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2019 | OriginalPaper | Chapter

Elastostatics of a Full-Mobility PKM with Flexible Links

Authors : Qi Sun, Jorge Angeles, James Richard Forbes

Published in: ROMANSY 22 – Robot Design, Dynamics and Control

Publisher: Springer International Publishing

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Abstract

The subject of this paper is the elastostatics of a novel three-limb, full-mobility parallel-kinematics machine (PKM) with flexible links, dubbed the SDelta robot. Due to the inherent flexibility of the light-weight limb rods under fast operations, they are modeled as identical linearly elastic beams. The moving platform of the PKM is assumed to be elastically attached to the base platform via a six-dof generalized spring. Because of the symmetric design of the SDelta robot, the constant generalized stiffness matrix becomes isotropic. Moreover, the posture-dependent Cartesian stiffness matrix is derived. Based on the preliminary design of a prototype at the desktop scale, its stiffness matrix is numerically evaluated.

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C, P and S stand for cylindrical, prismatic and spherical joints, respectively, the actuated joint being underlined.

The moment is defined w.r.t. the MP c.o.m.

A small-amplitude rotation reduces to a vector [13].

At this posture the Jacobian matrix of the SDelta robot, mapping the twist of the MP into the actuated joint rates, attains its minimum condition number.

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Title: Elastostatics of a Full-Mobility PKM with Flexible Links
Authors: Qi Sun
Jorge Angeles
James Richard Forbes
Publisher: Springer International Publishing
Book: ROMANSY 22 – Robot Design, Dynamics and Control
Print ISBN: 978-3-319-78962-0

Electronic ISBN: 978-3-319-78963-7

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-319-78963-7_6