RESEARCH PAPERS: Mechanisms Papers

Application of Timoshenko Beam Theory to the Dynamics of Flexible Legged Locomotion

[+] Author and Article Information
E. M. Bakr, A. A. Shabana

Department of Mechanical Engineering, University of Illinois at Chicago, P.O. Box 4348, Chicago, IL 60680

J. Mech., Trans., and Automation 110(1), 28-34 (Mar 01, 1988) (7 pages) doi:10.1115/1.3258900 History: Received December 04, 1986; Online November 19, 2009


A method for the dynamic analysis of flexible legged locomotion systems that accounts for the rotary inertia and shear deformation effects is presented. The motion of the flexible components in the legged vehicle is described using a set of inertia-variant Timoshenko beams that undergo large rotations. A shape function that accounts for the combined effect of rotary inertia and shear is employed to describe the deformation relative to a selected component reference and the rigid-body modes of the shape function are eliminated using a set of reference conditions. Kinetic and strain energies are derived for each Timoshenko beam, thus identifying the beam mass and stiffness matrices which account for the rotary inertia and shear deformation effects. A new set of time-invariant matrices that describe the nonlinear inertia coupling between the reference motion and elastic deformation and account for the rotary inertia and shear is developed and it is shown that the form of these matrices as well as the mass and stiffness matrices are significantly affected by the inclusion of rotary inertia and shear. Numerical experimentations indicate that shear and rotary inertia can have a significant effect on the dynamics of flexible legged locomotion.

Copyright © 1988 by ASME
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