A new mobility formula for spatial mechanisms

Charles Wampler, Blake T. Larson, Arthur G. Erdman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

11 Scopus citations

Abstract

A new formula for predicting the mobility of spatial mechanisms is introduced. Instead of counting rigid links and the constraints between them, as is done in the usual Grübler-Kutzbach formulae, we count vertices and edges in a polyhedral model of the mechanism. It is well known that the conventional formula underpredicts the mobility of certain exceptional classes of mechanisms, and in particular, does not easily accommodate compound spatial mechanisms that contain planar or spherical sub-mechanisms. The new approach provides a correct mobility whenever the conventional formula does and accounts for planar and spherical sub-mechanisms in a simple manner. Additionally, we present simple modifications to correctly model certain mechanisms that have remote spherical centers. We illustrate the method on compound mechanisms constructed from scissors linkages.

Original languageEnglish (US)
Title of host publication2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
Pages561-570
Number of pages10
DOIs
StatePublished - 2008
Event31st Mechanisms and Robotics Conference, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 - Las Vegas, NV, United States
Duration: Sep 4 2007Sep 7 2007

Publication series

Name2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
Volume8 PART A

Other

Other31st Mechanisms and Robotics Conference, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007
CountryUnited States
CityLas Vegas, NV
Period9/4/079/7/07

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