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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June 2018
Research-Article
A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices
Genliang Chen,
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
and Vibration,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: leungchan@sjtu.edu.cn
Search for other works by this author on:
Zhuang Zhang,
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
for Thin-Walled Structures,
Shanghai Jiao Tong University,
800 Dongchuan Road,
Shanghai 200240, China
e-mail: z.zhang@sjtu.edu.cn
Search for other works by this author on:
Hao Wang
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
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
Search for other works by this author on:
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
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
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
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. Jun 2018, 10(3): 031012 (10 pages)
Published Online: April 5, 2018
Article history
Received:
September 28, 2017
Revised:
December 22, 2017
Citation
Chen, G., Zhang, Z., and Wang, H. (April 5, 2018). "A General Approach to the Large Deflection Problems of Spatial Flexible Rods Using Principal Axes Decomposition of Compliance Matrices." ASME. J. Mechanisms Robotics. June 2018; 10(3): 031012. https://doi.org/10.1115/1.4039223
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