一种少自由度3-SPR并联机构的刚度和弹性变形分析

Analysis of Stiffness and Elastic Deformation of a 3-SPR Limited-DOF Parallel Manipulator

针对并联机构中的约束反力会影响机构的刚度和产生弹性变形的问题,以传统的3-SPR并联机构为例,采用基于驱动/被动约束力求解其总刚度矩阵和弹性变形的方法。首先,分析该并联机构受力位置并确定驱动/被动约束力的姿态。然后,分析该机构的驱动约束分支的弹性变形,导出驱动约束分支的伴随矩阵。最后求解出该并联机构的总刚度矩阵和弹性变形。得到结论:当建立3-SPR并联机构的总刚度矩阵和求解弹性变形时,必须考虑约束力/矩的影响。

As the constraint force can affect the stiffness and produce elastic deformation in parallel manipulator, the method based on active/constrained force is used to solve the general stiffness matrix and elastic deformation, and a traditional parallel manipulator 3--SPR is analyzed to illustrate the method. Firstly, the force situations of the parallel manipulator are analyzed and the poses of the active/ constrained force are determined. Then, the elastic deformations of the active legs in the parallel manipulator are analyzed and compliance matrices of active/constrained legs are derived. Finally, the total stiffness matrix and elastic deformation of the parallel manipulator is solved. The results show that active/constrained forces have a huge impact to elastic deformation, and when establishing the total stiffness matrix and elastic deformation, constrained force/torque must be considered.