A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces

Sanchez-Garcia, A.J., Rico, J.M., Cervantes-Sanchez, J.J and Lopez Custodio, Pablo (2021) A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces. Journal of Mechanisms and Robotics, 13 (3). 031015. ISSN 1942-4302

Full content URL: https://doi.org/10.1115/1.4050096

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A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE(3) and Its Subspaces
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Abstract

This contribution presents a screw theory-based method for determining the mobility of fully parallel platforms. The method is based on the application of three stages. The first stage involves the application of the intersection of subalgebras of Lie algebra, se(3), of the special Euclidean group, SE(3), associated with the legs of the platform. The second stage analyzes the possibility of the legs of the platform generating a sum or direct sum of two subalgebras of the Lie algebra, se(3). The last stage, if necessary, considers the possibility of the kinematic pairs of the legs satisfying certain velocity conditions; these conditions reduce the platform’s mobility analysis to one that can be solved using one of the two previous stages. Several examples are illustrated.

Keywords:Mechanism design, mechanical admittance, screw theory, Lie algebras, Jacobian matrices
Subjects:H Engineering > H320 Mechanisms and Machines
H Engineering > H300 Mechanical Engineering
Divisions:College of Science > Lincoln Institute for Agri-Food Technology
ID Code:46490
Deposited On:19 Oct 2021 15:32

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