冗余驱动过约束并联机构受力分析

Force analysis of redundantly actuated overconstrained parallel mechanism

含有驱动冗余的过约束并联机构具有承载能力大、各向同性良好等特点,但其同时含有主动过约束和被动过约束,受力分析相当复杂。本文以4-PRRR冗余驱动过约束并联机构为对象对该类机构受力的超静定问题进行研究。首先针对主动过约束问题,基于特定的优化目标求解出各驱动力大小。然后针对被动过约束问题,建立各分支过约束力螺旋系的刚度矩阵和机构整体刚度矩阵,分析驱动力在过约束力螺旋系轴线方向产生的耦合变形,采用加权广义逆方法求解得到过约束力螺旋系幅值。联合Solid Works、ANSYS和ADAMS软件建立机构的刚柔混合模型并进行受力仿真分析,仿真结果与理论值基本一致,验证了理论分析结果的合理性。

A overconstrained parallel mechanism with actuation redundancy has a large capacity of load bearing and a good isotropy,but it contains both active and passive overconstraints. Therefore,it is quite complicated to conduct its force analysis. In this paper,the statically indeterminate problem of a 4-PRRR redundantly actuated overconstrained parallel mechanism is studied. In the light of active overconstraints,each driving force is solved based on the specific optimization goal. In order to solve the problem of passive overconstraints,the stiffness matrix of overconstrained force screw system of each branch and the stiffness matrix of the whole system are established,and the coupling deformation produced by the driving force in the direction of the axis of overconstrained force screw system are analyzed. The generalized inverse of weighted Moore-Penrose method is used to obtain the amplitude of the overconstrained force screw system. Combined with Solid Works,ANSYS and ADAMS software,the rigid flexible model of the mechanism is established and the force simulation analysis is carried out. The simulation results are consistent with the theoretical values,which verify the rationality of the theoretical analysis results.