Paradoxes in Rigid-Body Kinematics of Structures

[+] Author and Article Information
L. Mentrasti

Istituto di Scienza e Tecnica delle Costruzioni, Facoltà di Ingegneria, Università di Ancona, Via delle Brecce Bianche, 60131 Ancona, Italia

J. Appl. Mech 65(1), 218-222 (Mar 01, 1998) (5 pages) doi:10.1115/1.2789029 History: Received December 17, 1996; Revised July 12, 1997; Online October 25, 2007


The paper discusses two paradoxes appearing in the kinematic analysis of interconnected rigid bodies: there are structures that formally satisfy the classical First and Second Theorem on kinematic chains, but do not have any motion. This can arise when some centers of instantaneous rotation (CIR) relevant to two bodies coincide with each other (first kind paradox) or when the CIRs relevant to three bodies lie on a straight line (second kind paradox). In these cases two sets of new theorems on the CIRs can be applied, pointing out sufficient conditions for the nonexistence of a rigid-body motion. The question is clarified by applying the presented theory to several examples.

Copyright © 1998 by The American Society of Mechanical Engineers
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