• 论文 •

### 基于共形几何代数的空间并联机构位置正解

1. 1. 北方工业大学 机械与材料工程学院, 北京 100144;
2. 北方工业大学 柔性变截面辊弯成形北京市工程技术研究中心, 北京 100144
• 收稿日期:2016-12-06 修回日期:2017-03-06 出版日期:2017-12-20 发布日期:2017-05-10
• 通讯作者: 黄昔光 E-mail:marchbupt@126.com
• 作者简介:黄昔光,男,博士,副教授,硕士生导师。主要研究方向:机构学与机器人学。
• 基金资助:
国家自然科学基金（51105003）；北京市自然科学基金（3172010）

### Direct kinematics of a spatial parallel mechanism based on conformal geometric algebra

HUANG Xiguang1,2, HUANG Xu1

1. 1. School of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, China;
2. Beijing Engineering Research Center of Flexible Roll Forming, North China University of Technology, Beijing 100144, China
• Received:2016-12-06 Revised:2017-03-06 Online:2017-12-20 Published:2017-05-10
• Supported by:
National Natural Science Foundation of China (51105003); Beijing Natural Science Foundation (3172010)

Abstract: An algorithm is proposed for the direct kinematics analysis of a spatial general 3-RPS parallel mechanism based on conformal geometric algebra (CGA). The angle between the axis of an arbitrary kinematic chain and the plane of the fixed platform can be regarded as the unknown variable. The mathematical expression of the position of the spherical joint connecting the moving platform with the kinematic chain can be expressed in the unknown variable based on CGA. The outer product of two space balls and a flat surface are constructed two times, and the corresponding points of the remaining two vertices of the moving platform are obtained respectively. The 16th degree input-output polynomial equation in the unknown variable is straightforwardly obtained by distance formula and all 16 sets of closed-form solutions can be achieved. The algorithm avoids the use of rational angles or matrices, and complex computations for nonlinear and multivariable equations. A numerical example is given to demonstrate geometric characteristics of the motion and the algorithm is intuitive.