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Screw Systems Generated by Subalgebras: A Further Analysis

[+] Author Affiliations
A. Tadeo-Chávez

Instituto Tecnológico Superior de Irapuato, Irapuato, GUA, México

J. M. Rico, J. J. Cervantes-Sánchez, G. I. Pérez-Soto

Universidad de Guanajuato, Salamanca, GUA, México

A. Müller

University Duisburg-Essen, Duisburg, Germany

Paper No. DETC2011-48304, pp. 1037-1049; 13 pages
doi:10.1115/DETC2011-48304
From:
  • ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 35th Mechanisms and Robotics Conference, Parts A and B
  • Washington, DC, USA, August 28–31, 2011
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5483-9
  • Copyright © 2011 by ASME

abstract

This contribution presents further properties of screw systems generated from the sum of subalgebras of the Lie algebra, se(3 ), of the Euclidean group, SE(3 ). In particular, it is shown that they exhibit the property of having a locally constant rank. This property has been used, without proper formalization, in the design of parallel platforms. In addition, since the order of screws in a screw system — and therefore the order of their corresponding kinematic pairs within the kinematic chain that realize the screw system — is shown to be decisive for fulfilling the property of having a locally constant rank, the name screw systems may be not at all appropriate.

Copyright © 2011 by ASME
Topics: Screws

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