asynchronous curve in phase-position characteristics in a square-motion type end closure.

Fig. 19 is a diagram showing a synchronous curve and an asynchronous curve in phase-velocity characteristics in a square motion type end closure.

Fig. 20 is a diagram showing a synchronous curve and an asynchronous curve in phase-acceleration characteristics in a square motion type end closure device.

Fig. 21 is an enlarged view showing a synchronous curve and an asynchronous curve in phase-acceleration characteristics in a square motion type end closure.

Fig. 22 is a schematic diagram showing an example of a crank type end closure device.

Fig. 23 is a diagram showing the relationship between the electronic cam and the packaging film by abstracting the mechanism of the crank movement.

FIG. 24 is a diagram showing a synchronization curve (phase-position characteristic) in a cranking type synchronization control section.

FIG. 25 is a diagram showing a synchronization curve (phase-velocity characteristic) in a cranking type synchronization control section.

FIG. 26 is a diagram showing a synchronization curve (phase-acceleration characteristic) in a cranking type synchronization control section.

Fig. 27 is a diagram showing a synchronous curve and an asynchronous curve in phase-position characteristics in a crank type end closure device.

Fig. 28 is a diagram showing a synchronous curve and an asynchronous curve in the phase-velocity characteristics of the crank type end closure device.

Fig. 29 is a diagram showing a synchronous curve and an asynchronous curve in phase-acceleration characteristics in a crank type end closure device.

Detailed ways

FIG. 1 shows a control system for a packaging device as an example of a control system to which the present invention is applied. First, the packaging device to be controlled will be described. The packaging film 1 is sandwiched by a pair of feed rollers 2, and is continuously drawn out at a constant speed as the feed rollers 2 rotate. The packaging film 1 extracted in this way is formed into a cylindrical bag by the bag making device 3 . In addition, the packaged objects 5 conveyed at regular intervals by the packaged object conveying and supplying device (finger conveyor) 4 provided on the upstream side of the bag maker 3 are supplied to the bag maker at predetermined timings. within 3. As a result, the packaged objects 5 are contained at predetermined intervals in the packaging film 1 formed into a cylindrical bag, and are conveyed in this state. On the downstream side of the bag maker 3, a central sealing device 6 and an end sealing device 7 are arranged. The central sealing device 6 is composed of a pair of heating rollers, and pinches the overlapping portion of both side edges 1a in the packaging film formed into a cylindrical bag, and the two side edges 1a pass through the central sealing device 6 to be thermally sealed. The terminal sealing device 7 laterally seals and cuts a predetermined position (between the front and rear packaged objects) of the packaging film 1 formed into a cylindrical bag, and there are various types such as a square movement type and a crank movement type as described later. All types have a pair of upper and lower end closures, the front facing faces of the end closures being the closing faces. The sealing surfaces of the end closures move in a jointless prescribed trajectory, and the sealing surfaces of the pair of end closures clamp the packaging film from top to bottom every time the end closures rotate, and heat and pressurize to heat seal. In addition, a cutter is incorporated in the sealing surface of the end sealer, and the packaging film is cut while heat-sealing to manufacture the packaging body 8 .

The feeding roller 2, the central sealing device 6 and the end sealing device 7 are respectively linked with the driving motors M1-M3. Each of the drive motors M1 to M3 receives a command value from the controller 10 and is rotationally driven at a predetermined rotational speed. This controller 10 is assembled (installed) in a packaging device, and functions as a controller for the packaging device.

In this embodiment, since the packaging film 1 is moved at a constant speed, the first drive motor M1 also rotates at a constant speed and at a constant speed. In addition, the second driving motor M2 is rotationally driven at a certain speed so that the moving speed of the periphery of the heating roller of the central sealing device 6 (the position in contact with the both side edges 1a of the packaging film 1) is equal to or equal to the moving speed of the packaging film 1. Move at a slightly faster speed. In addition, when the speed of the first drive motor M1 increases or decreases due to various factors, and the conveying speed of the packaging film fluctuates, the rotation speed of the second drive motor M2 is also controlled to increase or decrease accordingly.

The third driving motor M3 is constituted by a servo motor, and the rotation speed is controlled to increase or decrease according to the conveying state of the packaging film 1 . That is, the packaging film 1 has marks printed at regular intervals on one side edge thereof. This mark is printed at a position deviated from the end-closed portion by a predetermined distance (including 0). Therefore, since the moving distance of the packaging film 1 from the marking sensor S1 to the end sealing device 7 and the conveying speed of the packaging film 1 are known, after the marking is detected by the marking sensor S1, the end sealing position corresponding to the marking reaches the end closing position. Timing of device 7. Therefore, asynchronous control is carried out during the period when the end sealer is away from the packaging film 1, so that when the end closure position of the packaging film 1 that does not carry out predetermined speed control reaches the end closure device 7, a pair of end closures clamp the packaging film. During this nipping period, the third drive motor M3 is controlled by synchronous control in accordance with the conveying speed of the packaging film 1 .

This packaging device operates based on a control signal from the controller 10 . The controller 10 includes a power supply unit 11 , an operation control unit (operation controller) 14 , and a data setting control unit (data setting controller) 15 for setting data in the operation control unit 14 . These units are electrically and mechanically connected through a backplane bus and other means. Of course, other units may also be connected. In addition, in the present embodiment, it is a dedicated controller for electronic cam control using a servo motor, but the operation control unit 14 and the data setting control unit 15 may also be used as units constituting a programmable logic controller (PLC), Connect with CPU unit or IO unit, etc., and integrate with PLC.

Since the movement of the end closure device 7 is controlled based on the movement of the packaging film 1, the conveyance of the packaging film is the main axis, and the movement of the end closure device 7 (the third drive motor M3) is the driven axis. The operation of the spindle (conveyance of the packaging film 1 ) is determined based on the output of the spindle encoder PG1 . The spindle encoder PG1, for example, can make the rotating shaft of the spindle encoder PG1 contact with the packaging film 1, and the spindle encoder PG1 can rotate along with the movement of the packaging film 1, and can also be connected with the rotating shaft of the feeding roller 2, and various Way. The detection signal of the spindle encoder PG1 is supplied to the operation control unit 14 . In addition, a detection signal of the mark sensor S1 is also input to the operation control unit 14 . Then, calculation processing is performed in the operation control unit 14 , and a command value (or pulse train) based on the calculation result is output to the servo driver 20 . The servo driver 20 controls (synchronous control, asynchronous control) the third drive shaft encoder PG2 based on the command value supplied from the motion control unit 14 and the output signal of the driven shaft encoder PG2 associated with the third drive motor M3 serving as the driven shaft servo motor. Drive the rotation action of motor M3.

Next, the internal configurations of the data setting control unit 15 and the operation control unit 14 which are main parts of the present invention will be described. FIG. 2 schematically shows the packaging device side for convenience of description. The end closure device 7 to be controlled is schematically represented by a circle as an electronic cam as a driven shaft. Every time the electronic cam rotates once, the end sealer performs a circular movement with a prescribed track, clamps the packaging film 1 once from top to bottom on the way, and performs sealing and cutting.

Based on the output from the spindle encoder PG1, the distance by which the packaging film has moved from the reference position (reset position) is calculated. In the present embodiment, the movement distance (displacement) is not reset every time one package is produced, but is processed sequentially and cumulatively. Along with this, the phase (cam position: angle θ) of the driven shaft (electronic cam) is also integrated. In other words, assuming that in Figure 2, in the case where the top is taken as the reference position of the driven shaft at 0 degrees, the first cam position changes from 0 degrees to 360 degrees, but the second cam position changes from 360 degrees to 720 degrees. After that, continue to accumulate until it is reset.

As shown in FIG. 2 , the data setting control unit 15 includes a condition setting unit 15 a and a cam critical point generating unit 15 b. The condition setting unit 15a receives inputs of an operation start position, a synchronization start position, a synchronization range, a synchronization ratio, an asynchronous section designation passing point, and an operation end position. The accepted conditions are supplied to the cam critical point generator 15b.

Here, the operation start position and the operation end position are used to set where a series of packaging operations start and end. Generally, the phase (angle θ) of the driven shaft becomes 360 degrees×n (n is a positive integer) from 0 degrees.

The synchronous start position is used to designate the start position of the synchronous control section of the electronic cam, and is set by the phase (angle θs) of the slave shaft.

The synchronization range sets how long to synchronize from the synchronization start position to perform actions such as closing. By calculating the synchronization start position + synchronization range, the synchronization end position can be calculated.

The synchronization ratio sets the condition for changing the speed ratio of the slave axis while performing synchronization by multiplying and dividing the position of the master axis. The position of the slave shaft (cam position: angle θ) corresponding to the movement distance (position) of the master shaft in the synchronous control section is determined by the synchronization ratio, and the angular velocity of the slave shaft is also specified. In other words, a synchronization profile in the synchronization control section is designated.

The asynchronous section designation passing point is designated when there is a position to pass in the asynchronous control section. For example, specify the position of the slave axis with respect to the position of the master axis, etc.

The setting (data input) of each of these conditions is initially input by an operator using, for example, an operation panel (programmable display, touch panel, etc.) mounted on the packaging device. In addition, a person performs resetting while seeing the actual situation of packaging processing, etc., or resetting is performed automatically based on sensor output.

The cam critical point generation unit 15b obtains the cam position and the cam position of the critical point of the synchronous curve and the non-synchronous curve based on each condition set as a reference by the condition setting unit 15a and the current spindle position x acquired via the operation control unit 14. speed and cam acceleration. The synchronization curve is uniquely determined according to the mechanism of the end closure device to be controlled and the film conveying speed, specifically, it is determined by the synchronization ratio. Therefore, the main shaft position, cam position, cam speed and cam acceleration at the critical point of switching from the synchronous control section to the non-synchronous control section, and the main shaft position, cam position, cam position, and The cam speed and the cam acceleration are obtained based on the synchronization curve, respectively. In other words, the end position of the non-synchronous curve represents the start position of the synchronous curve, and find the four values as the critical point

xe = spindle position

θe = cam position

ωe = cam speed

αe = cam acceleration.

Similarly, the starting position of the non-synchronous curve represents the end position of the synchronous curve, and the four values of the critical point are calculated as

xs = spindle position

θs = cam position

ωs = cam speed

αs = cam acceleration.

Specifically, the main shaft positions xe and xs of each displacement point in the first packaging process are provided by the condition setting unit 15a, and the synchronization curve is also provided in advance to the cam critical point generation unit 15b, so that by calculating the cam of each main shaft position Position, cam speed, and cam acceleration can be obtained. Furthermore, as described above, since the main shaft position and the cam position are accumulated, the main shaft positions xe, xs at each critical point when the packaging process is performed for the second time or later can be obtained only by sequentially adding the distance of the packaging pitch (end sealing interval). Can ask for. In addition, the cam positions θe and θs of each critical point can be obtained by adding 360 degrees. In addition, if there is no change in condition setting, the cam speed and cam acceleration at each critical point will take the same value in the packaging process after the second time. Since the spindle position information is obtained from the motion control unit 14 , the number of packaging processes currently being performed can be identified based on this value, and each value of a new critical point can be calculated as needed and set in the motion control unit 14 .

On the other hand, in the case where the asynchronous section specified passing point is set, four values among the passing points (specific points) specified based on the asynchronous curve are calculated based on the asynchronous curve

xm = spindle position

θm = cam position

ωm = cam speed

αm = cam acceleration.

Here, the asynchronous curve is a quintic curve for cam position, a quartic curve for cam velocity, and a cubic curve for cam acceleration. In other words, the quintic curve in which the cam position passes through the asynchronous curve start position (synchronous curve end position) and the asynchronous curve end position (synchronous curve start position) in the asynchronous control section becomes the basic control curve in the asynchronous control section. Then, when the designated passing point of the asynchronous section is designated, a quintic curve passing through the designated passing point (specific point) is obtained and used as a control curve (asynchronous curve) of the asynchronous control section.

As shown in FIG. 2 , the motion control unit 14 includes: a current information acquisition unit 14a for acquiring current position information of the main shaft, etc., a control curve generation unit 14b, a cam setting unit 14c, a command setting unit 14d, and a current position reset unit. 14e.

The current information acquisition unit 14a includes a ring counter, and by counting the pulse output from the spindle encoder PG1 by the ring counter, the current spindle position (distance from the reference position) is obtained, and further, the distance from the spindle position per unit time is obtained. Calculate the current spindle speed from the distance, and then calculate the spindle acceleration according to the change of the spindle speed to solve the problem. The calculated current spindle position, spindle speed, and spindle acceleration are supplied to the cam critical point generation unit 15b, the control curve generation unit 14b, and the command setting unit 14d.

The current position resetting unit 14e resets the ring counter of the current information acquiring unit 14a, and restarts the reference position from 0. For example, it can be issued at any time based on the detection signal from the mark sensor S1. For example, when a separately prepared reset switch (a mechanical switch, an electronic switch based on a touch of an operation panel (programmable display, touch panel, etc.) , and issue a reset command to the current information acquisition unit 14a. In this way, not limited to the input by the user, for example, when a mark detection signal is input from the mark sensor S1 after the start of normal operation, or when the mark detection by the mark sensor S1 reaches a certain number, etc., when it matches a predetermined condition, It is also possible to reset the ring counter.

The control profile generator 14b is used to generate a synchronous profile and an asynchronous profile. That is, the control curve generator 14b obtains four values (xe=spindle position, θe=cam position, ωe= Cam speed, αe=cam acceleration), four values of non-synchronous curve start position (synchronous curve end position) (xs=spindle position, θs=cam position, ωs=cam speed, αs=cam acceleration), synchronization ratio. Furthermore, the current main axis position x is received from the current information acquisition unit 14a.

Then, it is judged whether the acquired current spindle position is within the synchronous control interval, if within the synchronous control interval, a synchronous curve is generated, and if it is within the asynchronous control interval, an asynchronous control curve is generated. Specifically, the synchronization curve generates a synchronization position curve, a synchronization speed curve, and a synchronization acceleration curve based on the synchronization ratio.

On the other hand, the asynchronous curve substitutes the obtained value of the main shaft position (x) into the following formula to calculate the quintic curve for the specified cam position, the quartic curve for the specified cam speed, and the cubic curve for the specified cam acceleration.

[Equation 1]

coefficient

A ₅ ＝6(θe-θs)/(xe-xs) ⁵ -3(ωe+ωs)/(xe-xs) ⁴ +0.5(αe-αs)/(xe-xs) ³

A ⁴ ＝-15(θ _e -θ _s )/(x _e -x _s ) ⁴ +(7ω _e +8ω _s )/(x _e -x _s ) ³ +(1.5α _s -α _e )/(x _e -x _s ) ²

A ₃ ＝10(θ _e -θ _s )/(x _e -x _s ) ³ -2(2ω _e +3ω _s )/(x _e -x _s ) ² +0.5(α _e -3α _s )/(x _e -x _s )

quintic curve

θ(deg)＝A ₅ (xx _s ) ⁵ +A ₄ (xx _s ) ⁴ +A ₃ (xx _s ) ³ +0.5α _s (xx _s ) ² +ωs(xx _s )+θ _s

Quartic curve

dθ/dx(deg/mm)＝5A ₅ (xx _s ) ⁴ +4A ₄ (xx _s ) ³ +3A ₃ (xx _s ) ² +α _s (xx _s )+ω _s

cubic curve

d ² θ/dx ² (deg/mm ² )＝20A ₅ (xx _s ) ³ +12A ₄ (xx _s ) ² +6A ₃ (xx _s )+α _s

In the above formula, data acquired from the cam critical point generator 15 b of the data setting control unit 15 are used for the four values related to the asynchronous curve end position. However, regarding the asynchronous curve start position, when entering the first asynchronous curve generation process in the asynchronous control section, from the next control cycle of the cycle using the data obtained from the cam critical point generation part 15b, the previous one The cycle spindle position x _s , cam position θ _s , cam speed ω _s , and cam acceleration α _s are set as the starting position of the asynchronous curve. These respective values are set using values calculated by the lower-stage cam setting unit 14 .

In this way, real-time interpolation control for the synchronization curve of the quintic curve in the servo system can be performed. In other words, when there is a change in the target value during a packaging process, the values obtained in the previous control cycle are usually used as the start position of the asynchronous curve, and the distance between the start position of the asynchronous curve and the target value is calculated. The quintic curve and other curves can suppress discrete and sharp changes in the command value. Of course, when this real-time interpolation control is unnecessary, the data acquired from the cam critical point generator 15b may be used for the asynchronous curve start position.

The cam setting unit 14c obtains each curve (synchronous curve and asynchronous curve) generated by the control curve generating unit 14b, and at the same time obtains the current position x of the main shaft obtained by the current information obtaining unit 14a, and sets the cam for the current main shaft position. Position, Cam Velocity, and Cam Acceleration.

That is, the control profile generation unit 14b generates either a synchronous profile or an asynchronous profile based on the current spindle position, and supplies the generated profile to the cam setting unit 14c. Accordingly, the cam setting unit 14c obtains the cam position, the cam speed, and the cam acceleration by substituting the value of the current spindle position into the variable x in the function representing the provided curve.

The cam position θ, cam speed dθ/dx, and cam acceleration d ² θ/dx ² obtained in this way are sent to the control curve generating unit 14b for the next control cycle, and are also sent to the command setting unit 14d. The command setting unit 14d acquires the spindle speed dx/dt (mm/sec) and the spindle acceleration d ² x/dt ² (mm/sec ² ) from the current information acquiring unit 14a. Based on these acquired information, the position of the driven shaft, the speed of the driven shaft, and the acceleration of the driven shaft are calculated based on the following formulas, and are supplied to the servo driver 20 .

[Equation 2]

Driven shaft position = cam position θ

Driven shaft speed dθ/dt(deg/sec)=(dθ/dx)*(dx/dt)

Driven shaft acceleration d ² θ/dt ² (deg/sec ² )=(d ² θ/dx ² )*(dx/dt) ² +(dθ/dx)*(d ² x/dt ² )

FIG. 3 shows an operation flowchart of the operation control unit 14 . This operation flowchart is executed every control cycle. That is, first, the current information acquisition unit 14a acquires the current position x of the main shaft from the main shaft encoder PG1 (S1). Then, the control curve generator 14b judges whether the spindle position is within the synchronous control zone based on the obtained current position x (S2), and generates a synchronous curve (S3) in the case of the synchronous control zone, and not in the synchronous control zone (in the asynchronous control zone). In the case of the control area), an asynchronous curve (a quintic curve, a quartic curve, a cubic curve) is generated (S4). In addition, the specific processing of each curve is as above-mentioned.

Next, the cam setting unit 14c sets the current value (cam position, cam speed, cam acceleration) of the electronic cam based on the profile (synchronous profile/asynchronous profile) generated by executing processing step S3 or S4 (S5). Then, the set value is sent to the control curve generator 14b as the asynchronous curve start position in the next control cycle (S6).

Based on each value of the cam obtained by executing the processing step S5, a command value to the servo driver 20 is obtained and output (S7). Then, judge whether to continue (S8), and in the case of continuing, return to processing step S1 and enter the next control loop. Whether or not to continue is determined based on, for example, whether an end command or a stop command of the packaging process is input, or whether it matches a preset condition (number of packages, end time), or the like.

An example of a control curve (asynchronous curve) in the above-mentioned asynchronous control section is shown in FIGS. 4 to 6 . Fig. 4 shows the correlation relationship with respect to the displacement (cam position of the driven shaft) with respect to the phase (main shaft position), Fig. 5 shows the phase relation with respect to the velocity of the phase (main shaft position), and Fig. 6 shows the acceleration with respect to the phase (main shaft position) related relationship. Assuming that there is no change in the synchronous target position (critical point such as the end position or start position of the asynchronous control section), the cam position, cam speed, and cam acceleration in the asynchronous control section are repeated according to the curves shown in each figure. The same applies to the case where the asynchronous curve is generated by using the values set based on the current spindle position as the asynchronous curve start position in the next control cycle by processing step S6. In any case, since the velocity and acceleration at the critical point are 0 (approximately 0), it can be smoothly connected to the synchronous curve in the synchronous control section, and no vibration, shock, etc. are generated at the critical point.

Here, as shown in Figures 7 to 9, the main axis position xs = 200mm, the slave axis position θs = 225deg, the speed ωs = 0.382deg/mm, and the acceleration αs = -0.00509deg/mm are set as the starting position of the asynchronous curve. ² . And set the master axis position xe=271mm, slave axis position θe=495deg, speed ωe=0.267deg/mm, acceleration αe=0.00250deg/mm ² at the original asynchronous curve end position (synchronous curve start position).

In this state, when the main shaft position is 255mm, the main shaft position xe=271mm, the slave shaft position θe=600deg, the speed ωe=0.763deg/mm, and the acceleration αe are changed to the asynchronous curve end position (synchronous curve start position) =0.02012 deg/mm ² . Then, since the asynchronous curve connecting the previous position, velocity, acceleration and changed values of the spindle position of 255 mm is re-set, mechanical shock and vibration can be prevented.

In addition, assuming that when the main shaft position is 255 mm, there are changes in the target values as described above, for example, resetting the control that connects the main shaft position xs = 200 mm, which is the start position of the asynchronous control section this time, and the new target value The curve (non-synchronous curve), sometimes compared with the current value of 255mm, the values (position, speed, acceleration) at 255mm are very different, so that, as shown in the figure, it is not connected by a continuous curve. This discontinuity point may cause mechanical shock and vibration.

In this way, for a synchronous curve whose speed is not constant in the synchronous control interval and whose acceleration occurs at both ends, it is also possible to connect the position, speed, and acceleration. Position, velocity, acceleration and drive servos. Thereby, the shock and vibration given to the mechanical system can be reduced, and smooth operation can also be performed for changes in the start position, speed, and acceleration of the synchronous curve.

Next, the correspondence in the case where a midway point in the asynchronous control section is specified will be described. That is, when the condition setting unit 15a of the data setting control unit 15 sets the designated passing point of the asynchronous section (the midway point in the asynchronous control section), information about the midway point (xm=spindle position , θm=cam speed, ωm=cam speed, αm=cam acceleration) are supplied to the control curve generator 14b via the cam critical point generator 15b.

Therefore, when the current spindle position is within the asynchronous control interval, the control curve generator 14b generates the asynchronous curve. However, at this time, when the current spindle position x is xs≤x≤xm, the In the calculation formulas for the above-mentioned asynchronous curves, xe=xm and θe=θm are set. Furthermore, when the main shaft current position x exceeds xm, xs=xm and θs=θm are set in the calculation formulas for obtaining the above-mentioned asynchronous curves.

In other words, connect between quintic curves through specified intermediate points. Thus, at the intermediate point, the velocity and acceleration become 0 (approximately 0).

As an example, then as shown in Figure 10 to Figure 12, the quintic curve of the asynchronous curve passes through a specific passing point on the way from the asynchronous curve start position (synchronous curve end position), as shown in the figure, to the asynchronous curve The curve at the end position (synchronous curve start position) designates the midway point and connects the quintic curve and the quintic curve. The master axis position xs = 200 mm, the slave axis position θs = 225 deg, the velocity ωs = 0.382 deg/mm, and the acceleration αs = -0.00509 deg/mm ² are set as the start position of the asynchronous curve. The main axis position xe=271mm, the slave axis position θe=495deg, the velocity ωe=0.267deg/mm, and the acceleration _αe =-0.00250deg/mm ² are set as the end position of the asynchronous curve (start position of the synchronous curve). The specific passing point on the way is set as the main axis position xm=250mm, the driven axis position θm=400deg, the speed ωm=(θe-θm)/(xe-xm)=4.524deg/mm, the acceleration αm=0(deg/mm ² ). Therefore, instead of stopping the speed as shown in FIG. 11 showing the relationship between the phase and speed, smooth motion can be performed while continuing the acceleration as shown in FIG. 12 showing the relationship between the phase and speed.

Next, the case where the end closure device 7 is a square movement type will be described. Fig. 13 is a diagram schematically showing a square movement type end closure device. As shown in this FIG. 13 , the rotational force of the third motor M3 constituted by a servo motor is transmitted to the rotary plate 7b via transmission members 7a such as belts and chains. The rotary plate 7b has a slider 7c that can move back and forth in the radial direction. The slider 7c performs an orbital movement with the rotation of the rotary plate 7b, and can move radially during the orbital movement. Furthermore, the slider 7c is connected to the square guide groove 7d. As a result, the slider 7c revolves along with the rotation of the rotary plate 7b, but the movement locus follows the endless locus defined by the guide groove 7d. Therefore, by creating a section 7d' of horizontal movement of the packaging film 1 along the guide groove 7d, the slider 7c moves forward while maintaining the same distance along the packaging film 1 for a certain period of time, and then performs an action so as to reach the position after moving up→moving backward→moving backward. Section 7d that moves downward and moves horizontally along the reference. In addition, in the drawing, only the upper side is described for convenience, but the same mechanism is also present on the lower side.

Furthermore, by connecting the slider 7c to the end closure and integrating it, the end closure also moves along the movement locus of the slider 7c. At this time, the closing surface of the end closure that is moving in the above-mentioned horizontal movement section 7d' can touch the packaging film 1 and clamp it from top to bottom. By rotating the rotating plate 7b, the moving speed of the end closure and the packaging The conveying speed of the film 1 is consistent, and synchronous control can be performed. In addition, the intervals other than this are asynchronous control intervals.

In addition, FIG. 13 shows a substantially rectangular locus (each corner is a circular arc) (two-dot chain line), but the locus of the asynchronous control section is arbitrary. Furthermore, the mechanism for moving along the predetermined trajectory can also adopt various forms, and the rotating plate 7b and the like may not be used, and the end closure itself may be a slider 7c. What is important is that, with the rotation of the third drive motor M3, the end closure moves on a predetermined jointless trajectory, as long as it moves parallel to the packaging film 1 during the movement (at this time, the packaging film is clamped and closed) The section is sufficient, and the mechanism for moving on this trajectory is arbitrary. In addition, the rotary plate 7b may rotate once every time the third drive motor M3 rotates, or it may be different. The angle of the electronic cam described above corresponds to the rotation angle of the rotary plate 7b in FIG. 13 .

Figure 14 abstracts the mechanism of the square motion, representing the electronic cam and the packaging film 1. As shown in FIG. 14 , the synchronization starts when the packaging film 1 of the main shaft is conveyed from the reference position (0 mm) to x1 and ends when the main shaft position reaches x2. Therefore, the moving distance of the packaging film 1 in the synchronous control section is x2-x1. On the other hand, the packaging process starts from the reference position of the electronic cam at 0 degrees on the driven shaft, but in the first packaging process, synchronously starts from θ1 and performs synchronous control before θ2. Therefore, the synchronous control interval is the angular range of θ2-θ1.

Then, it becomes an asynchronous control section, the end position of the asynchronous control section (the start position of the next synchronous control section) is the main axis position x3, the cam position of the slave axis is θ3, and the end position of the synchronous control section (below The starting position of a non-synchronous control interval) the position of the master axis is x4, and the position of the slave axis is θ4.

The cam curve for square movement in packaging machinery is as follows. The main axis x and the driven axis θ are synchronous control intervals when x1≤x≤x2 and θ1≤θ≤θ2 respectively. The synchronous curves of the cam position θ, the cam speed d θ/dx, and the cam acceleration d ² θ/dt ² in the synchronous control interval are expressed in the following formula [Formula 3].

[Equation 3]

Coefficient for moving the synchronization start point forward and backward: xa Coefficient for changing the synchronization ratio: b as z=b(x-xa)

cam position

θ＝180[1-1/π*tan ^-1 {(x ₂ +x ₁ -2z)/(x ₂ -x ₁ )*tan(π(θ ₂ -θ ₁ )/360)}]

cam speed

$\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; *</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Cam acceleration

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1440</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; *</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Based on the above formula, in the following synchronous control section, based on the position of the main shaft, the following position, speed, and acceleration are set and moved for each control signal of the controller.

Spindle speed dx/dt(mm/sec)

Spindle acceleration d ² x/dt ² (mm/sec ² )

Driven shaft position = cam position θ

Driven shaft speed dθ/dt(deg/sec)=(dθ/dx)*(dx/dt)

Driven shaft acceleration d ² θ/dt ² (deg/sec ² )=(d ² θ/dx ² )*(dx/dt) ² +(dθ/dx)*(d ² x/dt ² )

Furthermore, the operation curves in the synchronous control interval of the square motion based on the above formula are shown, for example, in FIGS. x0=0mm, x1=50mm, x2=200mm, θ0=0deg, θ1=135deg, θ2=225deg, R=106mm, y=75mm.

Next, calculation of the control curve in the asynchronous control section will be described. First, at the start position of the non-synchronous curve (the end position of the square motion synchronous curve) is the main axis x=x2 (mm). If there is no change in the synchronization start point, each formula for specifying the above synchronous curve is as shown in [Formula 4] below, and by substituting x=x2 for [Formula 4], as shown in [Formula 5], the end of synchronization can be obtained Values of each cam position, cam speed, and cam acceleration in position.

[Equation 4]

Square Action Cam Profile (Original Cam)

cam position

θ＝180[1-1/π*tan ^-1 {(x ₂ +x ₁ -2x)/(x ₂ -x ₁ )*tan(π(θ ₂ -θ ₁ )/360)}]

cam speed

$\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; *</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; *</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Cam acceleration

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1440</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; *</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; *</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

[Equation 5]

cam position

θ=θ2(deg)=180+(θ ₂ -θ ₁ )/2

cam speed

$\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; mm</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; *</span>\frac{\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ]</span>}$

Cam acceleration

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; mm</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1440</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; *</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Thus, xs=x2, θs=θ2, ωs=ω2, and αs=α2 are taken in as the values of the cam before the asynchronous curve is obtained.

In addition, when there is no change of the target value, the next synchronous control section starts when the main shaft position x=x3, and controls according to the synchronous curve when the main shaft position is x3≤x≤x4. Then, the cam position θ, cam speed dθ/dx, and cam acceleration d ² θ/dx ₂ in the next synchronous control section are respectively controlled according to the synchronous curve shown in the following formula [Formula 6].

[Equation 6]

Square motion cam profile (next cam)

cam position

θ＝180[1-1/π*tan ^-1 {(x ₄ +x ₃ -2x)/(x ₄ -x ₃ )*tan(π(θ ₄ -θ ₃ )/360)}]

cam speed

$\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; *</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; *</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Cam acceleration

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1440</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; *</span>\frac{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{{<span\; class="notranslate">\; [</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; *</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Furthermore, the values of the respective cam positions, cam speeds, and cam accelerations at the start position (x=x3) of the synchronous control section can be obtained by executing [Equation 7]. Then, the obtained values are the values of the end positions in the asynchronous control interval in which the position of the main axis x is in the interval of x2≦x≦x3, that is, the respective target values in the asynchronous control interval. In other words, as xe=x3, θe=θ3, ωe=ω3, αe=α3, it is set at any time for the asynchronous curve.

[Equation 7]

cam position

θ=θ3(deg)=180+(θ ₄ -θ ₃ )/2

cam speed

$\mathrm{<span\; class="notranslate">\; d\&theta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; dx</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&omega;</span>}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; mm</span>}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; *</span>\frac{\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ]</span>}$

Cam acceleration

${\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&alpha;</span>}\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; mm</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>$

$<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1440</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; *</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span>}{{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 360</span>}<span\; class="notranslate">\; \}</span><span\; class="notranslate">\; ]</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Furthermore, since the target value (main shaft position at the end position of the asynchronous control section) xe when the main shaft position x=x2 is x3, a quintic curve passing through two points is generated. Furthermore, when the current position x (mm) of the main shaft is xs≤x≤xe, that is, x2≤x≤x3, the curve is obtained five times per control cycle and moved. In addition, once entering the asynchronous control interval, if each set value (cam position, cam speed, cam acceleration) is obtained, then it is set as the next control cycle with the execution of the processing step S6 in the flow chart of Fig. 3 . The starting position of the asynchronous curve. In this way, the starting position of the asynchronous curve is updated successively, and at the same time, the asynchronous control based on the quintic curve is performed until the spindle position x=x3.

Afterwards, the control operation interval and the non-control operation interval are alternately executed, and when the target value is changed midway, calculation processing is performed each time, and the asynchronous curve is a quintic curve, which is connected with the synchronous curve.

An example is shown in Figure 18 to Figure 21. In other words, as shown in FIG. 18 , as shown in FIG. 18 , even if the position or the synchronization ratio to start the synchronization of the square curve is changed such as the phase and displacement, the speed is smoothly connected at the critical point as shown in the characteristics of the phase and speed shown in FIG. 19 . Similarly, in the characteristics of the phase and acceleration shown in FIG. 20 , as can be confirmed in the enlarged view of FIG. 21 , the acceleration is also connected at a critical point. Thus, shock and vibration hardly occur. Furthermore, since the servo target position, target speed, and target acceleration of the slave axis are set for each control cycle, it is possible to respond even if the ratio is changed when starting synchronization online.

Next, a case where the end closure device 7 is of a crank type will be described. Fig. 22 is a diagram schematically showing a crank type end closure device. As shown in FIG. 22 , the rotational force of the third motor M3 constituted by a servo motor is transmitted to a rotating plate (functioning as a crank arm) 7b via a transmission member 7a such as a belt or a chain. A crank pin 7f is provided near the periphery of the rotary plate 7b, and one end of a connecting rod 7g is rotatably connected to the crank pin 7f. The other end of the connecting rod 7g is connected with a slide block 7h, and the slide block 7h can move linearly back and forth in the guide rail 7i. Thereby, when the rotating plate 7b rotates with the rotation of the 3rd drive motor M3, the slider 7h repeats the reciprocating linear motion by the crank mechanism accompanying this. Also, an end closure is attached to this slider 7h so as to be movable up and down.

Of course, in FIG. 22, only the upper side mechanism of the packaging film 1 is described, but the same mechanism is also provided on the lower side. Furthermore, the end sealer moves up and down at a predetermined timing, and when it reaches the synchronous start point, it clamps the packaging film from top to bottom, and moves forward in this state, and when it reaches the synchronous end point, the end sealer moves away. The closure then moves back and forth on a defined trajectory and reaches the basic synchronous start point.

In this way, when the end closure clamps the packaging film, the rotation speed of the rotating plate 7b is controlled (synchronously controlled) so that the forward movement speed of the end closure, that is, the slider 7h, is consistent with the conveying speed of the packaging film 1. In the asynchronous control section, when the next end closure part of the packaging film reaches the synchronization start point, control is performed so that the end sealer reaches the synchronization start point.

FIG. 23 abstracts the mechanism of the crank movement, showing the crank mechanism and the packaging film 1 . As shown in FIG. 23, when the packaging film 1 of the main shaft is conveyed from the reference position (0 mm) to x1, synchronization starts, and when the main shaft position reaches x2, synchronization ends. Therefore, the moving distance of the packaging film 1 in the synchronous control section is x2-x1. On the other hand, on the driven shaft, the wrapping process is started from the reference position where the position of the electronic cam is 0 degrees. In the first wrapping process, synchronization is started from θ1, and synchronous control is performed until θ2. Therefore, the synchronous control interval is the angular range of θ2-θ1.

Then, it becomes an asynchronous control section, the end position of the asynchronous control section (the start position of the next synchronous control section) is the main axis position x3, the cam position of the slave axis is θ3, and the end position of the synchronous control section (below The starting position of a non-synchronous control interval) the position of the master axis is x4, and the position of the slave axis is θ4.

The cam curve for crank motion is as follows. When the main axis x and the driven axis θ are x1≤x≤x2 and θ1≤θ≤θ2 respectively, it is a synchronous control interval. The synchronous curves of the cam position θ, cam speed dθ/dx, and cam acceleration d ² θ/dx ² in the synchronous control interval are expressed in the following formula [Formula 8].

[Equation 8]

Coefficient of moving forward and backward of the synchronization start point: xa Coefficient of changing the synchronization ratio: b

y, R, L are constants.

z=b(x-xa)

$\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}$

$\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}\mathrm{<span\; class="notranslate">\; by</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">z</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="b"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">b</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; yz</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">z</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

cam position

clockwise

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="R\; z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">R</figure-callout></span><figure-callout\; id="2"\; label="R\; z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}\sqrt{{\mathrm{<span\; class="notranslate">\; </span>}}^{}}\sqrt{{\mathrm{<span\; class="notranslate">z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}$

counterclockwise

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="R\; z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">R</figure-callout></span><figure-callout\; id="2"\; label="R\; z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}\sqrt{{\mathrm{<span\; class="notranslate">\; </span>}}^{}}\sqrt{{\mathrm{<span\; class="notranslate">z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}$

cam speed

$\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 90</span>}\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; z</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="z"\; filenames="C20051012544000341.png,C20051012544000392.png"\; state="\{\{state\}\}">z</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;<figure-callout\; id="2"\; label="R\; z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">R</figure-callout></span><figure-callout\; id="2"\; label="R\; z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}\sqrt{{\mathrm{<span\; class="notranslate">\; </span>}}^{}}\sqrt{{\mathrm{<span\; class="notranslate">z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">z</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}$

Cam acceleration

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 90</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">z</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; \&pi;<figure-callout\; id="2"\; label="R\; z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">R</figure-callout></span><figure-callout\; id="2"\; label="R\; z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}\sqrt{{\mathrm{<span\; class="notranslate">\; </span>}}^{}}\sqrt{{\mathrm{<span\; class="notranslate">z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="z"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">z</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Based on the above formula, in the synchronous control section below, the following positions, speeds, and accelerations are set and moved based on the position of the main shaft for each control cycle of the controller.

Spindle acceleration d ² x/dt ² (mm/sec ² )

Driven shaft position = cam position θ

Driven shaft speed dθ/dt(deg/sec)=(dθ/dx)*(dx/dt)

Driven shaft acceleration d ² θ/dt ² (deg/sec ² )=(d ² θ/dx ² )*(dx/dt) ² +(dθ/dx)*(d ² x/dt ² )

Furthermore, the operation curves in the synchronous control interval of the crank motion based on the above-mentioned formula are shown, for example, in FIGS. x0=44.2mm, x1=200mm, θ0=135 degrees, θ1=225 degrees, R=70mm, y=70mm, L=200mm.

Next, calculation of the control curve in the asynchronous control section will be described. First, at the start position of the non-synchronous curve (the end position of the crank cam synchronous curve), the main axis x=x2 (mm). If there is no change in the synchronization start point, each equation for specifying the above-mentioned synchronization curve is as shown in [Equation 9] below, and by substituting x=x2 for [Equation 4], as shown in [Equation 10], the end of synchronization can be obtained Values of each cam position, cam speed, and cam acceleration in position.

[Equation 9]

y, R, L are constants.

z=b(x-xa)

$\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}$

$\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}\mathrm{<span\; class="notranslate">\; yx</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

cam position

clockwise

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}$

counterclockwise

$\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}$

cam speed

$\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}$

Cam acceleration

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; \&pi;R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

[Equation 10]

Crank Cam Profile (Original Cam)

y, R, L are constants.

z=b(x-xa)

$\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\text{<span class="notranslate"> 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

cam position

clockwise

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}$

counterclockwise

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}$

cam speed

$\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; mm</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}$

Cam acceleration

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; mm</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; \&pi;R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Thus, xs=x2, θs=θ2, ωs=ω3, and αs=α2 are taken in as the values of the cam before the asynchronous curve is obtained. In addition, when there is no change of the target value, the next synchronous control section starts when the main shaft position x=x3, and controls according to the synchronous curve when the main shaft position is x3≤x≤x4. Then, the cam position θ, cam speed dθ/dx, and cam acceleration d ² θ/dx ² in the next synchronous control section are respectively controlled according to the synchronous curve shown in the following formula [Formula 11].

[Equation 11]

Crank Cam Profile (Next Cam)

y, R, L are constants.

$\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; the\; tan</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{\mathrm{<span\; class="notranslate">\; the\; y</span>}}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}$

$\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

$\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 360</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}{{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}}_{\text{<span class="notranslate"> 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

cam position

clockwise

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}$

counterclockwise

${\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 180</span>}}{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}<span\; class="notranslate">\; [</span>{\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\frac{{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; <figure-callout\; id="2"\; label="y"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">y</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}}<span\; class="notranslate">\; ]</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}$

cam speed

$\mathrm{<span\; class="notranslate">\; \&omega;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; mm</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}}{\mathrm{<span\; class="notranslate">\; \&pi;R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}$

Cam acceleration

$\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; deg</span>}<span\; class="notranslate">\; /</span>{\mathrm{<span\; class="notranslate">\; mm</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

$<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 90</span>}<span\; class="notranslate">\; \{</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; R</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}{\mathrm{<span\; class="notranslate">\; \&pi;R</span>}\sqrt{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}{<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; d\&theta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; d\&beta;</span>}}{\mathrm{<span\; class="notranslate">\; dx</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; the\; tan</span>}<span\; class="notranslate">\; \{</span>\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 180</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \}</span><span\; class="notranslate">\; -</span>\frac{{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}}{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">d</figure-callout></span><figure-callout\; id="2"\; label="d\; x"\; filenames="C20051012544000381.png,C20051012544000391.png"\; state="\{\{state\}\}">\; </figure-callout>}{\mathrm{<span\; class="notranslate">\; </span>}}^{}{\mathrm{<span\; class="notranslate">x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}$

Furthermore, the values of the respective cam positions, cam speeds, and cam accelerations at the start position (x=x3) of the synchronous control section can be obtained by executing [Equation 12]. Then, the obtained values are the values of the end positions in the asynchronous control interval in which the position of the main axis x is between x2≤x≤x3, that is, the respective target values in the asynchronous control interval. In other words, as xe=x3, θe=θ3, ωe=ω3, αe=α3, it is set at any time for the asynchronous curve.

[Equation 12]

cam position

θ(deg)＝A5(x-xs) ⁵ +A4(x-xs) ⁴ +A3(x-xs) ³ +0.5αs(x-xs) ² +ωs(x-xs)+θs

cam speed

dθ/dx(deg/mm)＝5*A5(x-xs) ⁴ +4*A4(x-xs) ³ +3*A3(x-xs) ² +αs(x-xs)+ωs

Cam acceleration

d ² θ/dx ² (deg/mm ² )＝20*A5(x-xs) ³ +12*A4(x-xs) ² +6*A3(x-xs)+αs

coefficient

A ₅ ＝6(θe-θs)/(xe-xs) ⁵ -3(ωe+ωs)/(xe-xs) ⁴ +0.5(αe-αs)/(xe-xs) ³

A ₄ ＝-15(θ _e -θ _s )/(x _e -x _s ) ⁴ +(7ω _e +8ω _s )/(x _e -x _s ) ³ +(1.5α _s -α _e )/(x _e -x _s ) ²

A ₃ ＝10(θ _e -θ _s )/(x _e -x _s ) ³ -2(2ω _e +3ω _s )/(x _e -x _s ) ² +0.5(α _e -3α _s )/(x _e -x _s )

Furthermore, since the target value xe (the main shaft position at the end position of the asynchronous control section) when the main shaft position x=x2 is x3, a quintic curve passing through two points is generated. Furthermore, when the current position x (mm) of the main shaft is xs≤x≤xe, that is, x2≤x≤x3, the curve is obtained five times per control cycle and moved. In addition, once entering the asynchronous control interval, if each set value (cam position, cam speed, cam acceleration) is obtained, then it is set as the next control cycle with the execution of the processing step S6 in the flow chart of Fig. 3 . The starting position of the asynchronous curve. In this way, the starting position of the asynchronous curve is updated successively, and at the same time, the asynchronous control based on the quintic curve is performed until the spindle position x=x3.

Afterwards, the control operation interval and the non-control operation interval are alternately executed, and when the target value is changed midway, calculation processing is performed each time, and the asynchronous curve is a quintic curve, which is connected with the synchronous curve.

An example is shown in Figure 27 to Figure 29. In other words, as shown in FIG. 27 , as shown in the phase and displacement, even if the position or the synchronization ratio to start the synchronization of the square curve is changed, as shown in the characteristics of the phase and speed shown in FIG. 28 , the speed is smoothly connected at the critical point. Likewise, in the characteristics of the phase and acceleration shown in FIG. 29, the acceleration is also connected at a critical point. Thus, shock and vibration hardly occur. Furthermore, since the servo target position, target speed, and target acceleration of the slave axis are set for each control cycle, it is possible to respond even if the ratio is changed when starting synchronization online.

In each of the above-mentioned embodiments, an example of being applied to the control of the driving motor (servo motor) for the end sealing device of the packaging machine has been shown, but the present invention is not limited thereto, for example, it can also be used to control the drive motor (servo motor) for the packaging film supply Control of the driving motor (servo motor) of the packaged object conveying and supplying part. That is, since the conveying speed of the packaged object and the conveying speed of the packaging film are usually different, for example, in the case of conveying the packaging film at a certain speed, the conveying speed of the packaged object should be adjusted only during the supply of the packaged object to the packaging film. It is synchronized with the conveying speed of the packaging film, and asynchronously controlled with the conveying speed of the packaging film during other periods, and can be controlled by a predetermined asynchronous curve (a quintic curve, etc.).

As one form of the end closure device 7, there is also a type called rotation in addition to the above-mentioned square motion type or crank motion type. In the rotary type end closure device 7 , the end closures are directly or indirectly installed on the upper and lower pairs of rotating shafts, respectively. Then, as the rotation shaft rotates, the end sealers also rotate, and the upper and lower end sealers clamp the packaging film from top to bottom at predetermined timing, and perform sealing and cutting.

Here, similar to the above-mentioned types of end closure devices, the position of the main shaft at the start position of the initial synchronous control section is x1 and the position of the driven shaft is θ1, and the position of the main shaft at the end position of the synchronous control section (start position within the non-synchronous control section) is x2 and the slave axis position is θ2. Furthermore, the master axis position at the start position of the next synchronous control section is x3 and the slave axis position is θ3, and the master axis position at the end position of the synchronous control section (asynchronous control section start position) is x4 and the slave axis position is θ4. Then, the relationship of θ1≤θ2≤θ3≤θ4 and x1≤x2≤x3≤x4 arises.

Also, the synchronization curve is given by

(θ-θ1)=(θ2-θ1)/(x2-x1)*(x-x1)

express. Here, θ is the position of the driven shaft and x is the position of the main shaft.

Differentiating the above formula with x, it becomes

dθ/dx=(θ2-θ1)/(x2-x1).

That is, the cam speed is

ω1=ω2=(θ2-θ1)/(x2-x1).

Further differentiating the above formula by x, it becomes

d ² θ/dx ² =0. The cam acceleration is 0.

Likewise, the next synchronization curve is denoted as

(θ-θ3)=(θ4-θ3)/(x4-x3)*(x-x3).

Differentiating the above formula by x, it becomes

dθ/dx=(θ4-θ3)/(x4-x3).

The cam speed is

ω3=ω4=(θ4-θ3)/(x4-x3). Furthermore, when differentiated by x, d ² θ/dx ² =0, and the cam acceleration becomes 0.

The above values, that is, if xs=x2, xe=x3, θs=θ2, θe=θ3 are substituted into the formula of [Formula 12], then

ωs=ω2=(θ2-θ1)/(x2-x1)

ωe=ω3=(θ4-θ3)/(x4-x3)

By substituting αs=0αe=0, an asynchronous curve connecting synchronous curves is generated.

Thereby, a smooth waveform can be obtained. Furthermore, according to the above embodiment, since the previous cam values are substituted for xs, θs, ωs, and αs, even if the next synchronization curve is changed, the cam position, cam speed, and cam acceleration can be connected.

Consider the case where it is applied to the synchronous action of a ball screw and a rack and pinion pair. A mechanical system that mounts the servomotor of the driven shaft to a ball screw or a rack and pinion pair. A ball screw or rack and pinion pair is placed parallel to the main shaft components. The operation in this case is as follows.

y=p×θ

Here, y is the movement amount of the ball screw or the rack and pinion pair, generally expressed in mm. Also, in the case of a ball screw, becomes

P = pitch of the ball screw/360 (degrees),

In the case of a rack and pinion pair, becomes

P = pinion diameter π/360 (degrees).

x is the position of the main axis,

Due to the relationship of y2=p×θ2, y1=p×θ1, the synchronization curve is from

(y-y1)=(y2-y1)/(x2-X1)*(x-x1), expressed as

(θ-θ1)=(θ2-θ1)/(x2-X1)*(x-x1).

Here, θ is the position of the slave axis, x is the position of the master axis, θ2 is the end position of the synchronization curve of the slave axis, θ1 is the start position of the synchronization curve of the slave axis, x2 is the end position of the synchronization curve of the master axis, and x1 is the master axis The starting position of the synchronization curve.

Differentiating the above formula by x, it becomes

dθ/dx=(θ2-θ1)/(x2-x1).

That is, the cam speed is

ω1=(θ2-θ1)/(x2-x1).

If further differentiated by x, it becomes

d ² θ/dx ² =0, the cam acceleration is 0.

The position where the driven axis moves out, that is, the start position of the asynchronous curve is that the position of the main axis is x0, the position of the driven axis is 0, the cam position ω0=0, the cam acceleration α0=0, the end position of the asynchronous curve (the start position of the synchronous curve ) is the position of the main axis is x1, and the position of the driven axis is θ1.

Also, the cam speed is

ω1=(θ2-θ1)/(x2-x1),

The cam acceleration is

α1=0.

Furthermore, by substituting xs=x0, xe=x1, θs=θ0, θe=θ1, ωs=ω0=0, ωe=ω1=(θ2-θ1)/(x2-x1) into the above-mentioned [Formula 12], αs=0, αe=0, generate an asynchronous curve connecting the synchronous curves.

The end position of the synchronous curve (the start position of the non-synchronous curve) is the position x2 of the master axis, and the position of the slave axis is θ2. Cam speed ω2=(θ2-θ1)/(x2-x1), and cam acceleration is 0. The position where the driven axis stops, that is, the end position of the asynchronous curve, is x3 at the position of the main axis, and θ3 at the position of the driven axis. Also, the cam speed and cam acceleration α0 are zero.

Similarly, substitute xs=x2, xe=x3, θs=θ2, θe=θ3, ωs=ω2=(θ2-θ1)/(x2-x1), ωe=0, αs=0, αe= 0, it can generate asynchronous curves connecting synchronous curves.

As an application of synchronous control other than packaging machines, printing machines are also effective. In the printing machine, the printed matter such as paper and the roller with the printing surface move synchronously. In this operation, it may be necessary to correct the printing start position forward and backward. This correction operation can be performed smoothly by using the asynchronous control of the quintic curve of the present invention.

A ball screw or rack and pinion pair needs to be stopped due to the bounds at both ends. Therefore, by using the present invention, a smooth waveform can be obtained. Furthermore, by applying the above-mentioned embodiment, since previous cam values are input to xs, θs, ωs, and αs, even if the synchronous curve is changed, the cam position, cam speed, and cam acceleration can be connected.

Furthermore, it can also be applied to a separate cutting device instead of a closing device. In addition, objects to be sealed or cut are not limited to packaging films, but can also be applied to various sheet-shaped things. Furthermore, it is not limited to such a closing device or a cutting device, and of course it can be applied to a control method and a control system of an electronic cam using a servo motor.

For example, regarding the synchronous cutting of building materials, the processing of electronic components or bases through synchronous delivery or the insertion of components, the synchronous cutting or processing of glass, the synchronous control of synchronous processing or inserting parts of automobiles transported along the assembly line, etc., The asynchronous control of the present invention can have a smooth waveform by using the asynchronous section. Furthermore, by applying the above-described embodiment, even if the synchronization curve is changed, the cam position, the cam speed, and the cam acceleration can be connected.

Furthermore, as for the synchronous control of multiple axes of a linear robot, horizontal, cylindrical, and vertical robots, a smooth waveform can be obtained by applying the asynchronous control of the present invention to the movement of each axis of the robot in the asynchronous section. Furthermore, by applying the above-described embodiment, even if the synchronization curve is changed, the cam position, the cam speed, and the cam acceleration can be connected.

Claims (7)

1. servo control system, it is characterized in that, have and make as the driven shaft of controlling object thing synchro control interval for the control of main spindle's synchronization action, and be used to make described controlling object thing to move to the asynchronous control interval of control of the starting position in next synchro control interval from the end position in this synchro control interval, this system comprises:

The stagnation condition set parts is set the starting position of relevant asynchronous control interval and main spindle's, cam position, cam speed, the cam acceleration of end position;

Decision means based on the main spindle's of obtaining, is judged in the synchro control interval or in asynchronous control interval;

The control curve generates parts, judged result in this decision means is under the situation of asynchronous control interval, based on the starting position of described asynchronous control interval and cam position, cam speed, the cam acceleration of end position, the asynchronous curve with respect to the acceleration of main spindle's of the asynchronous curve of asking the asynchronous curve that constitutes by five functions, constituting by biquadratic function, cubic function with respect to the cam speed of main spindle's with respect to the cam position of main spindle's; And

Based on generating each asynchronous curve and the described main spindle's of obtaining that parts are obtained, generate and output is used to make the parts of the output information of servomotor action by this control curve.

2. servo control system as claimed in claim 1, it is characterized in that, even in the asynchronous control interval, also can import main spindle's, cam position, the cam speed of the end position of this asynchronous control interval, the value of cam acceleration, described control curve generates parts and generates described each asynchronous curve one by one based on each value of this input.

3. servo control system as claimed in claim 2, it is characterized in that, described control curve generates parts and is included in each Control Circulation in the asynchronous control interval, previous round-robin main spindle's, cam position, cam speed, cam acceleration is generated the function of the asynchronous curve in this Control Circulation as the starting position of asynchronous curve.

4. servo control system as claimed in claim 1, it is characterized in that, described control curve generates parts and is included in each Control Circulation in the asynchronous control interval, previous round-robin main spindle's, cam position, cam speed, cam acceleration is generated the function of the asynchronous curve in this Control Circulation as the starting position of asynchronous curve.

5. as any one described servo control system of claim 1 to 4, it is characterized in that, comprise the specific parts that pass through point in the way of setting described asynchronous control interval,

When described control curve generation parts generate asynchronous curve in asynchronous control interval, ask described five functions, make the specific cam position that passes through point in its way for main spindle's by described setting, and ask cubic function, so that specific cam acceleration by point is 0 processing in this way.

6. servo control system as claimed in claim 5 is characterized in that, described control curve generates parts and is included in the described synchro control interval, generates the function based on the synchronous curve of square curve movement or crank-motion curve setting.

7. as any one described servo control system of claim 1 to 4, it is characterized in that, described control curve generates parts and is included in the described synchro control interval, generates the function based on the synchronous curve of square curve movement or crank-motion curve setting.

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