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research-article

A Complete Geometric Singular Characterization of the 6/6 Stewart Platform

[+] Author and Article Information
Michael Slavutin

School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
slavutin@post.tau.ac.il

Avshalom Sheffer

School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
sheffer@mail.tau.ac.il

Offer Shai

School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
shai@eng.tau.ac.il

Yoram Reich

School of Mechanical Engineering, Tel Aviv University, Ramat Aviv 69978, Israel
yoram@eng.tau.ac.il

1Corresponding author.

ASME doi:10.1115/1.4040133 History: Received December 12, 2017; Revised April 17, 2018

Abstract

This paper introduces the 3D dual Kennedy theorem in statics, and demonstrates its application to characterize the singular configuration of the 6/6 Stewart Platform (6/6 SP). The proposed characterization is articulated as a simple geometric relation that is easy to apply and check. We find two lines that cross four of the six legs of the platform. Each one of these two lines has a parallel line that crosses the remaining two legs. Each pair of parallel lines defines a plane. The 6/6 SP is in a singular position if the intersection of these two planes is perpendicular to the common normal of the remaining two legs. The method developed for the singular characterization is also used for the analysis of the mobility and forces of the SP. Finally, the proposed method is compared to some known singular configurations, such as Hunt's and Fichter's singular configurations and the 3/6 Stewart Platform (3/6 SP) singularity. The relation between the reported characterizations of the 6/6 SP and other reported works is highlighted. Moreover, it is shown that the known 3/6 SP characterization is a special case of the results reported in the paper. Finally, a characterization of a platform that does not appear in the literature, 5/6 SP, is developed based on the new approach to demonstrate its utility.

Copyright (c) 2018 by ASME
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