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On the Maximization of Joint Velocities and Generalized Reactions in the Workspace and Singularity Analysis of Parallel Mechanisms

Published online by Cambridge University Press:  14 December 2018

Pavel Laryushkin Open the ORCID record for Pavel Laryushkin [Opens in a new window] ,
Victor Glazunov  and
Ksenia Erastova
Pavel Laryushkin
Affiliation:
Fundamentals of Machine Design Department, Bauman Moscow State Technical University, 2-ya Baumanskaya st. 5, Moscow 105005, Russia. E-mail: pav.and.lar@gmail.com
Victor Glazunov
Affiliation:
Mechanical Engineering Research Institute of the Russian Academy of Sciences (IMASH RAN), Maly Kharitonyevsky Pereulok 4, Moscow 101990, Russia. E-mail: vaglznv@mail.ru
Ksenia Erastova*
Affiliation:
Fundamentals of Machine Design Department, Bauman Moscow State Technical University, 2-ya Baumanskaya st. 5, Moscow 105005, Russia. E-mail: pav.and.lar@gmail.com
*
*Corresponding author. E-mail: erastovakg@gmail.com
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Summary

An approach for calculating the maximum possible absolute values of joint velocities or generalized reactions in a leg of a parallel mechanism has been considered in this paper. The Jacobian analysis and the Screw theory-based methods have been used to acquire the result. These values are calculated for the “worst” directions of the external load or end-effector’s velocity for each leg. The feasibility of using these parameters as the measures of closeness to different types of parallel mechanism singularity is discussed. Further, how this approach is related to the state-of-the-art methods has been illustrated. The key aspect of the discussed approach is that the normalization of vectors or screws is carried out separately for angular and linear components. One possible advantage of such an approach is that it deals only with the kinematic and statics of the mechanism while still providing physically meaningful and practically applicable measures. Case studies of a 3-Degrees Of Freedom translational parallel mechanism and a planar parallel mechanism are presented for illustration and comparison.

Keywords

Parallel mechanismWorkspaceCloseness to singularitySingularity analysisScrew theoryJacobian
Type
Articles
Information
Robotica , Volume 37 , Issue 4 , April 2019 , pp. 675 - 690
Copyright
Copyright © Cambridge University Press 2018 

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