空间并联机构运动学分析的共形几何代数方法  

Conformal Geometric Algebra Method for Kinematics Analysis of Spatial Parallel Mechanisms

作　　者：张忠海[1,2] 李端玲[1] 

机构地区：[1]北京邮电大学自动化学院,北京100876 [2]北京航天测控技术有限公司,北京100041

出　　处：《农业机械学报》2015年第4期325-330,共6页Transactions of the Chinese Society for Agricultural Machinery

基　　金：国家自然科学基金资助项目(51375058);新世纪优秀人才支持计划资助项目(NCET-12-0796);高等学校博士学科点专项科研基金资助项目(20120005110008)

摘　　要：提出了空间并联机构运动学分析的集几何表示和计算为一体的共形几何代数方法。以动平台上的坐标原点描述动平台的位置,以欧拉角描述动平台的姿态,给出了动平台上任意一点在定坐标系中位置的共形几何代数表达式,进而提出了一种建立空间并联机构运动学方程的数学建模方法。根据所建立的运动学方程,可进行空间并联机构的运动学正解和运动学反解分析。通过一种4-UPU空间并联机构运动学分析,进一步阐述了所提出的共形几何代数运动学分析方法,通过数值实例验证了所提出方法的正确性和有效性。As a new geometric representation and calculation system, the conformal geometric algebra has been recognized as a research hotspot in recent years. But as a new branch of algebra, the conformal geometric algebra is still in the process of development, especially its application in theory of mechanism is relatively deficient at present. The new geometric algebra method for the kinematics analysis of spatial parallel mechanisms was studied and a conformal geometric algebra method integrating geometric representation and calculation was proposed. With the origin of coordinates on the moving platform describing its position and Euler angles describing its orientation, the conformal geometric algebra expression of an arbitrary point＇ s location on the moving platform in the fixed coordinate system was presented. Then a method to establish kinematics equations for the kinematics analysis of spatial parallel mechanisms was proposed to conduct the forward and inverse kinematics analysis of spatial parallel mechanisms. A 4-UPU parallel mechanism was taken as an example to illustrate the proposed conformal geometric algebra method for kinematics analysis of spatial parallel mechanisms. And a numerical example was given to verify correctness and effectiveness of the proposed approach. The proposed conformal geometric algebra method was a new method for the kinematics analysis of spatial parallel mechanisms by integrating geometric representation and computation.

关 键 词：空间并联机构 运动学分析 运动学正解 运动学反解 共形几何代数 

分 类 号：TH112[机械工程—机械设计及理论]