• CN：11-2187/TH
• ISSN：0577-6686

• 机构学及机器人 •

### 基于加权广义逆求解被动过约束刚-柔耦合并联机构的受力问题*

1. 1. 燕山大学河北省并联机器人与机电系统实验室 秦皇岛 066004;
2. 先进锻压成形技术与科学教育部重点实验室(燕山大学) 秦皇岛 066004);
• 出版日期:2016-12-05 发布日期:2016-12-05
• 作者简介:

刘文兰，女，1990年出生，博士研究生。主要研究方向为过约束并联机构的受力分析。

E-mail：wenlanl@163.com

赵永生(通信作者)，男，1962年出生，博士，教授，博士研究生导师。主要研究方向为并联机构学理论及其应用技术。

E-mail：yszhao@ysu.edu.cn

• 基金资助:
* 国家自然科学基金(51275439)、国家重点基础研究发展计划(973计划， 2013CB733000)和燕山大学青年教师自主研究计划课题(13LGA001)资助项目; 20160303收到初稿，20160912收到修改稿;

### Solving the Force Problem of Passive Overconstrained Rigid-flexible Mixed Parallel Mechanisms Based on the Generalized Inverse of Weighted Moore-Penrose

LIU Wenlan1, XU Yundou1，2, CHEN Liangliang1, YAO Jiantao1，2, ZHAO Yongsheng1，2

1. 1. Hebei Provincial Key Laboratory of Parallel Robot and Mechatronic System， Yanshan University， Qinhuangdao 066004;
2. Key Laboratory of Advanced Forging & Stamping Technology and Science (Yanshan University)， Ministry of Education of China， Qinhuangdao 066004);
• Online:2016-12-05 Published:2016-12-05

Abstract:

A method to solve the statically indeterminate force problem of the general passive overconstrained parallel mechanisms (PMs) is proposed by using the generalized inverse of weighted Moore-Penrose of the force mapping matrix. The general passive overconstrained PMs refer to the PMs in which each limb supplies one or more constraint forces/couples (including driving forces/torques) to the moving platform. The general expression for the stiffness matrix of the limb’s constraint wrenches is derived based on the superposition principle of micro-deformation and screw theory. The mapping relationship between the magnitudes of all limbs’ constraint wrenches and the external wrench is obtained, which just is the generalized inverse of weighted Moore-Penrose of the force mapping matrix. The weighted factor matrix is the inverse matrix of a block diagonal matrix composed of the stiffness matrices of each limb’s constraint wrenches. Taking 3-RRC overconstrained PM and a parallel vibration platform as examples, the magnitudes of all limbs’ constraint wrenches are solved through the generalized inverse of weighted Moore-Penrose of the force mapping matrix. The correctness of the method is verified by the simulation work. The solving process of the statically indeterminate force problem of passive overconstrained PMs is greatly simplified, and the solution is obtained with a unified and simple form by using the generalized inverse of weighted Moore-Penrose.