This paper introduces the three-dimensional (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.
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August 2018
Research-Article
A Complete Geometric Singular Characterization of the 6/6 Stewart Platform
Michael Slavutin,
Michael Slavutin
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: slavutin@post.tau.ac.il
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: slavutin@post.tau.ac.il
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Avshalom Sheffer,
Avshalom Sheffer
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: sheffer@mail.tau.ac.il
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: sheffer@mail.tau.ac.il
Search for other works by this author on:
Offer Shai,
Offer Shai
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
Tel Aviv University,
Ramat Aviv 69978, Israel
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Yoram Reich
Yoram Reich
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: yoram@eng.tau.ac.il
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: yoram@eng.tau.ac.il
Search for other works by this author on:
Michael Slavutin
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: slavutin@post.tau.ac.il
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: slavutin@post.tau.ac.il
Avshalom Sheffer
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: sheffer@mail.tau.ac.il
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: sheffer@mail.tau.ac.il
Offer Shai
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
Tel Aviv University,
Ramat Aviv 69978, Israel
Yoram Reich
School of Mechanical Engineering,
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: yoram@eng.tau.ac.il
Tel Aviv University,
Ramat Aviv 69978, Israel
e-mail: yoram@eng.tau.ac.il
1Corresponding author.
2Deceased.
Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received December 12, 2017; final manuscript received April 17, 2018; published online June 1, 2018. Assoc. Editor: Shaoping Bai.
J. Mechanisms Robotics. Aug 2018, 10(4): 041011 (10 pages)
Published Online: June 1, 2018
Article history
Received:
December 12, 2017
Revised:
April 17, 2018
Citation
Slavutin, M., Sheffer, A., Shai, O., and Reich, Y. (June 1, 2018). "A Complete Geometric Singular Characterization of the 6/6 Stewart Platform." ASME. J. Mechanisms Robotics. August 2018; 10(4): 041011. https://doi.org/10.1115/1.4040133
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