五自由度混联机构圆弧插补算法研究

摘要

提出了一种由两自由度并联机构和三自由度串联机构构成的五自由度混联机构-2SPU+U+RRR.建立了该混联机构的三维模型并搭建了试验样机,通过分析将其等效为U+ RRR串联机构.对等效后的U+RRR串联机构进行运动学正反解分析,并验证了正反解求解的正确性,同时对两自由度并联机构进行了运动学反解计算,为机构控制奠定了理论基础.针对传统空间圆弧插补算法计算的复杂性,提出了一种基于等弧度数据采样的新型空间圆弧插补算法,简化了插补算法的计算量.通过Matlab仿真和样机实验,验证了上述插补算法的正确性.%A novel 2SPU + U + RRR 5-DOF hybrid mechanism with one 2-DOF parallel mechanism and one 3-DOF serial mechanism was presented.This 5-DOF hybrid mechanism had advantages of large workspace and high stiffness compared with traditional hybrid mechanism.A prototype of this hybrid mechanism was constructed and it was equivalent to a U + RRR parallel mechanism,the analytic formulas for solving its inverse/forward displacement kinematics were derived and the forward displacement was derived based on D-H method.The unique solution of the inverse kinematics was determined based on the shortest distance rule,and the correctness of the analytical expression of the inverse/forward displacement kinematics was verified.The length of the two SPU active legs were derived based on the rotation angle of the Hooke hinge,thus the analytic formulas for solving the inverse displacement kinematics of the 2-DOF parallel mechanism was derived.Theoretical kinematics formulas and results provided foundation for the control of the hybrid mechanism,structure optimization design,dynamics performance analysis,manufacturing and applications and the study also enriches the application area of lower-mobility parallel mechanisms.A novel interpolation algorithm for an arc based on equal radian data sampling was derived,the calculation of interpolation algorithm was greatly simplified.In order to verify the correctness of the interpolation algorithm for an arc,the experimental prototype and its control system were built.The simulation result by Matlab and the experimental prototype result showed that the interpolation algorithm for an arc was correctness and this algorithm had great application prospect.