A Coordinate-Free Approach to the Design of Generalized Griffis-Duffy Platforms  

作　　者：Chengwei Shen Xu Pei Lubin Hang Jingjun Yu 

机构地区：[1]College of Optical,Mechanical and Electrical Engineering,Zhejiang A&F University,Hangzhou 311300,China [2]School of Mechanical Engineering and Automation,Beihang University,Beijing 100191,China [3]School of Mechanical and Automotive Engineering,Shanghai University of Engineering Science,Shanghai 201620,China

出　　处：《Chinese Journal of Mechanical Engineering》2024年第3期95-103,共9页中国机械工程学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant Nos.U1813221,52075015);Personnel Startup Project of Zhejiang A&F University Scientific Research Development Foundation of China (Grant No.2024LFR015)。

摘　　要：Architectural singularity belongs to the Type II singularity,in which a parallel manipulator(PM)gains one or more degrees of freedom and becomes uncontrollable.PMs remaining permanently in a singularity are beneficial for linearto-rotary motion conversion.Griffis-Duffy(GD)platform is a mobile structure admitting a Bricard motion.In this paper,we present a coordinate-free approach to the design of generalized GD platforms,which consists in determining the shape and attachment of both the moving platform and the fixed base.The generalized GD platform is treated as a combination of six coaxial single-loop mechanisms under the same constraints.Owing to the inversion,hidden in the geometric structure of these single-loop mechanisms,the mapping from a line to a circle establishes the geometric transformation between the fixed base and the moving platform based on the center of inversion,and describes the shape and attachment of the generalized GD platform.Moreover,the center of inversion not only identifies the location of rotation axis,but also affects the shape of the platform mechanism.A graphical construction of generalized GD platforms using inversion,proposed in the paper,provides geometrically feasible solutions of the manipulator design for the requirement of the location of rotation axis.

关 键 词：Generalized Griffis-Duffy platforms SELF-MOTION INVERSION Coordinate-free determination Manipulator design 

分 类 号：TP241[自动化与计算机技术—检测技术与自动化装置] TH122[自动化与计算机技术—控制科学与工程]