Title: Matroid application to self-aligning mechanisms: enumeration and analysis

Authors: Andrea Piga Carboni; Henrique Simas; Daniel Martins

Addresses: Department of Mobility Engineering, UFSC – Federal University of Santa Catarina, Joinville, SC, Brazil ' Department of Mechanical Engineering, UFSC – Federal University of Santa Catarina, Florianópolis, SC, Brazil ' Department of Mechanical Engineering, UFSC – Federal University of Santa Catarina, Florianópolis, SC, Brazil

Abstract: The study of mechanisms is one of the most important areas on which machine design relies. Research in mechanism can be roughly divided into two main problems: mechanism analysis and mechanism synthesis. This paper focuses on topology analysis of mechanism, by means of screw theory representation of mechanisms. Freedoms and constraints in mechanisms are thus described applying the Kirchhoff's laws adaptation to multibody systems proposed by Davies. Based on this modelling, overconstraint in mechanisms is analysed in terms of free motions and constraints. The self-aligning mechanisms kinematically equivalent to an overconstraint mechanism are investigated. Two new algorithms for enumerating all self-aligning kinematically equivalent mechanisms to an overconstrained one and for selecting an optimal self-aligning topology, based on a set of criteria, are proposed. All algorithms have been implemented in Sage software and run in polynomial time. Examples of applications are presented, and the results obtained are validated with literature cases.

Keywords: mechanism; self-aligning; matroid theory.

DOI: 10.1504/IJMRS.2018.096299

International Journal of Mechanisms and Robotic Systems, 2018 Vol.4 No.4, pp.305 - 322

Received: 15 Mar 2018
Accepted: 01 Aug 2018
Published online: 22 Nov 2018 *

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