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Research Papers

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 Road,
Shanghai 200240, China
e-mail: leungchan@sjtu.edu.cn

Zhuang Zhang

Shanghai Key Laboratory of Digital Manufacture
for Thin-Walled Structures,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: z.zhang@sjtu.edu.cn

Hao Wang

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

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 28, 2017; final manuscript received December 22, 2017; published online April 5, 2018. Assoc. Editor: James J. Joo.

J. Mechanisms Robotics 10(3), 031012 (Apr 05, 2018) (10 pages) Paper No: JMR-17-1331; 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 deflection problems of spatial flexible links in compliant mechanisms. Based on the principal axes decomposition of structural compliance matrices, a particular type of elements, which relate to spatial six degrees-of-freedom (DOF) serial mechanisms with passive elastic joints, is developed to characterize the force-deflection behavior of the discretized small segments. Hence, the large deflection problems of spatial flexible rods can be transformed to the determination of static equilibrium configurations 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 efficient gradient-based searching algorithms. Two kinds of typical equilibrium problems are intensively discussed and the correctness has been verified by means of physical experiments. In addition, a 2DOF planar compliant parallel manipulator is provided as a case study to demonstrate the potential applications.

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Figures

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Fig. 1

Principal axes decomposition of a general compliance

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Fig. 2

Mechanism approximation of the segment elements

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Fig. 3

Hyper-redundant mechanism approximation of flexible rods

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Fig. 4

Experimental setup for the large deflection problems

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Fig. 5

Experimental result of the flexible rod with large deflection

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Fig. 6

Accuracy evaluation of the proposed method

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Fig. 7

A planar 2DOF translational compliant mechanism

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Fig. 8

Verification via the simulation results of FEA model

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Fig. 9

Residual errors of the proposed method from FEA model

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Fig. 10

Consuming time versus computational accuracy

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