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Forward kinematics modeling of spatial parallel linkage mechanisms based on constraint equations and the numerical solving method

Published online by Cambridge University Press:  19 June 2015

Liyang Gao  and
Weiguo Wu
Liyang Gao
Affiliation:
School of Mechatronics Engineering, Harbin Institute of Technology, Heilongjiang, Harbin, P. R. China
Weiguo Wu*
Affiliation:
School of Mechatronics Engineering, Harbin Institute of Technology, Heilongjiang, Harbin, P. R. China
*
*Corresponding author. E-mail: wuwg@hit.edu.cn
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Summary

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In order to solve general kinematics modeling problems and numerical stability problems of numerical methods for spatial parallel linkage mechanisms, a general modeling method and its numerical solving algorithm is proposed. According to the need for avoiding direct singular configurations, valid joint variable space and valid forward kinematics solutions (VKSs) are defined. Taking numerical convergence near singular points into account, the pseudo-arc length homotopy continuation algorithm is given to solve the kinematics model. Finally as an example, the joint variable space of the general Stewart platform mechanism is analyzed, which is proved to be divided into subspaces by direct singular surfaces. And then, forward kinematics solutions of 200 testing points are solved separately using the pseudo-arc length homotopy continuation algorithm, the Newton homotopy continuation algorithm and the Newton–Raphson algorithm (NRA). Comparison of the results shows that the proposed method is convergent to the same solution branch with the initial configuration on all the testing points, while the other two algorithms skip to other solution branches on some near singular testing points.

Keywords

Spatial parallel linkage mechanismForward kinematicsNumerical solutionsDirect singularityHomotopy continuation method

Information

Type
Articles
Information
Robotica , Volume 35 , Issue 2 , February 2017 , pp. 293 - 309
Copyright
Copyright © Cambridge University Press 2015 

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