WO1999011947A1

WO1999011947A1 - Transmission device

Info

Publication number: WO1999011947A1
Application number: PCT/CA1998/000831
Authority: WO
Inventors: Jorge Angeles; Max Antonio Gonzales-Palacios
Original assignee: Mcgill University
Priority date: 1997-09-04
Filing date: 1998-09-01
Publication date: 1999-03-11
Also published as: AU8969398A

Abstract

A transmission mechanism (12) for transmitting motion with a uniform speed transmission factor between first and second moveable elements (14, 16) comprises a set of cams (54, 56) adapted to rotate with the first moveable element (14) about a revolving axis, and corresponding arrays (70, 72) of spaced-apart rollers connected to the second moveable element (16) for movement therewith. The cams (54, 56) cooperate in relays with the corresponding arrays (70, 72) of spaced-apart rollers (85) to continuously communicate motion between the first and second moveable elements (14, 16). The cams (54, 56) are in rolling contact with the corresponding arrays (70, 72) of rollers (85), whereby torque and force transmission can be performed smoothly. Furthermore, the transmission mechanism (12) allows for the reversal of both the direction of the input speed and the roles of the first and second moveable elements (14, 16).

Description

TRANSMISSION DEVICE

BACKGROUND OF THE INVENTION

1. Field of the invention The present invention relates to a transmission device and, more particularly, to a transmission device having rolling contact surfaces for transmitting motion between first and second moveable elements.

2. Description of the Prior Art Over the years, various power transmission systems have been developed to overcome the inherent drawbacks of conventional gear transmissions. One of these alternative transmission systems is the cycloidal speed changing device. Such a device is disclosed in U.S. Patent No. 5,123,883 issued to Fukaya on June 23, 1992 and in U.S. Patent No. 5,286,237 issued to Minegishi on February 15, 1994.

Basically, the cycloidal speed changing device consists of an internal meshing planetary gear construction which comprises an input shaft, an external -tooth gear mounted on the input shaft through an eccentric body, a stationary internal -tooth gear adapted to mesh with the external -tooth gear, and an output shaft connected to the external -tooth gear by means of a plurality of inner pins fixed to the output shaft and extending through a plurality of corresponding inner holes defined in the external -tooth gear so that rotation of the input shaft is transmitted to the output shaft. The internal-tooth gear has teeth of circular arc profile which may consist of pins or combination of pins and rollers, whereas the external -tooth gear has teeth of trochoidal profile.

In accordance with the above construction, the output shaft will rotate in the opposite direction to the input shaft at a speed dependent upon the difference in the number of teeth between the external -tooth gear and the internal -tooth gear.

Although utilization of such transmission gears is well established, it is noted that the cycloidal speed changing devices are constrained to coaxial input and output shafts and that the tooth profile of the external- tooth gears thereof, i.e. the succession of concave and convex curves on the outer periphery of the external -tooth gears, causes stress concentrations, which is detrimental to the service life of the gear mechanism.

Alternative transmission devices, such as harmonic drive and direct drive, have also been proposed to overcome the inherent problems of conventional gear speed changing devices. These two relatively novel types of drives solve the problems of gears to some extent, the first, by means of a very flexible element, which brings about high power losses and undesirable flexibility; and the second, by eliminating the transmission mechanism which requires the utilization of massive motors. Besides, harmonic drives are limited to coaxial input and output shafts, while direct drives, as their name dictates, transmit power directly from the motor shaft and hence, are inherently limited to coaxial shafts as well.

SUMMARY OF THE INVENTION

It is therefore an aim of the present invention to provide a new transmission device which is adapted to transmit motion between two moveable elements. It is a further aim of the present invention to provide a transmission device which is adapted to transmit power from an input element to an output element through a transmission mechanism having rolling-contact, thereby generating low friction resistance and low power losses.

It is a further aim of the present invention to provide a transmission device which produces low backlash and which is thus particularly suitable in specific areas that call for high accuracy and smooth operations.

It is an aim of the present invention to provide a transmission device which operates at low noise level .

It is a further aim of the present invention to provide a transmission device which can be designed to couple parallel or intersecting shafts at angles varying from 0 to 180 degrees.

It is a still further aim of the present invention to provide a transmission device which is adapted to link a revolving shaft to a translating rack.

Therefore, in accordance with the present invention, there is provided a transmission mechanism for transmitting motion between first and second moveable elements, comprising a set of cam means adapted to rotate with said first moveable element, and corresponding arrays of spaced-apart roller means connected to said second moveable element for movement therewith, said set of cam means being adapted to alternately cooperate with said spaced-apart roller means of said corresponding arrays of spaced-apart roller means to communicate motion to one of said first and second moveable elements in response to a driving action of the other of said first and second moveable elements.

BRIEF DESCRIPTION OF THE DRAWINGS

Having thus generally described the nature of the present invention, reference will now be made to the accompanying drawings, showing by way of illustration a preferred embodiment thereof and m which:

Fig. 1 is a perspective view partly in cross- section of a transmission device m accordance with the present invention;

Fig. 2 is a perspective view partly m cross- section showing a housing of the device of Fig. 1 ;

Fig. 3 is a perspective view partly m cross- section showing an arrangement of conjugate cams rigidly mounted on an input shaft of the device of Fig. 1 ;

F g. 4 is a perspective view partly m cross- section showing two sets of rollers revolvably disposed about the periphery of a circular carrier member which is m turn fixedly mounted to an output shaft of the device of Fig. 1;

Fig. 5 is a front elevational view of a cam member of the present invention;

Fig. 6 is a perspective view partly m cross- section of a second preferred embodiment m accordance with the present invention;

Fig. 7 is a perspective view partly m cross- section showing a housing of the device of Fig. 6;

Fig. 8 is a perspective view partly m cross- section showing an arrangement of conjugate cams rigidly mounted on an input shaft of the device of Fig. 6;

Fig. 9 is a perspective view partly m cross- section showing two sets of rollers revolvably disposed about the periphery of a carrier member which is m turn fixedly mounted to an output shaft of the device of Fig. 6 ; Fig. 10 is a schematic perspective view partly m cross-section of a transmission device m accordance with a third embodiment of the present invention for transforming a rotary motion into a linear motion or vice versa; and Fig. 11 is a schematic side elevational view of the transmission device of Fig. 10.

DESCRIPTION OF THE PREFERRED EMBODIMENTS Now referring to the drawings, and in particular to Fig. 1, a transmission device embodying the elements of the present invention and generally designated by numeral 10 will be described.

The transmission device 10 generally comprises a housing 12, an input shaft 14 and an output shaft 16 rotatably mounted within the housing 12 and connected to each other through a transmission mechanism having a constant speed reduction ratio.

More specifically, as shown in Fig. 2, the housing 12 includes two side plates 18 and 20 which are spaced apart by a front plate 22 and a rear spacer 24 secured thereto by means of any suitable fasteners 25 such as screws or the like. A groove 26 following a curved path is defined on the interior side of each side plate 18 and 20 for receiving the side edges of a cover shell 28. The output shaft 16 is rotatably mounted to the housing 12 through a pair of bearings 30 which are respectively disposed within a bearing aperture defined in the side plates 18 and 20. The housing 12 also includes two adjustable side plates 32 and 34 each capable of undergoing submillimetric translations along a horizontal channel 36 and a vertical channel 38 which mate respectively with a horizontal protrusion 40 and a vertical protrusion 42 extending from a front portion of each side plate 18 and 20. The main purpose of this arrangement is to allow a preloading of the rollers in contact with the cam, in order to ensure a force transmission without backlash. Accordingly, the adjustable side plate 32 can be slidably engaged onto the front portion of the side plate 18 while the adjustable side plate 34 can be slidably engaged onto the front portion of the side plate 20. Each adjustable side plate 32 and 34 is provided with a bearing 43 for rotatably supporting the input shaft 14. As illustrated in Fig. 2, a nut 44 engages a screw 46 which extends through the left corner of the front plate 22 and through the adjustable side plate 32 so as to slidably displace the adjustable side plate 32 relative to the front portion of the side plate 18. In a similar manner, the adjustable side plate 34 may be displaced relative to the front portion of the side plate 20. Therefore, translational misalignments of the input shaft 14 relative to the output shaft 16 may be compensated.

The housing 12 is also provided with a base portion in the form of two L-shape plates 48 and 50 which are respectively secured to the side plates 18 and 20 by way of fasteners 52. Referring now to Fig. 3, it can be seen that two cam plates 54 and 56 are mounted on the input shaft 14 with a predetermined phase difference by means of a square key 58 which cooperates with a key way defined in both cam plates 54 and 56 to fixedly secure the same onto the input shaft 14, as it is well known in the art. Alternatively, and in order to allow a stiffer device, the two cam plates 54 and 56 and the shaft 14 thereof can be cut from a single blank, thereby eliminating the necessity of having a key way and square key assembly which require precise machining in order to avoid backlash.

More particularly, in the present embodiment, the two cam plates 54 and 56 are symmetrically installed at an angle of 180 degrees corresponding to each other, thereby forming a conjugate arrangement of cams.

A separating bushing 60 having a predetermined length is fitted on the input shaft 14 between the cam plates 54 and 56 to set the relative axial position thereof. Furthermore, an aligning bushing 62 is provided to set the axial position of the conjugate cams arrangement onto the input shaft 14 when the latter is installed into the housing 12. A lock nut 64 and an external retaining ring 66 are mounted to the opposed ends of the input shaft 14 to restrict the axial displacement of the input shaft 14 within the housing 12.

As shown in Fig. 4, a carrier member 68 supporting a first row of rollers 70 and a second row of rollers 72 is fixedly mounted on the output shaft 16 through a coupling bushing 74 defining a key way (not shown) for receiving a square key 76 extending on the outer periphery of the output shaft 16. The carrier member 68 includes a front disc 78, a rear disc 80 and a middle disc 82 with the relative axial position thereof being dictated by the coupling bushing 74 and by both rows of rollers 70 and 72 which are respectively disposed on either side of the middle disc 82 between the front disc 78 and the rear disc 80. The front and the rear discs 78 and 80 are provided with cutout portions 84 with the twofold purpose of reducing weight and easing the assembly of the rollers. Circular holes 86, or holes of alternative shapes, are also defined in the front disc 78, the rear disc 80 and the middle disc 82 for further reducing the weight of the carrier member 68. The front and the rear discs 78 and 80 are secured to the coupling bushing 74 by fasteners 88 and by the dowell pin 87. -

Each roller 85 of the first row of rollers 70 is freely mounted on a roller pin 90 which extends through holes defined in the middle disc 82 and the front disc 78. In a similar manner, each roller 85 of the second row of rollers 72 is freely mounted on a roller pin 90 which extends through holes defined in the middle disc 82 and the rear disc 80. Therefore, the front disc 78, the middle disc 82 and the rear disc 80 rotate about the axis of the output shaft 16 as a single unit.

As clearly seen from Fig. 4, the first and the second rows of rollers 70 and 72 are shifted in phase by a predetermined angle which is a function of the number of rollers 85. For example, if the first and second rows of rollers 70 and 72 each includes eight rollers 85 uniformly distributed around the periphery of the carrier member 68, as in the preferred embodiment illustrated in Figs. 1 to 5, the angle between two adjacent rollers 85 of the same row is 360°/8 = 45° and the phase difference between the first row and the second row of rollers 70 and 72 is equal to 45°/2 = 22.5° .

A lock nut 92 and an external retaining ring 94 are mounted on the opposed ends of the output shaft 16 to restrict the axial displacement of the output shaft 16 within the housing 12.

When the input shaft 14 and the output shaft 16 are assembled to the housing 12 as shown in Fig. 1, the cam plates 54 and 56 are respectively aligned with the first and second rows of rollers 70 and 72 such that rotation of the input shaft 14 will cause the cam plates 54 and 56 to alternately push on a roller 85 of the corresponding row of rollers 70 and 72 to thus transmit a torque from the input shaft 14 to the output shaft 16. In the contact condition shown _ in Fig. 1, that is at a particular instant of operation, the torque transmission is essentially effected through the cam plate 56 because the input shaft 14 rotates in the direction indicated by arrow 96. It is noted that even though, at that moment of operation, the cam plate 54 does not contribute to the torque transmission, it does not interfere with any other parts, since it is in relatively pure- rolling contact with the associated rollers 85 at all times. Indeed, the unique profile of both cam plates 54 and 56 allows the maintenance of relatively pure- rolling between the contact surface of the cam plates 54 and 56 and the associated first and second row of rollers 70 and 72, thereby providing a transmission device having superior efficiency and durability.

Moreover, the profile of the cam plates 54 and 56 ensures that a constant speed reduction ratio is obtained. As shown in Fig. 5, each cam plate 54 and 56 consists of a planar body having a cardioid-like shape which provides an essentially convex contact surface with the only concave portion thereof being at a dead point of this particular cam- follower arrangement, i.e. at a point where no torque transmission occurs, thereby preventing stress concentrations from affecting the service life of the transmission device. It is to be noted that the dead points of each cam-follower arrangement are out of phase by a maximum angle of 180°; thus, when one of the cams operates at a dead point, its conjugate (or conjugates) takes up the load, thus allowing for a continuous torque transmission. More particularly, the profile of the cam plates 54 and 56 is generated by a vector r_c which is defined as follows: a_x ₃ <

1 + 1/N h ^Qi

1 + N

c₂ = (as cos φ + aι — k )² + a .² sin² φ

α₃ sin φ fc₃ = arctan α₃ cos φ -f- a_\ — kι

wherein : l/N: speed reduction ratio, for an integer N; >: angle of rotation of the input shaft with respect to the housing; φ: angle of rotation of the output shaft with respect to the housing; ay. distance between output and input shafts; a₃ -. distance between output shaft and roller centers a₄ : radius of the rollers; kj_ : temporary variables, where i= 1,2,3... λ: real number defining one specific point along the contact line. It varies continuously between λ_mi_n and λmax-

The vector r_c defines the position of a point of the cam surface and thus, it may be used to generate a complete cam profile which will enable to transmit a motion with a uniform velocity from an input shaft to and output shaft having parallel axes. In other words, this equation allows the construction of a cam profile necessary to obtain a desired speed reduction ratio l/N between two parallel shafts.

In operation, the rotation of the input shaft 14 directly drives the cam plates 54 and 56 which will in turn act on the rollers 85 to cause the carrier member 68 rotating the output shaft 16 in the opposite direction with a reduced rotational speed according to the profile of the cam plates 54 and 56. Indeed, the motion of the carrier member 68 and thus of the output shaft 16 depends upon the shape of the cam plates 54 and 56.

It is noted that when it is desired that the rotation of the output shaft 16 be in the same direction to that of the input shaft 14, the cam members 54 and 56 may be disposed within the circular path defined by the first and the second row of rollers 70 and 72 instead of outside as in the above described embodiment. This embodiment corresponds to an angle between shafts at 180°, while that of Fig. 1 corresponds to an angle of 0°.

Fig. 6 shows a second possible embodiment of the present invention wherein the longitudinal axis of the input shaft 204 intersects the longitudinal axis of the output shaft 206 at right angles, but the device can accommodate other angles between shafts. As shown in Fig. 7, the housing 202 of the second embodiment is essentially the same as the one described above except that the input shaft 204 is supported by a pair of bearings 205 disposed in a bearing housing 207 secured to a front plate 208. It is also noted that the housing 202 lacks any adjustable side plates. The remaining features of the housing 202 are similar to those of the embodiment shown in Figs. 1 to 5 , and thus their duplicate description will be omitted.

Referring to Fig. 8, it can be seen that two cams 212 and 214 are mounted apart from each other onto the input shaft 204 with a predetermined phase difference (180° m this embodiment) by means of two square keys 216 and 218 which respectively cooperate with a key way defined m both cams 212 and 214 to fixedly secure the same onto the input shaft 204, as it is well known m the art.

A lock nut 220 is provided at each end of the input shaft to restrict the axial displacement of the cams 212 and 214 and of the input shaft itself within the housing 202. Referring now to Fig. 9, it can be seen that a carrier member 222 supporting an internal row of rollers 224 and an external row of rollers 226 is mounted to the output shaft 206 for rotation therewith. The carrier member 222 is provided with a key way (not shown) which is adapted to slidably engage a square key 228 extending along a portion of the length of the output shaft 206. The axial positioning of the carrier member 222 to the output shaft 206 is ensured by an aligning bushing 230.

The carrier member 222 includes a disc 232 and an integral ring 234 extending at an angle from the periphery of the disc 232 for supporting the internal and external sets of rollers 224 and 226 Geometrically, the integral ring 234 corresponds to a segment of a sphere, i.e. a portion of a sphere contained between two parallel planes both intersecting the sphere. The integral ring 234 has holes 236 regularly distributed along the surface thereof for roller pins 238 to pass through.

As easily seen from Fig. 9, each roller pm 238 has a head 240 and a longitudinal body having a threaded portion which is adapted to cooperate with a bolt 242 to retain the roller pm 238 on the integral ring 234 and to restrict the axial displacement of a roller 244 mounted onto the longitudinal body of the roller pm 238. The roller p s 238 are alternately assembled to the integral ring 234 with the longitudinal body thereof extending inwardly and outwardly of the integral ring 234 such that adjacent roller pms 238 extend m opposite direction with respect to each other, whereby the internal and external row of rollers 224 and 226 are shifted m phase by an angle which is equal to 360°/number of roller pms.

The rollers 244 have a frusto-conical shape. As best seen Fig. 9, the rollers 244 disposed outwardly of the integral ring 234 are mounted to the roller pms 238 with the smallest radius section thereof facing the head 240 of the roller pms 238, whereas the rollers 244 disposed inwardly of the integral ring 234 are mounted on the roller pms 238 with the greatest radius section thereof facing the head 240 of the roller pms 238.

As for the first embodiment, a lock nut 246 and an external retaining ring 248 are mounted on the opposed ends of the output shaft 206 to restrict the axial displacement of the output shaft 206 withm the housing 202.

When the input shaft 204 and the output shaft 206 are assembled to the housing 202 as shown m Fig. 6, the cams 212 and 214 are respectively m rolling contact with the internal and external rows of rollers 224 and 226 such that rotation of the input shaft 204 will cause the cams 212 and 214 to alternately push on a roller 244 of the corresponding row of rollers 224 and 226 to thus transmit a torque from the input shaft 204 to the output shaft 206. As for the first embodiment, the profile of the cams 212 and 214 is the key element to ensure that a constant speed reduction ratio is obtained. Accordingly, the profile of the cams 212 and 214 is generated by a position vector r_c which is expressed as follows :

₃ < arctan

kι = arctan ,

k₂ = COS(QI - kι) cos φ sm a₃ + cos α₃ sin(αι — k_x)

&₃ = sin ₃ sin φ kή, = cos ₃ cos(αι - fci ) - cos <p sin ₃ sin(αι - fcj )

k$ = arctan ^' /kξ ¥Λ C4

fcβ = arctan -—

kγ = sin kι cos(k₅ - α₄) + cos k sin( c₅ - α₄) cos k_e

—kγ sin φ + sin( c₅ — ) sin kβ cos ψ λ -k₇ cos ψ - sin(k₅ — α₄) sin fee sin t/' cos fcx cos(A;₅ — Q₄) — sin Aii sin(fcs — ) cos k₆

wherein : α^_ : angle between output and input shafts; α.3 : angle between output shaft and the axis of rotation of the rollers;

04 : angle of the roller cone;

Fig. 10 shows a third embodiment of the present invention which may act as a substitute for a conventional rack and pinion transmission to communicate a revolution of a first element into a linear motion of another element or vice versa. More specifically, the transmission device 300 comprises a rotary shaft 304 on which a pair of spaced- apart cam plates 306 and 308 are mounted with a predetermined phase difference (180° in this embodiment) for respectively engaging first and second rows of rollers 310 and 312 distributed on opposed longitudinal sides of an elongated member 314.

It is noted that the cams 306 and 308 may be cut with the rotary shaft 304 from a unique blank, in one single piece to add stiffness to the transmission device 300. This concept is correspondingly applicable to the first two embodiments, i.e., to the transmission devices 10 and 200. Unlike the first two embodiments, the transmission device 300 does not require a housing, since one of the moveable elements of the transmission mechanism, i.e. the elongated member 314, has a translational motion, and hence, the length of the stroke thereof is limited only by each application, the device 300 providing for an unlimited stroke length. However, the rotary shaft 304 is mounted on a supporting frame (not shown) , which plays the role of a housing, by means of bearings 316 provided at opposed ends thereof. The elongated member 314 or rack is supported by way of rollers 318. Each roller 318 is journalled at opposed ends thereof within bearings 320 having respective external rings fixed to the supporting frame (not shown) . The rollers 318 are thus constrained to a pure rotation about their revolving axes, without translating.

The rollers 310 and 312 are mounted on pins 322 extending at right angles from both sides of the elongated member 314. The pins 322 are uniformly distributed on each side of the elongated member 314. As shown in Fig. 10, the first and second row of rollers 310 and 312 are shifted in phase by a predetermined distance which is a function of the number of rollers. The transmission device 300 is characterized by a speed transmission factor or pitch p defined as the quotient between the linear velocity of the elongated member 314 (m/s) by the angular velocity of the rotating shaft 304 (rad/sec) .

As for the first and second embodiments, the profile of the cam members 306 and 308 is the key element to ensure that a constant speed transmission is obtained. Accordingly, the profile of the cam members 306 and 308 is generated by a position vector r_c, which is expressed as follows :

α₃ <

1 + 1/N

— 2πα₃w sin αi kr, = arctan

(aι + ₃)N + 2 rα₃ sin ct_\

k_x cos i> + (k - α₄) cos(A;₃ - ib) -k_x sin ψ + (k₂ - α₄) sin( c₃ - )

X

wherein : l/N: speed reduction ratio, for an integer N; ψ : angle of rotation of the rotating shaft with respect to the supporting frame; ot_]_ : angle between the rotating shaft and the longitudinal axis of the elongated member; ay. distance between the revolving axis of the rotating shaft and a reference line parallel to a longitudinal axis of the elongated member; a₃ : distance between the reference line and roller centers; a₄ : radius of rollers;

As seen in Fig. 11, the center of the rollers 310 and 312 are disposed along a common line 324 which is spaced by a distance a₃ from a reference line 326 parallel to a longitudinal axis of the elongated member 314. The variable α, is also established with reference to the line 326.

In operation, the rotary shaft 304 may be driven to cause the cam members 306 and 308 to alternately act on the corresponding row of rollers 310 and 312 to translate the elongated member 314 in a direction parallel to the longitudinal axis thereof. Alternatively, the elongated member 304 may be driven such as to successively push a roller of the first and second rows 310 and 312 against the cam members 306 and 308, respectively, to cause the rotary shaft 304 to rotate.

It is understood that although the longitudinal axis of the elongated member 314 is at right angles with the axis of the shaft 304 in the embodiment illustrated in Fig. 10, the transmission device 300 can accommodate other angles .

One advantage of the three above-described embodiments resides in the fact that they allow for a reversal of both the direction of the input speed and the roles of the input and output elements.

The present invention is not limited to the above-described embodiments. For example, double trains or multiple trains (i.e. multistage transmission devices) can be provided and linked to obtain a higher speed ratio of the transmission. The present invention also includes in its scope a construction in which the three above described embodiments are used in combination.

Claims

I Claim :

1. A transmission mechanism for transmitting motion between first and second moveable elements, comprising a set of cam means adapted to rotate with said first moveable element, and corresponding arrays of spaced-apart roller means connected to said second moveable element for movement therewith, said set of cam means being adapted to alternately cooperate with said spaced-apart roller means of said corresponding arrays of spaced-apart roller means to communicate motion to one of said first and second moveable elements m response to a driving action of the other of said first and second moveable elements.

2. A transmission mechanism as defined m claim 1, wherem said cam means are shifted m phase by a prescribed angle, and wherem said corresponding arrays of spaced- apart roller means are connected to said second moveable element with a prescribed phase difference, each said corresponding array of spaced-apart roller means including a plurality of uniformly distributed rollers which are configured to be engaged by corresponding cam means.

3. A transmission mechanism as defined claim 2, wherem said cam means have respective contoured cam surfaces configured to be m rolling- contact with said rollers of said corresponding arrays of spaced-apart roller means to achieve a prescribed speed transmission factor l/N between said first and second moveable elements, N being an integer.

4. A transmission mechanism as defined claim 3, wherem each said cam means has a cardioid-like shape.

5. A transmission mechanism as defined m claim 4, wherem said first and second moveable elements respectively include first and second shafts having parallel axes, said cam means being disposed at axially spaced-apart locations on said first shaft for rotation therewith about said axis of said first shaft, each of said cam means being m a common plane with one of said corresponding arrays of spaced-apart roller means, said rollers of each said corresponding arrays of spaced-apart roller means being distributed along a circle concentric with said second shaft, said circle having a radius a₃, each said roller having a cylindrical configuration and being axially disposed relative to said second shaft, and where said contoured cam surface of each of said cam means is generated by a vector r_c which is defined as follows:

αi ₃ <

1 + 1/N k_ = 1 + N

= /( α₃ cos tέ + αi - ;ι )² + ₃ ² sin" φ

kz = arctan α₃ cos <p + a_\ — k_\ k_\ cos ib + {k — α ) cos(ι/> — fc₃)

To = —hi s φ — (fø - α) sιn(^ - fc₃) λ

wherem: ψ : is an angle of rotation of the first shaft; φ: is an angle of rotation of the second shaft; ay. is the distance between the first and second shafts ; a₄ : is the radius of the rollers; kj_ : are temporary variables, where i= 1,2,3... λ: is a real number defining one specific point along the contoured cam surface .

6. A transmission mechanism as defined in claim 5, wherein said first and second shafts are mounted to distinct moveable parts of a frame structure for providing a preloading of said rollers in contact with said contoured cam surfaces .

7. A transmission mechanism as defined in claim 5, wherein said arrays of spaced-apart roller means are assembled to a carrier member fixedly mounted on said second shaft .

8. A transmission mechanism as defined in claim 5, wherein said set of cam means includes two cams which are out of phase by an angle of 180 degrees and which operate in relays with the rollers of two corresponding arrays of spaced-apart roller means to provide a continuos torque transmission between said first and second shafts, said arrays of spaced-apart roller means being shifted in phase by an angle which is equal to the quotient of 360 degrees by the number of rollers.

9. A transmission mechanism as defined in claim 3, wherein said first and second moveable elements respectively include first and second shafts having intersecting axes, said cam means being disposed at axially spaced-apart locations on said first shaft for engaging corresponding arrays of spaced-apart roller means encircling said second shaft, said rollers of each said arrays of spaced-apart roller means having a frusto-conical shape and a rotating axis which is angled with respect to said second shaft, and wherein said contoured cam surface of each said cam means is generated by a vector r_c which is defined as follows:

α₃ < arctan

fci = arctan

k = cos(aι - kι) cos φ sin as + cos cc₃ sm^' (aι - kι) k_ = sin ₃ sin φ fc = cos ₃ COS(QI — fci) - cos<psinα₃ sin( ι - k_\)

k₆ = arctan ( ₇- I

= sin Ai cos(;₅ — α₄) + cos hi sin(A,₅ — α ) cos kg

—kj sinφ + si (fc₅ — α ) sink^ cosφ

= λ —kγcos — sin(c₅ — α₄)si A;₆ sin^>

_cos kι cos(A;₅ — α ) — sin kι sin(:₅ — α₄) cos kg

wherein: ψ: is an angle of rotation of the first shaft; φ: is an angle of rotation of the second shaft; a_ : is the angle between the axes of the first and second shafts; α₃ : is the angle between the axis of the second shaft and the axis of rotation of the rollers; α₄ : is an angle of the roller cone ; kj_ : are temporary variables, where i= 1,2,3... λ: is a real number defining one specific point along the contoured cam surface.

10. A transmission mechanism as defined in claim 9, wherein said set of cam means includes first and second cams disposed at axially spaced-apart locations on said first shaft for respectively engaging first and second corresponding arrays of spaced-apart roller means, said rollers of said first corresponding array of spaced-apart roller means being uniformly distributed along an outer surface of a ring member concentrically mounted to said second shaft, while said rollers of said second corresponding array of spaced-apart roller means being uniformly distributed along an inner surface of said ring member, said first and second corresponding arrays of spaced-apart roller means being shifted in phase by an angle which is equal to the quotient of 360 degrees by the number of rollers.

11. A transmission mechanism as defined in claim 10, wherein said ring member geometrically corresponds to a segment of a sphere .

12. A transmission mechanism as defined in claim 10, wherein said ring member extends from a periphery of a disc member secured to said second shaft .

13. A transmission mechanism as defined in claim 4, wherein said first and second moveable elements respectively include a rotating shaft and a linearly translating member having nonparallel axes, said cam means being disposed at axially spaced-apart locations on said rotating shaft for rotation therewith about said axis of said rotating shaft, each said cam means being in a common plane with one of said corresponding arrays of spaced-apart roller means placed in axially extending rows on said linearly translating member, said axially extending^" rows being parallel to a direction of motion of said linearly translating member, and wherein said contoured cam surface of each said cam means is generated by a vector r_c which is defined as follows :

a_x α₃ <

1 + 1/N

arctan

k_ cos + (c₂ — α₄) cos(;₃ — ψ) τ_r = —kι sin- + (k₂ — α₄) sin( ;₃ — φ)

X wherein: ψ : is an angle of rotation of the rotating shaft; αη_ : is the angle between the rotating shaft and the linearly translating member; ay. is a distance between the axis of the rotating shaft and a reference line parallel to the direction of motion of said linearly translating member; ^a3 : is a distance between the reference line and an axis passing through the center of the rollers; a₄ : is a radius of the rollers; kj_ : are temporary variables, where i= 1,2,3... λ: is a real number defining one specific point along the contoured cam surface.

14. A transmission mechanism as defined in claim 13, wherein said set of cam means includes first and second cams adapted to engage corresponding first and second arrays of spaced-apart rollers means laterally disposed on opposed longitudinal sides of said linearly translating member.

15. A transmission mechanism as defined in claim 14, wherein said first and second cams are shifted in phase by an angle of 180 degrees.

16. A transmission mechanism as defined in claim 1, wherein said cam means are integrally formed with said first moveable element.

17. A transmission mechanism for transmitting motion between first and second moveable elements, comprising a set of cam means for rotating with said first moveable element about a common axis, and corresponding arrays of spaced-apart roller means connected to said second moveable element for movement therewith, said set of cam means cooperating in relays with said spaced-apart rollers of said corresponding arrays of spaced-apart roller means to continuously communicate motion to one of said first and second moveable elements in response to a driving action of the other of said first and second moveable elements.