CN102501246B - Three-drive extensible dexterous mechanical arm - Google Patents
Three-drive extensible dexterous mechanical arm Download PDFInfo
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Abstract
一种三驱动可扩展灵巧机械臂,目的在于简化机械臂结构,增加自由度,可灵巧有效地对空间目标进行捕获。三驱动可扩展灵巧机械臂的动力源为三个安装在基座上的驱动单元,其中两个驱动单元通过丝杠、丝杠螺母、推杆及连杆的运动传递控制三驱动可扩展灵巧机械臂的姿态;第三个驱动单元控制三驱动可扩展灵巧机械臂整体的旋转运动,这样可利用三个驱动单元控制2N+5(N为自然数)个自由度。三驱动可扩展灵巧机械臂的关节为十字轴、关节外壳和凹凸限位机构的组合体,关节可弯曲旋转,同时关节可串联扩展,使得机械臂具有极高的自由度和灵巧性。
A three-drive expandable dexterous manipulator aims to simplify the structure of the manipulator, increase the degree of freedom, and capture space targets smartly and effectively. The power source of the three-drive expandable smart robot arm is three drive units installed on the base, two of which drive the control of the three-drive expandable smart robot through the motion transmission of the screw, screw nut, push rod and connecting rod The attitude of the arm; the third drive unit controls the overall rotational motion of the three-driver expandable dexterous manipulator, so that three drive units can be used to control 2N+5 (N is a natural number) degrees of freedom. The joints of the three-drive expandable dexterous manipulator are a combination of cross shafts, joint housings, and concave-convex limit mechanisms. The joints can be bent and rotated, and the joints can be extended in series, making the manipulator with a high degree of freedom and dexterity.
Description
技术领域technical field
本发明涉及机器人机构设计技术领域,确切的说,设计一种三驱动可扩展机械臂,用于空间目标的灵活抓取与捕获。The invention relates to the technical field of robot mechanism design, specifically, a three-drive expandable mechanical arm is designed for flexible grasping and capturing of space objects.
背景技术Background technique
随着空间探索的不断深入,在空间对接、在轨服务、货物搬运、目标捕获等工程领域,空间机械臂发挥着至关重要的作用。面对复杂的太空环境、种类繁多的操作对象以及日益复杂的操作任务,要求空间机械臂具有高可靠性、经济性、安全性、灵巧性等特点。With the continuous deepening of space exploration, space manipulators play a vital role in engineering fields such as space docking, on-orbit service, cargo handling, and target acquisition. Facing the complex space environment, a wide variety of operating objects, and increasingly complex operating tasks, the space manipulator is required to have the characteristics of high reliability, economy, safety, and dexterity.
目前,空间机械臂多为六自由度,每个关节都要安装一个由电机和减速器组成的驱动单元,在增加空间机械臂结构复杂性的同时加大了空间机械臂的质量和转动惯量,不利于节省能量。为了在节能的同时提高空间机械臂的灵巧性,设计出具有结构紧凑、重量轻、转动惯量小、多自由度、少驱动等特点的空间机械臂具有重要的意义。At present, most space manipulators have six degrees of freedom, and each joint must be equipped with a drive unit composed of a motor and a reducer. This increases the structural complexity of the space manipulator and increases the mass and moment of inertia of the space manipulator. Not conducive to saving energy. In order to improve the dexterity of the space manipulator while saving energy, it is of great significance to design a space manipulator with the characteristics of compact structure, light weight, small moment of inertia, more degrees of freedom, and less drive.
发明内容Contents of the invention
本发明提出一种三驱动可扩展机械臂,具有驱动单元数量少,自由度数高、灵巧性高等特点,能够用于空间对接、在轨服务、货物搬运、目标捕获等工程领域。The invention proposes a three-drive expandable robotic arm, which has the characteristics of fewer drive units, high degrees of freedom, and high dexterity, and can be used in engineering fields such as space docking, on-orbit service, cargo handling, and target capture.
本发明的技术方案如下:Technical scheme of the present invention is as follows:
一种三驱动可扩展机械臂,包括驱动单元、丝杠、丝杠螺母及推杆、连杆、偏摆环、关节、圆环及末端执行器接口,其特征在于:A three-drive expandable mechanical arm, including a drive unit, a lead screw, a lead screw nut and a push rod, a connecting rod, a yaw ring, a joint, a ring and an end effector interface, characterized in that:
所述驱动单元为旋转型电机和谐波减速器的组合体,安装于三驱动可扩展机械臂的机座上,所述丝杠通过联轴器连接于驱动单元的输出轴上驱动丝杠螺母做往复直线运动,丝杠螺母带动推杆做往复直线运动,所述推杆与连杆一端铰接,连杆另一端与偏摆环外壁铰接,所述关节为十字轴、关节外壳和凹凸限位机构的组合体,所述圆环中有一直径轴,圆环与关节外壳通过销钉连接,所述末端执行器接口为法兰式,可连接不同类型的末端执行器。The drive unit is a combination of a rotary motor and a harmonic reducer, installed on the base of the three-drive expandable mechanical arm, and the lead screw is connected to the output shaft of the drive unit through a coupling to drive the lead screw nut Do reciprocating linear motion, the lead screw nut drives the push rod to do reciprocating linear motion, the push rod is hinged with one end of the connecting rod, the other end of the connecting rod is hinged with the outer wall of the yaw ring, the joints are cross shafts, joint shells and concave-convex limiters A combination of mechanisms, the circular ring has a diameter shaft, the circular ring and the joint shell are connected by pins, and the end effector interface is flange type, which can be connected with different types of end effectors.
进一步的,三驱动可扩展机械臂共包括三个驱动单元,其中两个驱动单元通过联轴器与丝杠相连,依次通过丝杠螺母、连杆及推杆的力传递,实现偏摆环的上下及左右偏摆运动,第三个驱动单元通过联轴器与第一个关节的输入端相连,实现三驱动可扩展机械臂绕自身轴线的整体旋转运动。Furthermore, the three-drive expandable robotic arm includes three drive units in total, two of which are connected to the lead screw through a coupling, and are sequentially transmitted through the force of the lead screw nut, connecting rod and push rod to realize the rotation of the yaw ring. Up and down and left and right yaw movements, the third drive unit is connected to the input end of the first joint through a coupling to realize the overall rotation of the three-drive expandable mechanical arm around its own axis.
进一步的,丝杠通过丝杠螺母带动推杆做往复直线运动,推杆通过连杆与偏摆环外壁铰接。Further, the lead screw drives the push rod to perform reciprocating linear motion through the lead screw nut, and the push rod is hinged to the outer wall of the deflection ring through the connecting rod.
进一步的,关节结构具有可扩展性,前一个关节的输出端同时又是后一个关节的输入端,在三驱动可扩展机械臂结构中关节的数量可扩展至N,其中,N为自然数;关节中的凹凸限位机构具有球铰的全向转动功能,同时又受到凹凸结构上的限位,在三驱动可扩展机械臂的运动过程中起到定位与导向作用。Furthermore, the joint structure is scalable, the output end of the previous joint is also the input end of the latter joint, and the number of joints in the three-drive scalable manipulator structure can be expanded to N, where N is a natural number; the joint The concave-convex limiting mechanism has the function of omnidirectional rotation of the spherical hinge, and at the same time is limited by the concave-convex structure, which plays a role in positioning and guiding during the movement of the three-drive expandable mechanical arm.
进一步的,前一关节的十字轴与后一关节的十字轴之间通过关节外壳连接,偏摆环在推杆产生的推拉力作用下发生偏摆,带动第一关节内的十字轴偏摆,第一关节内的十字轴又会通过第一和第二关节之间的关节外壳带动第二关节内的十字轴偏摆,同时第一关节内的凹凸限位机构作为第二关节偏摆的支点和限位;随后的运动传递原理与上述原理相同,通过多个关节偏摆运动的累积,使三驱动可扩展机械臂实现大范围的偏摆运动。Furthermore, the cross shaft of the previous joint is connected to the cross shaft of the subsequent joint through the joint shell, and the deflection ring is deflected under the action of the push-pull force generated by the push rod, which drives the deflection of the cross shaft in the first joint, The cross shaft in the first joint will drive the cross shaft in the second joint to deflect through the joint shell between the first and second joints, and the concave-convex limit mechanism in the first joint will serve as the fulcrum for the deflection of the second joint and limit; the subsequent motion transmission principle is the same as the above-mentioned principle, through the accumulation of the yaw motion of multiple joints, the three-drive expandable robotic arm can achieve a wide range of yaw motion.
本发明设计的三驱动可扩展机械臂,包括安装在机座上的三个驱动单元、两根丝杠及其丝杠螺母、推杆、连杆、关节和圆环,末端带有法兰式末端执行器接口,可根据任务需求,连接不同末端执行器。The three-drive expandable mechanical arm designed by the present invention includes three drive units installed on the machine base, two lead screws and their lead screw nuts, push rods, connecting rods, joints and rings, and the ends have flanged The end effector interface can be connected to different end effectors according to the task requirements.
三个驱动单元为三驱动可扩展机械臂的动力源,丝杠及丝杠螺母将电机的旋转运动转化为推杆往复直线运动;其中两个驱动单元带动丝杠及螺母运动,通过与螺母联动的推杆与连杆的作用于偏摆环,改变第一关节姿态,通过十字轴与第一关节与第二关节之间的外壳力传递作用,将力传递到第二关节,而后通过与之相连的十字轴与关节外壳,继续改变后续关节的偏摆方向,依次类推,达到控制三驱动可扩展机械臂上下左右等弯曲偏摆姿态的目的;第三个驱动单元带动三驱动可扩展机械臂第一关节输入端旋转,通过关节依次传递旋转运动直至末端,达到三驱动可扩展机械臂整体回转的目的。The three driving units are the power source of the three-drive expandable robotic arm. The screw and the screw nut convert the rotational motion of the motor into the reciprocating linear motion of the push rod; two of the driving units drive the screw and the nut to move, and through linkage with the nut The push rod and connecting rod act on the yaw ring to change the posture of the first joint, and transmit the force to the second joint through the cross axis and the shell force between the first joint and the second joint, and then pass it to it The connected cross shaft and the joint shell continue to change the yaw direction of the subsequent joints, and so on, to achieve the purpose of controlling the bending and yaw posture of the three-drive expandable manipulator up and down; the third drive unit drives the three-drive expandable manipulator The input end of the first joint rotates, and the rotational motion is sequentially transmitted through the joints to the end, so as to achieve the purpose of the overall rotation of the three-drive expandable robotic arm.
关节为十字轴、关节外壳和凹凸限位机构的组合体,关节外壳可绕十字轴上下左右偏摆,其特点与万向节相同,关节外壳两端安装有凹凸限位机构,凹凸限位机构为凹凸配合的具有球铰功能的限位机构,相互凹凸配合的两个构件可沿任意方向偏摆,但相对偏摆到一定角度,由于机械限位的存在,则停止偏摆,达到控制偏摆角度大小的目的。The joint is a combination of the cross shaft, the joint shell and the concave-convex limit mechanism. The joint shell can swing up and down around the cross axis. It is a limit mechanism with the function of a spherical hinge that is concave-convex. The two components that are concave-convex with each other can deflect in any direction, but when they deflect relative to a certain angle, due to the existence of the mechanical limit, the deflection will stop to achieve control deflection. The purpose of pendulum angle size.
本发明的优点在于:The advantages of the present invention are:
1.三驱动可扩展机械臂的驱动单元数量少,结构紧凑,整体质量轻;1. The number of driving units of the three-drive expandable robotic arm is small, the structure is compact, and the overall weight is light;
2.驱动单元数量远远小于三驱动可扩展机械臂的自由度数,灵巧性高;2. The number of drive units is far less than the number of degrees of freedom of the three-drive expandable robotic arm, which has high dexterity;
3.三驱动可扩展机械臂的可扩展性强,可根据实际任务需求自由调整关节数量。3. The three-drive expandable robotic arm has strong scalability, and the number of joints can be freely adjusted according to actual task requirements.
附图说明Description of drawings
图1是以N=2为例设计的三驱动可扩展机械臂的总体结构主视图;Figure 1 is a front view of the overall structure of a three-drive expandable robotic arm designed with N=2 as an example;
图2是以N=2为例设计的三驱动可扩展机械臂的总体结构俯视图;Figure 2 is a top view of the overall structure of a three-drive expandable robotic arm designed with N=2 as an example;
图3是偏摆环、轴承与第一关节外壳配合示意图;Fig. 3 is a schematic diagram of cooperation between the yaw ring, the bearing and the shell of the first joint;
图4是第一关节外壳示意图;Fig. 4 is a schematic diagram of the first joint shell;
图5是十字轴示意图;Fig. 5 is a schematic diagram of the cross axis;
图6是第一关节与第二关节之间外壳示意图;Fig. 6 is a schematic diagram of the casing between the first joint and the second joint;
图7是三驱动可扩展机械臂第二关节外壳示意图;Fig. 7 is a schematic diagram of the shell of the second joint of the three-drive expandable robotic arm;
图8是第一关节与第二关节配合示意图;Fig. 8 is a schematic diagram of cooperation between the first joint and the second joint;
图9是圆环示意图;Figure 9 is a schematic diagram of a ring;
图10是三驱动可扩展机械臂第二关节外壳、圆环、执行器接口与手爪配合示意图;Fig. 10 is a schematic diagram of the coordination of the second joint shell, the ring, the actuator interface and the gripper of the three-drive expandable manipulator;
图11是主视图1中偏摆环受两个推力联合作用后,三驱动可扩展机械臂的弯曲示意图;Figure 11 is a schematic diagram of the bending of the three-drive expandable manipulator after the deflection ring in front view 1 is combined with two thrusts;
图12是主视图1中偏摆环受两个拉力联合作用后,三驱动可扩展机械臂的弯曲示意图;Figure 12 is a schematic diagram of the bending of the three-drive expandable mechanical arm after the deflection ring in the front view 1 is subjected to the joint action of two tension forces;
图13是俯视图2中偏摆环受一个推力与一个拉力联合作用后,三驱动可扩展机械臂的弯曲示意图;Fig. 13 is a schematic diagram of bending of the three-drive expandable manipulator after the deflection ring in top view 2 is combined with a push force and a pull force;
图14是俯视图2中偏摆环受一个拉力与一个推力联合作用后,三驱动可扩展机械臂的弯曲示意图;Fig. 14 is a schematic diagram of the bending of the three-drive expandable mechanical arm after the deflection ring in top view 2 is combined with a pulling force and a pushing force;
图中标识:驱动单元1、33、34,联轴器2、29、32,丝杠3、31,丝杠螺母4、30,推杆5、28,第一关节输入端6,铰链7、9、25、27,连杆8、26,偏摆环10,轴承11,第一关节外壳12,十字轴13、15,第一关节与第二关节外壳14,第二关节外壳16,销钉17,末端执行器接口18,手爪19,圆环20,凹凸限位机构21、22、23,固定座24。Marks in the figure:
具体实施方式Detailed ways
下面结合附图对该机械臂结构作进一步说明。The structure of the mechanical arm will be further described below in conjunction with the accompanying drawings.
如图1、2所示,三个驱动单元1、33、34为整个机械臂提供动力,其中驱动单元1、34的输出端通过联轴器2、32分别与丝杠3、31进行相连;丝杠3、31上分别安装有丝杠螺母4、30,丝杠螺母4、30分别与推杆5、28相连,可推动推杆做往复直线运动;推杆末端分别有铰链7、27,通过连杆8、26与偏摆环10外壁连接。通过丝杠螺母4、30的滑动,分别推动推杆5、28,通过连杆8、26的力传递作用,可以控制偏摆环10的偏摆;驱动单元33输出端通过联轴器29与第一关节输入端6相连,可带动第一关节转动,通过关节运动的传递,可使整个三驱动可扩展机械臂一同旋转。As shown in Figures 1 and 2, three
如图2、3所示,偏摆环10与第一关节外壳12通过轴承11进行连接,偏摆环10与第一关节外壳12之间嵌套轴承11,当驱动单元1、34带动丝杠螺母4、30,通过推杆5、28与连杆8、26作用于偏摆环10时,偏摆环10偏摆,带动轴承11偏摆,轴承11带动第一关节外壳12偏摆;而当驱动单元33作旋转运动时,带动第一关节外壳12与轴承11内壳旋转,偏摆环不旋转;这样通过控制偏摆环10可控制里面第一关节外壳12偏摆,但偏摆环不随第一关节旋转。As shown in Figures 2 and 3, the
如图4、5、6所示,分别为第一关节外壳12、十字轴13、第一关节与第二关节之间关节外壳14,关节外壳12、14均为空心圆柱形,关节外壳12与关节外壳14通过十字轴13进行连接,两关节外壳能够相对上下左右摆动,当两关节外壳旋转轴线不在同一直线上时,依然能传递旋转运动;关节外壳12右端与关节外壳16左端形成凹凸限位机构22,关节外壳14左端为凹凸限位机构23的凸部分,关节外壳14右端为凹凸限位机构21的凹部分。As shown in Figures 4, 5, and 6, they are respectively the first
如图7所示,第二关节外壳16通过十字轴15与关节外壳14相连,第二关节外壳16左端为凹凸限位机构22凸部分结构,凸起部分与关节外壳12右端的凹槽配合,形成凹凸限位机构21。As shown in Figure 7, the second
图8为图4、5、6、7的装配示意图,图4与图5所示部件通过十字轴13连接,图5与图6通过十字轴14连接,关节外壳12右端的凹部分与关节外壳16左端凸部分配合,形成凹凸限位机构22;相互凹凸配合的两个构件面可沿任意方向偏摆,具有球铰功能,但与球铰略有不同,凹面与凸面不完全接触,且所示的凸部分上的圆环在凹凸面配合转动时,能起到限位的作用,使得凹凸面配合的两构件相对转动到一定角度就会停止运动。Figure 8 is a schematic diagram of the assembly of Figures 4, 5, 6, and 7. The components shown in Figure 4 and Figure 5 are connected by a
如图9所示为可绕第二关节外壳16对应旋转副转动的的圆环20,圆环中间的轴起末端执行器接口18的支撑作用,同时末端执行器接口18可绕该轴旋转。As shown in FIG. 9 , it is a
该三驱动可扩展机械臂的工作原理主要分为以下四种运动模式:The working principle of the three-drive expandable robotic arm is mainly divided into the following four motion modes:
(1)两驱动单元同时推动推杆:当驱动单元1、34同时旋转分别带动丝杠3、31,丝杠通过丝杠螺母4、30推动推杆5、28,推杆5、28分别带动连杆8、26作用于偏摆环10,偏摆环10受到两个推力的联合作用后,相当于受到一个弯矩作用,从而绕着固定座24向上(如图11)旋转倾斜,带动与之通过轴承11相连的第一关节外壳12向上旋转倾斜;第一关节外壳12通过十字轴13带动第一关节与第二关节外壳14绕着以固定座24为支点向上旋转倾斜,且由于凹凸限位机构23的存在,第一关节与第二关节外壳14相对于第一关节外壳12只能向上倾斜到一定的角度;同时,旋转倾斜的关节外壳14又通过十字轴15的联动作用,带动第二关节外壳16向上以凹凸限位机构22凹槽为支点旋转倾斜一定的角度;最后通过凹凸限位机构21与圆环20的支撑导向作用,末端执行器接口18会以凹凸限位机构21凹槽为支点随着关节外壳16倾斜一定的角度;这样,通过关节偏摆的角度累积,整个机械臂向上弯曲形成一段圆弧;通过驱动单元33带动各个关节旋转,整个机械臂连同手爪可同时旋转。偏摆后的三驱动可扩展机械臂的整体结构如图11所示;(1) Two driving units simultaneously push the push rods: when the driving
(2)两驱动单元同时拉动推杆:当驱动单元1、34同时旋转分别带动丝杠3、31,丝杠通过丝杠螺母4、30拉动推杆5、28,推杆5、28分别带动连杆8、26作用于偏摆环10,偏摆环10受到两个拉力的联合作用后,相当于受到一个弯矩作用,从而绕着固定座24向下(如图12)旋转倾斜,带动与之通过轴承11相连的第一关节外壳12向下旋转倾斜;第一关节外壳12通过十字轴13带动第一关节与第二关节外壳14绕着以固定座24为支点向下旋转倾斜,且由于凹凸限位机构23的存在,第一关节与第二关节外壳14相对于第一关节外壳12只能向下倾斜到一定的角度;同时,旋转倾斜的关节外壳14又通过十字轴15的联动作用,带动第二关节外壳16向下以凹凸限位机构22凹槽为支点旋转倾斜一定的角度;最后通过凹凸限位机构21与圆环20的支撑导向作用,末端执行器接口18会以凹凸限位机构21凹槽为支点随着关节外壳16倾斜一定的角度;这样,通过关节偏摆的角度累积,整个机械臂向下弯曲形成一段圆弧;通过驱动单元33带动各个关节旋转,整个机械臂连同手爪可同时旋转。偏摆后的三驱动可扩展机械臂的整体结构如图12所示;(2) Two drive units pull the push rods simultaneously: when the
(3)一个驱动单元推动推杆,一个驱动单元拉动推杆:当驱动单元1旋转带动丝杠3,丝杠通过丝杠螺母4推动推杆5,推杆带动连杆28向偏摆环10施加一个推力,驱动单元34旋转带动丝杠31,丝杠通过丝杠螺母30拉动推杆28,推杆带动连杆26向偏摆环10施加一个拉力时,偏摆环10受到一个推力和一个拉力的联合作用后,相当于受到一个弯矩作用,从而绕着固定座24向下(如图13)旋转倾斜,带动与之通过轴承11相连的第一关节外壳12向下旋转倾斜;第一关节外壳12通过十字轴13带动第一关节与第二关节外壳14绕着以固定座24为支点向下旋转倾斜,且由于凹凸限位机构23的存在,第一关节与第二关节外壳14相对于第一关节外壳12只能到倾斜一定的角度;同时,旋转倾斜的关节外壳14又通过十字轴15的联动作用,带动第二关节外壳16向下以凹凸限位机构22凹槽为支点旋转倾斜一定的角度;最后通过凹凸限位机构21与圆环20的支撑导向作用,末端执行器接口18会以凹凸限位机构21凹槽为支点随着关节外壳16倾斜一定的角度;这样,通过关节偏摆的角度累积,整个机械臂越来越向上弯曲,形成一段圆弧线;通过驱动单元33带动各个关节旋转,整个机械臂连同手爪可同时旋转。偏摆后的三驱动可扩展机械臂整体结构如图13所示;(3) One drive unit pushes the push rod, and one drive unit pulls the push rod: when the drive unit 1 rotates to drive the
(4)一个驱动单元拉动推杆,一个驱动单元推动推杆:当驱动单元1旋转带动丝杠3,丝杠通过丝杠螺母4拉动推杆5,推杆带动连杆28向偏摆环10施加一个拉力,驱动单元34旋转带动丝杠31,丝杠通过丝杠螺母30推动推杆28,推杆带动连杆26向偏摆环10施加一个推力时,偏摆环10受到一个拉力和一个推力的联合作用后,相当于受到一个弯矩作用,从而绕着固定座24向上(如图14)旋转倾斜,带动与之通过轴承11相连的第一关节外壳12向上旋转倾斜;第一关节外壳12通过十字轴13带动第一关节与第二关节外壳14绕着以固定座24为支点向上旋转倾斜,且由于凹凸限位机构23的存在,第一关节与第二关节外壳14相对于第一关节外壳12只能到倾斜一定的角度;同时,旋转倾斜的关节外壳14又通过十字轴15的联动作用,带动第二关节外壳16向上以凹凸限位机构22凹槽为支点向上旋转倾斜一定的角度;最后通过凹凸限位机构21与圆环20的支撑导向作用,末端执行器接口18会以凹凸限位机构21凹槽为支点随着关节外壳16向上倾斜一定的角度;这样,通过关节偏摆的角度累积,整个机械臂向上弯曲形成一段圆弧;通过驱动单元33带动各个关节旋转,整个机械臂连同手爪可同时旋转。偏摆后的三驱动可扩展机械臂整体结构如图14所示。(4) One drive unit pulls the push rod, and one drive unit pushes the push rod: when the drive unit 1 rotates to drive the
综上所述,通过两个驱动单元1、34的协调控制,可使三驱动可扩展机械臂大范围偏摆,通过控制驱动单元33,可使三驱动可扩展机械臂整体旋转;这样,结合了整体偏摆与旋转功能的三驱动可扩展机械臂,可方便灵巧的对空间目标进行抓取与捕获。To sum up, through the coordinated control of the two
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| CN113386107B (en) * | 2021-06-21 | 2023-05-23 | 杨壬达 | Passive mechanical auxiliary limb device |
| CN113681590B (en) * | 2021-08-27 | 2022-09-09 | 中国矿业大学 | Modular robot docking device and docking method |
| CN115179271A (en) * | 2022-08-26 | 2022-10-14 | 筑橙科技(深圳)有限公司 | High-expansion-ratio cross hinge type multi-shaft manipulator |
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