基于拓扑结构分析的求解6-SPS并联机构位置正解的研究  

Research on Forward Position Solutions for 6-SPS Parallel Mechanisms Based on Topology Structure Analysis

作　　者：沈惠平[1] 尹洪波[1] 王振[1] 黄涛[1] 李菊[1] 邓嘉鸣[1] 杨廷力[1] 

机构地区：[1]常州大学机械工程学院,常州213016

出　　处：《机械工程学报》2013年第21期70-80,共11页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51075045;51375062);江苏省重大科技支撑与自主创新(BE2010074)资助项目

摘　　要：建立机构拓扑结构复杂性和位置正解求解难易性的关系,提出按机构耦合度k大小来分类求解并联机构位置正解全部实数解的数值法,可使正解问题求解容易,具体内容包括:对39种不同构型的6-SPS并联机构,按6种基本机型、33种衍生机型的拓扑结构及其耦合度值分为k=0、1、2、3四类,分析得到了动平台边数、支链类型影响耦合度k值大小的规律。对不同k值的并联机构的位置正解求解指明明确的求解方向,即:对k=0的机构可容易地直接求解其解析正解;对k>0的机构,通过虚设k个SPS型支链,使之转化为k=0的虚拟并联机构,并基于杆长条件建立k个仅含一个变量的杆长相容性方程,再采用k维搜索法求出实数解。以六自由度球面Stewart机构为例,给出了求解耦合度k=1的任意6-DOF SPS并联机构位置正解全部实数解一维搜索法的具体步骤。这种基于拓扑结构分析的6-SPS并联机构位置正解求解的数值法,求解原理简单,计算量小,且具有一般意义。The relationship between complexity of mechanism topology structure and difficulty of solving forward position is discussed and established. A general numerical method, which is used to separately solve all real forward position solutions of parallel mechanism according to the value of coupling degree, is also presented. This method makes solving forward solution easy and the details can be listed as follows： 39 kinds of configurations of 6-SPS mechanism are analyzed and classified into four categories,i.e, k=0, 1 ~ 2, 3 according to their coupling degree. At the same time, the law that the numbers of geometric side of moving platform and chain types can affect coupling degree is found. The definite analysis direction for solving forward positions of parallel mechanism with different k is indicated, that is： For mechanisms with k=-0, it is easy to directly obtain their analytical forward solutions. For mechanisms with k〉0, they are transformed into mechanisms with k=0 by virtually setting k SPS chain, then based on the condition of link length, establish k geometric compatibility equations, each of which contains only one variable. At last, k-dimensional search method is used to obtain all real forward solutions. Taking 6-DOF Stewart spherical mechanism as an example, the detailed steps of solving forward kinematics of any 6-DOF SPS parallel mechanisms with k=-I by using one-dimensional search method are listed. This general numerical method used to solve forward position solutions of 6-SPS parallel mechanism based on analyzing the complexity of topology structure has many advantages such as clear geometry meaning, simple solving principle, less calculation and good adaptability.

关 键 词：并联机构 拓扑结构分析 耦合度 位置正解 6-SPS机构 一维搜索法 

分 类 号：TH11[机械工程—机械设计及理论]