TY - GEN

T1 - The duality between the singularity of Bricard mechanism and the singularity of Stewart Platform

AU - Slavutin, Michael

AU - Shai, Offer

AU - Müller, Andreas

N1 - Publisher Copyright:
Copyright © 2014 by ASME.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Body bar graph

KW - Cyclohexane molecule

KW - Relative twist screw

KW - Singularity

KW - Wrench screw

UR - http://www.scopus.com/inward/record.url?scp=84926039996&partnerID=8YFLogxK

U2 - 10.1115/DETC2014-34638

DO - 10.1115/DETC2014-34638

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AN - SCOPUS:84926039996

T3 - Proceedings of the ASME Design Engineering Technical Conference

BT - 38th Mechanisms and Robotics Conference

PB - American Society of Mechanical Engineers (ASME)

T2 - ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2014

Y2 - 17 August 2014 through 20 August 2014

ER -