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research-article

A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices

[+] Author and Article Information
Genliang Chen

State Key Laboratory of Mechanical, System and Vibration, Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai, China
leungchan@sjtu.edu.cn

Zhuang Zhang

Shanghai Key Laboratory of Digital, Manufacture for Thin-walled Structures, Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai, China
z.zhang@sjtu.edu.cn

Hao Wang

State Key Laboratory of Mechanical System and Vibration, and Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures, Shanghai Jiao Tong University, A611 Mechanical Building, Dongchuan Road, Shanghai, 200240, China
wanghao@sjtu.edu.cn

1Corresponding author.

ASME doi:10.1115/1.4039223 History: Received September 28, 2017; Revised December 22, 2017

Abstract

This paper presents a general discretization-based approach to the large de?ection problems of spatial ?exible links in compliant mechanisms. Based on the principal axes decomposition of structural compliance matrices, a particular type of elements which relate to spatial 6-degree-of-freedom (DOF) serial mechanisms with passive elastic joints, is developed to characterize the force-de?ection behavior of the discretized small segments. Hence, the large de?ection problems of spatial ?exible rods can be transformed to the determination of static equilibrium con?gurations of their equivalent hyper-redundant mechanisms. The main advantage of the proposed method comes from the use of robot kinematics/statics, rather than structural mechanics. Thus, a closed-form solution to the system overall stiffness can be derived straightforwardly for ef?cient gradient-based searching algorithms. Two kinds of typical equilibrium problems are intensively discussed and the correctness has been veri?ed by means of physical experiments. In addition, a 2-DOF planar compliant parallel manipulator is provided as a case study to demonstrate the potential applications.

Copyright (c) 2018 by ASME
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