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Kinematic topology and constraints of multi-loop linkages

Published online by Cambridge University Press:  02 August 2018

Andreas Müller
Andreas Müller*
Affiliation:
Institute of Robotics, Johannes Kepler University, Linz, Austria
*
*Corresponding author. E-mail: [email protected]
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Summary

Modeling the instantaneous kinematics of lower pair linkages using joint screws and the finite kinematics with Lie group concepts is well established on a solid theoretical foundation. This allows for modeling the forward kinematics of mechanisms as well the loop closure constraints of kinematic loops. Yet there is no established approach to the modeling of complex mechanisms possessing multiple kinematic loops. For such mechanisms, it is crucial to incorporate the kinematic topology within the modeling in a consistent and systematic way. To this end, in this paper a kinematic model graph is introduced that gives rise to an ordering of the joints within a mechanism and thus allows to systematically apply established kinematics formulations. It naturally gives rise to topologically independent loops and thus to loop closure constraints. Geometric constraints as well as velocity and acceleration constraints are formulated in terms of joint screws. An extension to higher order loop constraints is presented. It is briefly discussed how the topology representation can be used to amend structural mobility criteria.

Keywords

TopologyKinematicsConstraintsMobilityJacobianScrewsLie Groups
Type
Articles
Information
Robotica , Volume 36 , Issue 11 , November 2018 , pp. 1641 - 1663
Copyright
Copyright © Cambridge University Press 2018 

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