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

Zhuang Zhang

Shanghai Key Laboratory of Digital, Manufacture for Thin-walled Structures, Shanghai Jiao Tong University, 800 Dongchuan Rd, Shanghai, China

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

1Corresponding author.

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


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.

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