Singularities of manipulators with non-unilateral constraints

  • Authors:

  • Jingzhou Yang;Karim Abdel-malek

  • Affiliations:

  • 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);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)

  • Venue:
  • Robotica
  • Year:
  • 2005

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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.