Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-31T23:52:37.618Z Has data issue: false hasContentIssue false
  • English
  • Français

Singularities of manipulators with non-unilateral constraints

Published online by Cambridge University Press:  23 August 2005

Jingzhou Yang  and
Karim Abdel-Malek
Jingzhou Yang
Affiliation:
US Army Virtual Soldier Research Program, Center for Computer-Aided Design, The University of Iowa, 111 Engineering Research Facility, Iowa City, IA 52242-1000 (USA)
Karim Abdel-Malek
Affiliation:
US Army Virtual Soldier Research Program, Center for Computer-Aided Design, The University of Iowa, 111 Engineering Research Facility, Iowa City, IA 52242-1000 (USA)
Get access Rights & Permissions [Opens in a new window]

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 kinematic chains or its modification for closed-loop kinematic chains. The method developed is based upon analytical criteria for determining singular behavior of the mechanism. Singularities of manipulators with non-unilateral constraints have never been reported. The complete mathematical formulation is presented and illustrated using 4 & 5 DOF spatial manipulators. Four types of singularities are classified: Type I sets are position Jacobian singularities; Type II sets are instantaneous singularities that are due to a generalized joint are reaching its apex; Type III sets are domain boundary singularities, which are associated with the time 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 and Type III singularities.

Keywords

Non-unilateralSingularityJacobian row rank deficiency
Type
Research Article
Information
Robotica , Volume 23 , Issue 5 , September 2005 , pp. 543 - 553
Copyright
© 2005 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)