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Singularity analysis of the H4 robot using Grassmann–Cayley algebra

Published online by Cambridge University Press:  12 January 2012

Semaan Amine,
Stéphane Caro,
Philippe Wenger and
Daniel Kanaan
Semaan Amine
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), 1, rue de la Noë, 44321 Nantes, France. E-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nantes.fr, philippe.wenger@irccyn.ec-nantes.fr, daniel.kanaan@irccyn.ec-nantes.fr
Stéphane Caro*
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), 1, rue de la Noë, 44321 Nantes, France. E-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nantes.fr, philippe.wenger@irccyn.ec-nantes.fr, daniel.kanaan@irccyn.ec-nantes.fr
Philippe Wenger
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), 1, rue de la Noë, 44321 Nantes, France. E-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nantes.fr, philippe.wenger@irccyn.ec-nantes.fr, daniel.kanaan@irccyn.ec-nantes.fr
Daniel Kanaan
Affiliation:
Institut de Recherche en Communications et Cybernétique de Nantes (IRCCyN), 1, rue de la Noë, 44321 Nantes, France. E-mails: semaan.amine@irccyn.ec-nantes.fr, stephane.caro@irccyn.ec-nantes.fr, philippe.wenger@irccyn.ec-nantes.fr, daniel.kanaan@irccyn.ec-nantes.fr
*
*Corresponding author. E-mail: stephane.caro@irccyn.ec-nantes.fr
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Summary

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This paper extends a recently proposed singularity analysis method to lower-mobility parallel manipulators having an articulated nacelle. Using screw theory, a twist graph is introduced in order to simplify the constraint analysis of such manipulators. Then, a wrench graph is obtained in order to represent some points at infinity on the Plücker lines of the Jacobian matrix. Using Grassmann–Cayley algebra, the rank deficiency of the Jacobian matrix amounts to the vanishing condition of the superbracket. Accordingly, the parallel singularities are expressed in three different forms involving superbrackets, meet and join operators, and vector cross and dot products, respectively. The approach is explained through the singularity analysis of the H4 robot. All the parallel singularity conditions of this robot are enumerated and the motions associated with these singularities are characterized.

Keywords

Grassmann–Cayley algebraParallel singularityScrew theoryArticulated nacelleProjective spaceSuperbracket

Information

Type
Articles
Information
Robotica , Volume 30 , Issue 7 , December 2012, pp. 1109 - 1118
Copyright
Copyright © Cambridge University Press 2012

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