Workspace analysis and visualization of mechanical manipulators with non-unilateral constraints

Jingzhou Yang, Karim Abdel-Malek

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

Abstract

An analytical method is presented to obtain all surfaces enveloping the workspace of a general n degree-of-freedom mechanism with non-unilateral constraints. The method is applicable to kinematic chains that can be modeled using the Denavit-Hartenberg representation method for serial manipulators. The method introduced in this paper is based upon analytical criteria for determining singular behavior of the mechanism. A perturbation approach is implemented to determine the interior and exterior of the workspace. The complete mathematical formulation is presented and illustrated using 3 and 4 DOF spatial manipulators. The paper present a rigorous analysis of the sub-Jacobians to determine a classification of singularities: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint that is reaching its apex; Type III sets are domain boundary singularities, which are associated with the initial and final values of the time interval; Type IV sets are coupled singularities, which are associated with a relative singular Jacobian, where the null space is reduced in one submatrix due to either of two occurrences: a Type II or Type III singularities. The paper presents a general formulation for determining the workspace.

Original languageEnglish
Title of host publicationProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conferences - DETC2005
Subtitle of host publication29th Mechanisms and Robotics Conference
PublisherAmerican Society of Mechanical Engineers
Pages717-726
Number of pages10
ISBN (Print)0791847446, 9780791847442
DOIs
StatePublished - 2005
EventDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - Long Beach, CA, United States
Duration: Sep 24 2005Sep 28 2005

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005
Volume7 B

Conference

ConferenceDETC2005: ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
CountryUnited States
CityLong Beach, CA
Period09/24/0509/28/05

Keywords

  • Jacobian row-rank deficiency
  • Non-unilateral
  • Singularity

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