一种平面并联机构位置正解分析的共形几何代数及Sylvester结式方法  

Conformal Geometric Algebra and Sylvester Resultant Method for Forward Displacement Analysis of a Planar Parallel Mechanism

作　　者：张忠海[1] 李端玲[1] 

机构地区：[1]北京邮电大学自动化学院,北京100876

出　　处：《北京理工大学学报》2014年第3期241-244,共4页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(51075039;51375058);中央高校基本科研业务费资助项目(2012LD03);清华大学摩擦学国家重点实验室开放基金资助项目;新世纪优秀人才支持计划资助项目(NCET-12-0796);国家教育部高等学校博士学科点专项科研基金资助课题(20120005110008)

摘　　要：研究一种平面并联机构位置正解分析的共形几何代数建模方法和改进的Sylvester结式消元求解方法.基于含有未知参数的5维共形空间的点表示,提出了位置正解分析的共形几何代数建模方法.提出了一种改进的Sylvester结式消元方法,即冗余因子消去法,求出了能得到准确解的一元6次方程.通过一个数值实例,得出了这个机构位姿的无增无漏的6组解,验证了所提出方法的正确性和有效性.Proposed a modeling approach using conformal geometric algebra and an improved Sylvester resultant elimination method for forward displacement analysis of a planar parallel mechanism. Based on representation of points in five-dimensional conformal space containing unknown parameters, the modeling approach using conformal geometric algebra for forward displacement analysis was presented. An improved Sylvester resultant elimination method was proposed, namely redundant factor elimination method. A six-degree equation with one unknown was derived by the proposed method to obtain correct roots. A numerical example of the parallel mechanism with six groups of solutions of positions and postures without extraneous roots or missing roots verifies that the proposed method is correct and effective.

关 键 词：共形几何代数 Sylvester结式 结式消元 平面并联机构 位置正解 

分 类 号：TH112[机械工程—机械设计及理论]