空间并联机构位置分析的连续法

Displacement Analysis of Spatial Parallel Mechanisms Using Continuation Mcthod

本文研究了四类由平台式机械手转化得到的空间并联机构的位置正解问题。当输入给定时，这些机构转化为ＲＲＲ—３Ｓ、ＲＲＰ—３Ｓ、ＲＰＰ—３Ｓ和ＰＰＰ—３Ｓ等四种空间多环结构共包括ＲＳＳＲ、ＲＳＳＰ、ＰＳＳＲ和ＰＳＳＰ等四种基本回路。对每个基本回路，用坐标变换矩阵法建立回路方程，进而得到上述四种空间结构的位置方程组，引入连续法，直接求出每种结构的全部位置解。数据实例表明，ＲＲＲ—３Ｓ结构与ＲＲＰ—３Ｓ结构各有１６组解，ＲＰＰ—３Ｓ结构有１２组解，ＰＰＰ—３Ｓ结构有８组解。

The forward displacement analysis of four classes of parallel mechanisms derived from platformmanipulators is presented in this paper. These mechanisms, when a set of actuator displacement is given, be-come RRR-3S ,RRP-3S ,RPP-3S and PPP-3S multiloop spatial structures which can be decomposedinto several basic loops of type RSSR, RSSP,PSSR and PSSP. The loop equation for each basic loop is es-tablished by coordinate transformation method,so that the displacement equation for each structure can beeasily determined.Continuation method is engaged to solve these equations and 16,16,12 and 8 solutionsare obtained for the four types of structures respectively.