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Machine Theory
Mechanism and Machine Theory 43 (2008) 738–753
ate/mechmt
Transitions in the velocity pattern of lower mobility
parallel manipulators
Alfonso Herna´ndez, Oscar Altuzarra *, Charles Pinto, Enrique Amezua
Department of Mechanical Engineering, University of The Basque Country, UPV/EHU, Bilbao 48013, Spain
Received 23 February 2007; received in revised form 7 May 2007; accepted 15 May 2007
Available online 9 July 2007
Abstract
Lower mobility parallel manipulators are designed to perform tasks that require less than six degrees of freedom. The
operational mode is given by the type of screw system spanned by the end-effector’s twist and it is configuration dependent.
A change in the dimension of such screw system occurs at singularities; a loss of freedom of the end-effector will make the
operation not feasible while a gain of freedom will produce uncontrolled motions. In this contribution the authors show
that there are also poses in which, being no quantitative alteration of the freedom of the moving platform, there are
changes in the type of its screw system. These changes are viewed as transitions in the velocity pattern of the end-effector.
Such transitions can alter the operational motion and produce a problem that should be avoided, but it can be also a useful
new operational mode. Because in many industrial applications the operational mode is viewed in terms of the pure trans-
lations and the rotations available in the end-effector, the authors have used such concepts to denote the type of motion. In
this paper the authors present a procedure to analyze these transitions and present an example.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Operational modes; Velocity pattern; Parallel manipulators; Lower mobility
1. Introduction
The capabilities of a robot are given by the possibilities of motion of its end-effector. For six degrees of
freedom (DOF) robots, the end-effector has ful