基于螺旋理论对3-RPS并联机器人运动学分析及仿真

3-RPS型并联机构具有3个结构对称的支链形式,每个支链由一个转动副连接基座,一个球面副与动平台相连接,转动副与球面副由移动副所连接。采用螺旋理论对3-RPS型并联机器人自由度分析,采用反螺旋的方法建立约束雅可比矩阵、运动雅可比矩阵和完整雅可比矩阵,导出了动平台的速度到驱动关节速度之间的映射,从而计算出末端执行器的速度、加速度并进行奇异性分析。基于Matlab SimMechanics软件建立3-RPS型并联机器人仿真模型,进行运动学仿真对比研究,结果表明:动平台的实际输出变化与给定的参考值变化基本相符,验证了该建模方法的正确性。

Kinematics Analysis and Simulation of 3-RPS-type Parallel Robot Based on Screw Theory

A 3-RPS-type parallel robot has three structurally symmetrical branch-chain,each of which consists of a revolute pair and prismatic pair,spherical pair.The revolute pair is connected with the base;the spherical pair is connected with the moving platform;revolute and spherical pairs are connected with a prismatic pair.This paper analyzed the degrees of freedom of a 3-RPS-type parallel robot based on the screw theory,and used anti-screw the method to establish the constraint Jacobian matrix,the motion Jacobian matrix and the complete Jacobian matrix;with the method the mapping between the motion speed of a moving platform and the speed of an actuation joint was derived;the velocity and acceleration of the end-executor was calculated and the singularity was anslyzed.Matlab SimMechanics was used to establish the simulation model of the 3-RPS-type parallel robot to perform kinematics simulation and comparative study.The results show that with the changes in the actual outputs of the moving platform are basically consistent with those in the given reference value,and the correctness of the modeling method is verified.