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Machine Theory
Mechanism and Machine Theory 43 (2008) 480–490
ate/mechmt
Non-singular assembly-mode changing motions
for 3-RPR parallel manipulators
Mazen Zein, Philippe Wenger, Damien Chablat *
Institut de Recherche munications et Cyberne´tique de Nantes RS 6597, 1, rue de la Noe¨,
BP 92101, 44312 Nantes Cedex 03, France
Received 28 July 2006; received in revised form 19 March 2007; accepted 22 March 2007
Available online 13 June 2007
Abstract
When moving from one arbitrary location at another, a parallel manipulator may change its assembly-mode without
crossing a singularity. Because the non-singular change of assembly-mode cannot be simply detected, the actual assem-
bly-mode during motion is difficult to track. This paper proposes a global explanatory approach to help better understand
non-singular assembly-mode changing motions for 3-RPR planar parallel manipulators. The approach consists in fixing
one of the actuated joints and analyzing the configuration-space as a surface in a three-dimensional space. Such a global
description makes it possible to display all possible non-singular assembly-mode changing trajectories.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Planar parallel robot; Singularities; Cusp points; Assembly-modes
1. Introduction
Most parallel manipulators have singularities that limit the motion of the moving platform. The most dan-
gerous ones are the singularities associated with the direct kinematics, where two assembly-modes coalesce.
Indeed, approaching such a singularity results in large actuator torques or forces, and in a loss of stiffness.
Hence, these singularities are undesirable. There exists three main ways of coping with singularities, which
have their own merits. A first approach consists in eliminating the singularities at the design stage by properly
determining the kinematic architecture, the geometric parameters and the joint limits [1,2]. This approach is