文档介绍：Mechanism and Machine Theory 44 (2009) 1386–1399
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Mechanism and Machine Theory
journal homepage: ate/mechmt
Singularity analysis of planar parallel manipulators based on forward
kinematic solutions
Flavio Firmani, Ron P. Podhorodeski *
Robotics and Mechanisms Laboratory, Department of Mechanical Engineering, University of Victoria, . Box 3055, Victoria, BC, Canada V8W 3P6
article info abstract
Article history: An efficient approach for determining the force-unconstrained poses (singularity loci) of
Received 22 May 2007 planar parallel manipulators (PPMs) is presented. The approach is implemented for the
Received in revised form 29 October 2008 3-RPR, 3-PRR, and 3-RRR PPMs, where the underline indicates the actuated joint. The
Accepted 10 November 2008
force-unconstrained poses are identified based upon concepts of reciprocal screws, kine-
Available online 23 December 2008
matics, and elimination methods. The use of screw quantities provides a clear insight as
to how the forces are acting on the mechanism. This allows finding conditions of singular
configurations that are related to displacements of passive joints. Based on these condi-
Keywords:
tions, the force-unconstrained poses are obtained by solving the forward kinematic analy-
Singularity
Planar parallel manipulators sis of manipulators with the same architecture but different actuation layouts. It is
Kinematics demonstrated that the singularity loci of the 3-RPR, 3-PRR, and 3-RRR PPMs can be
described with single-variable polynomials of degrees 2, 2, and 6, respectively.
Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction
. Parallel manipulators and singularities
Parallel manipulators (PMs) are closed-loop prised of a mobile platform connected to a fixed platform by
several independent chains or branches. PMs are prone of having force-unconstrained configurations. Ideally, a PM should
act as a rigid structure when the actu