The duality between the singularity of Bricard mechanism and the singularity of Stewart Platform

Michael Slavutin, Offer Shai, Andreas Müller

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The duality (known also as symmetry) between serial chain manipulators and fully parallel mechanisms is well known in the literature. This paper takes this idea one step further, by introducing a systematic method that transforms mechanical systems into other and different mechanical systems so that the wrench screws in the original system gives rise to the relative twist screws in the second system. The mathematical foundation of this work relies on using the BB graph, a variant of graph representation widely used in mechanisms, possessing both the topology and geometry of the original system. From the dual graph of the latter it is possible to construct the dual system at a specific configuration. Relying on the equivalence between the dual systems, it is proved that if the screw system of a mechanism is at the singular position, so is that of its dual. This idea is demonstrated by showing the dual system of a Bricard mechanism, which is a 6/6 Stewart Platform in the singular position. The paper also shows that the cyclohexane molecule is dual to the 6/3 Stewart platform at the singular position, providing another perspective of the known mobility of this molecule.

Original languageEnglish
Title of host publication38th Mechanisms and Robotics Conference
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791846360
DOIs
StatePublished - 2014
EventASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014 - Buffalo, United States
Duration: 17 Aug 201420 Aug 2014

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume5A

Conference

ConferenceASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014
Country/TerritoryUnited States
CityBuffalo
Period17/08/1420/08/14

Keywords

  • Body bar graph
  • Cyclohexane molecule
  • Relative twist screw
  • Singularity
  • Wrench screw

Fingerprint

Dive into the research topics of 'The duality between the singularity of Bricard mechanism and the singularity of Stewart Platform'. Together they form a unique fingerprint.

Cite this