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research-article

A Geometric Approach to Obtain the Closed-Form Forward Kinematics of H4 Parallel Robot

[+] Author and Article Information
Yujiong Liu

Robotics and Mechatronics Laboratory, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24060
yjliu@vt.edu

Minxiu Kong

Robotics Institute, School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, P. R. China 150001
exk@hit.edu.cn

Neng Wan

Advanced Controls Research Laboratory, Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
nengwan2@illinois.edu

Pinhas Ben-Tzvi

Member of ASME, Robotics and Mechatronics Laboratory, Department of Mechanical Engineering, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24060
bentzvi@vt.edu

1Corresponding author.

ASME doi:10.1115/1.4040703 History: Received March 16, 2018; Revised June 22, 2018

Abstract

To obtain the closed-form forward kinematics of parallel robots, researchers use algebra-based method to transform and simplify the constraint equations. However, this method requires a complicated derivation that leads to high-order univariate variable equations. In fact, some particular mechanisms, such as Delta, or H4 possess many invariant geometric properties during movement. This suggests that one might be able to transform and reduce the problem using geometric approaches. Therefore, a simpler and more efficient solution might be found. Based on this idea, we developed a new geometric approach called Geometric Forward Kinematics (GFK) to obtain the closed-form solutions of H4 forward kinematics in this paper. The result shows that the forward kinematics of H4 yields an 8th degree univariate polynomial, compared with earlier reported 16th degree. Thanks to its clear physical meaning, an intensive discussion about the solutions is presented. Results indicate that a general H4 robot can have up to eight non-repeated real solutions for its forward kinematics. For a specific configuration of H4, the non-repeated number of real roots could be restricted to only two, four or six. Two travelling plate configurations are discussed in this paper as two typical categories of H4. A numerical analysis was also performed for this new method.

Copyright (c) 2018 by ASME
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