基于多项式连续法的6-SPS并联机构正向位置分析

摘要

6自由度并联机构因其结构简单、运动容易和控制算法成熟而广泛应用，典型的并联机构就是Stewart平台。文章针对6-SPS并联机构正向位置分析所构造的非线性多项式方程组，结合多项式连续法和代数拓扑法，提出多项式连续拓扑法。与一般数值连续法相比，该方法可在无需初始值的情况下，利用多项式方程组的特殊属性，得到各封闭支链所有的正向运动位置解，同时消除诸如散度和分叉等问题，也被认为是一种有效逼近一个给定的非线性问题。对科学和工程应用中一些复杂环境下的非线性问题具有重要的借鉴意义。%6-DOF parallel manipulators has a wide range of application due to its simple structure、easily mo-tion and mature control algorithm,A representative sample belongs to Stewart platform. Analyzed the forward kinematics analysis of 6-SPS parallel mechanism which constructing the non-linear polynomial equations in this paper,combined with polynomial continuous method and algebraic topology method, proposed polyno-mial continuation method. Compared with the General numerical continuation method,this method can apply special properties of polynomial equations under withouting initial parameters,achieved the forward kinemat-ics position solutions of each closed branched-chain. Meanwhile,eliminated the numerical problems such as divergence and bifurcation, which had regarded as a Effective approach in a given nonlinear problem. It makes important sense on the nonlinear problem under some complex surroundings in scientific and engineer-ing applications.