新的6-PSS型并联机构正向运动学求解方法

Novel method for forward kinematics of 6-PSS parallel manipulator

针对6-PSS型并联机构,通过研究其正向运动学,利用各支链铰点在动坐标系、静坐标系和滑块铰点坐标系3种坐标系下的位置关系,推导出6-PSS型并联机构的运动学模型,得到一种简明的运动学正向求解方法。在此基础上,提出了基于多元牛顿法和最速下降法的组合数值方法,并运用数值分析理论和计算机机器算数思想,最大限度提高收敛速度和减少单步迭代计算量。最后,编制了机构运动学的正向求解程序,进行了数值仿真,结果表明:改进的组合数值方法不仅可以更加快速地收敛到真实解,还能降低对初始估计值的依赖,扩大收敛范围,可以有效应用于该型并联机器人系统。

Through the research of 6-PSS parallel manipulator,this paper developed the kinematics model based on the relationship between spherical joints′spatial positions in three kinds of coordinate systems,which respectively are the global coordinate system,the local coordinate system and the hinge-point coordinate systems fixed on sliding blocks.A composed numerical method based on multivariate Newton′s method and the steepest descent method was proposed.The theories of numerical analysis and machine computation were used to improve the convergence speed and decrease the amount of operations in a singlestep iterative process.Finally,the forward kinematics solution program was written for the numerical simulation.The results show that the improved composed numerical method can not only decrease the computational time and converge to the solution accurately,but also reduce the dependence on the initial estimate and expand the convergence range.This method can be effectively applied in robot system based on 6-PSS parallel manipulator.