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Modeling of Flexible-Link Manipulators with Prismatic Joints

Theodore, Rex J and Ghosal, Ashitava (1997) Modeling of Flexible-Link Manipulators with Prismatic Joints. In: IEEE Transactions on Systems, Man and Cybernetics, Part B, 27 (2). 296 -305.

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Abstract

The axially translating flexible link in flexible manipulators with a prismatic joint can be modeled using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, we present a nondimensional form of the Euler-Bernoulli beam equation using the concept of group velocity and present conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions lead to a time-dependent frequency equation for the translating flexible beam. We present a novel method to solve this time-dependent frequency equation by using a differential form of the frequency equation. We then present a systematic modeling procedure for spatial multi-link flexible manipulators having both revolute and prismatic joints. The assumed mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. We show, using a model-based control law, that the closed-loop dynamic response of modal variables become unstable during retraction of a flexible link, compared to the stable dynamic response during extension of the link. Numerical simulation results are presented for a flexible spatial RRP configuration robot arm. We show that the numerical results compare favorably with those obtained by using a finite element-based model.

Item Type: Journal Article
Additional Information: Copyright 1990 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 25 Aug 2008
Last Modified: 19 Sep 2010 04:25
URI: http://eprints.iisc.ernet.in/id/eprint/6273

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