含子闭环的并联机构运动学分析

Kinematics Analysis of Parallel Mechanism with Sub Closed-chains

为解决含子闭环的并联机构运动学建模问题,对含子闭环的机构进行界定。基于旋量运算得到子闭环中任意两构件的相对速度和加速度,并将结果整理成广义螺旋的形式。将子闭环这种新的表示形式与其所在同一串联支链中其他构件相对运动的传统旋量表示相结合,得到这类串联运动链的一、二阶影响系数。进而推导出含子闭环并联机构的输入速度和加速度向末端构件旋量速度和加速度映射的通用公式。分别以含有1自由度和2自由度子闭环的2个并联机构为例进行仿真验证,结果证明所讨论的方法是正确的。

In order to solve the problem of kinematics modeling of parallel mechanism with sub closedchains（ PMHSC）,definition of the mechanism was made. The concept of general screw was derived by discussing the motion relationship of planar four-bar linkage,and its inner connection with instantaneous equivalent screw of so-called general kinematic pair was explained. Based on the concept,the relative velocity and acceleration of any two bars in a sub closed-chain with multi-DOF were obtained,and the result was arranged to the form by using general screw. Combining the new screw representation of sub closed-chain with conventional screw form of relative motion of two rigid bodies that connected directly with a joint,the first and second order influence coefficients of single kinematic serial limb with sub closed-chain were obtained,the discussion was conducted from the serial with one sub closed-chain to multi ones. It revealed that the elements corresponding to the sub closed-chain contained the general screw,especially in the second order influence coefficient matrix,which was consisted of two parts,no longer the lie bracket form of two screws as usual. Furthermore,the universal formula that depicted the mapping from general input velocity and acceleration to screw velocity and acceleration of terminal body of PMHSC was derived. Simulation verification was conducted by using two parallel mechanisms. The first one was 6-（ PRRR） US type that had planar PRRR closed loop in each leg,it＇s a 1-DOF sub closedchain; and the second one was 5-UPS /（ RPRRR） RS type which had a 2-DOF sub closed-chain in the special limb. The results prove that the method discussed is correct.