3-RPS控制姿态用并联机器人机构的位置反解

INVERSE DISPLACEMENT ANALYSIS OF 3 RPS ORIENTATIONAL PARALLEL MANIPULATORS

首先揭示了３－ＲＰＳ控制姿态用并联机器人机构位置反解方程组解的分组特点，然后应用连续法求解多项式方程组时构造初始方程组的原则，给出了该机构位置反解的高效算法．对于给定的输出，３－ＲＰＳ控制姿态用并联机器人机构位置反解的数目为８（一般形式），４（当机构有且仅有一个最简ＲＰＳ支路时），２（当机构有且仅有两个最简ＲＰＳ支路时），１（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８，４，２和１条同伦路径得到．

The grouping of solutions to the set of equations for inverse displacement analysis of 3 RPS orientational parallel manipulators is revealed at first. The criteria for formulating the initial system 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 orientational parallel manipulators. The number of solutions to the inverse displacement analysis are respectively equal to 8 (for the general case), 4 (for the case with one and only one simple RPS sub chain), 2 (for the case with two and only two simple RPS sub chains), and 1 (for the case with three simple RPS sub chains). A simple RPS sub chain is the RPS sub chain the axes of R and P 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.