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Machine Theory
Mechanism and Machine Theory 43 (2008) 1129–1140
ate/mechmt
Increase of singularity-free zones in the workspace
of parallel manipulators using mechanisms of variable structure
Vigen Arakelian a,*,Se´bastien Briot a, Victor Glazunov b
a De´partement de Ge´nie Me´canique et Automatique – . EA3913, Institut National des Sciences Applique´es (.),
20 Avenue des Buttes de Coe¨smes – CS 14315, F-35043 Rennes, France
b Mechanical Engineering Research Institute, Russian Academy of Sciences, Str. 4, 101990 Moscow, Russia
Received 4 July 2006; received in revised form 12 September 2007; accepted 28 September 2007
Available online 26 November 2007
Abstract
This paper is focused on the study of singularity of planar parallel manipulators taking into account the force trans-
mission, . study of singularity of planar manipulator by introducing the force transmission factor. Thus the singularity
zones in the workspace of the manipulator are defined not only by kinematic criterions from the theoretical perfect model
of the manipulator but also by the quality of force transmission. For this purpose, the pressure angle is used as an indicator
of force transmission. The optimal control of the pressure angle for a given trajectory of the manipulator is realized by
means of legs with variable structure. The suggested procedure to determination of the optimal structure of the planar par-
allel manipulator 3-RPR is illustrated by two numerical simulations.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Parallel manipulator; Singularity-free zones; Pressure angle; Force transmissivity analysis
1. Introduction
It is well-known that the closed-loop of parallel manipulators limits the motion of the platform and creates
special singular zones inside the workspace [1]. The workspace of the parallel manipulators which is less than
the serial manipulators es smaller and limi