3-RPS控制位置用并联机器人机构的位置反解

系统研究了３－ＲＰＳ控制位置用并联机器人机构的位置反解问题。文中首先揭示了３－ＲＰＳ控制位置用并联机器人机构位置反解方程组解的分组特点，然后应用文［１］提出的用连续法求解多项式方程组时构造初始方程组的一条新原则，给出了该机构位置反解的高效算法。对于给定的输出，３－ＲＰＳ控制位置用并联机器人机构位置反解的数目为６４（对于一般形式）、３２（当机构有且仅有一个最简ＲＰＳ支路时）、１６（当机构有且仅有两个最简ＲＰＳ支路时）、８（当机构各个支路均为最简ＲＰＳ支路时），这些位置反解可分别通过跟踪６４、３２、１６和８条同伦路径得到。

Inverse Displacement Analysis of 3 RPS Regional Parallel Manipulators

The 3 RPS regional parallel manipulator is composed of a moving platform and a fixed platform connected by 3 RPS sub chains. The grouping of solutions to the set of equations for inverse displacement analysis of the manipulator is revealed at first. The new criterion for formulating the initial system proposed in to decrease the number of paths to be tracked in finding all solutions to a polynomial system using continuation is then applied to the inverse displacement analysis of the 3 RPS regional parallel maipulator. The numbers of solutions to the inverse displacement analysis are respectively equal to 64 for the general case, 32 for the case with one and only one simple RPS sub chain, 16 for the case with two and only two simple RPS sub chains, and 8 for the case with three simple RPS sub chains. A simple RPS sub chain is the RPS sub chain the axes of R pairs of which are perpendicular to and intersect with each other. The number of paths to be tracked to find all the sets of solutions to the inverse displacement analysis is equal to the corresponding number of solutions for each case.