一种运动可解耦的Stewart型并联机构的正运动学及奇异性

打开文本图片集

中图分类号：TH112

DOI：10.3969/j.issn.1004-132X.2025.09.006 开放科学（资源服务）标识码（OSID）：

Forward Kinematics and Singularity of Kinematically Decoupled StewarttypeParallelMechanisms

HUANG Ningning1 YOU Jingjing1，2* YE Pengda³ SHEN Huiping³ LI Chenggang4 WU Hongtao4 1.College of Mechanical and Electronic Engineering，Nanjing Forestry University，Nanjing，210037

2.State Key Laboratory of Mechanical Transmission for Advanced Equipment， Chongqing University， Chongqing，400044 3.College of Mechanical Engineering and Rail Transit ， Changzhou University， Changzhou， Jiangsu，213164

4.College of Mechanical and Electrical Engineering，Nanjing University of Aeronautics & Astronautics， Nanjing，210016

Abstract：The forward kinematics equation of the six-degree-of-freedom parallel mechanisms was nonlinear and strongly coupled，and generally did not have a symbolic positive solution，which was not conducive to the real-time feedback control of the robots.Thus，a“7-4”Stewart-type paralel mechanism was designed with weak coupling in structures but decoupled in motions. The forward kinematics equation and link length coordination equation were solved analytically，and the singularity research was carried out. Firstly，based on the“2-1” kinematic links，a six-degree-of-freedom“7-4” Stewart-type paralel mechanism was synthesized，and the structural coupling characteristics of the mechanisms were analyzed based on the azimuth feature set theory. Secondly，based on 13 compatible equations and the theory of tetrahedral geometry，an analytical algorithm for solving the forward kinematics equation was proposed. At the same time，it was proved that the number of real solutions under general configuration was 8（they were symmetrical about the same plane ）. Then，according to the geometric constraint relationship between the moving ball hinges，the link length coordination equation wasconstructed. It is found that the equation also has a symbolic solution. The Jacobian matrix of the mechanisms was derived，and various singular types were analyzed.Finally，the internal relationship between the forward kinematics and singularity of the parallel mechanisms was analyzed.

Key words： parallel mechanism；forward kinematics；type synthesis； singularity；kinematically de-coupled

0 引言

并联机构的本质功能是输出运动或者抵抗外负载，具有刚度大、输出精度高、动态特性好等诸多优点[1，可应用于光纤对接、航空航天、康复治疗等高精尖领域[2。（剩余13176字）