The Elastica With End-Load Flip-Over

[+] Author and Article Information
J. F. Wilson

School of Engineering, Duke University, Durham, NC 27706

J. M. Snyder

Department of Civil Engineering, Duke University, Durham, NC 27706

J. Appl. Mech 55(4), 845-848 (Dec 01, 1988) (4 pages) doi:10.1115/1.3173731 History: Received October 26, 1987; Revised May 26, 1988; Online July 21, 2009


A high flexure manipulator arm is modeled as an elastic cantilever beam with a tip payload and an eccentric tip follower load that drives the arm. Shapes of the resulting elastic curves for finite deformations (the elastica) are calculated in terms of nondimensional system parameters. For critical combinations of these parameters, a small increment in the driving follower load causes an abrupt change in the shape of the elastica. The abrupt change in tip angle is typically of the order of π radians. These results are applicable to the design of high flexure robotic manipulators.

Copyright © 1988 by ASME
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