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Chinese Journal of Mechanical Engineering
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Kinematic solution of spherical Stephenson-III six-bar mechanism

Chinese Journal of Mechanical Engineering volume 26, pages 851–860 (2013)Cite this article

Abstract

A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method. However, extra solutions would occur when solving the constraint equations of mechanism kinematics unless the constraint equations are established with a proper method and the solving approach is appropriate. In order to obtain a kinematic solution of the spherical Stephenson-III six-bar mechanism, spherical analytical theory is employed to construct the constraint equations. Firstly, the mechanism is divided into a four-bar loop and a two-bar unit. On the basis of the decomposition, vectors of the mechanism nodes are derived according to spherical analytical theory and the principle of coordinate transformation. Secondly, the structural constraint equations are constructed by applying cosine formula of spherical triangles to the top platform of the mechanism. Thirdly, the constraint equations are solved by using Bezout’s elimination method for forward analysis and Sylvester’s resultant elimination method for inverse kinematics respectively. By the aid of computer symbolic systems, Mathematica and Maple, symbolic closed-form solution of forward and inverse displacement analysis of spherical Stephenson-III six-bar mechanism are obtained. Finally, numerical examples of forward and inverse analysis are presented to illustrate the proposed approach. The results indicate that the constraint equations established with the proposed method are much simpler than those reported by previous literature, and can be readily eliminated and solved.

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Authors and Affiliations

  1. School of Manufacturing Science and Engineering, Sichuan University, Chengdu, 610065, China

    Yanfang Liu & Suixian Yang

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  1. Yanfang Liu
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  2. Suixian Yang
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Corresponding author

Correspondence to Suixian Yang.

Additional information

This project is supported by National Natural Science Foundation of China(Grant No. 50975186)

LIU Yanfang, born in 1986, is currently an engineer at Dongfang Electric Corporation Limited, China. She received her master’s degree on industrial design in Sichuan University, China, in 2011. Her research interests are kinematics of spherical mechanisms and mechanical design.

YANG Suixian, born in 1965, is currently a professor at School of Manufacturing Science and Engineering, Sichuan University, China. He received his PhD degree from Sichuan University, China, in 1997. His research interests include spatial mechanisms, computer aided design, product design and nondestructive testing.

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Liu, Y., Yang, S. Kinematic solution of spherical Stephenson-III six-bar mechanism. Chin. J. Mech. Eng. 26, 851–860 (2013). https://doi.org/10.3901/CJME.2013.05.851

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