Design of Planar Shape-Morphing Mechanism Arrays Using Harmonic Mechanisms

Abstract

is paper introduces a design concept for planar mechanism arrays using an interesting property of mechanisms that I have termed mechanism harmony. Just as a theory of musical harmony allows for a large number of notes to be played without harsh-sounding interference, mechanism harmony allows mechanism links to be arrayed so that they move coherently and with a small degree of freedom. The concept of mechanism harmony is based on permuting the arrangement of the moving links. For a four-bar mechanism, this yields six (3!) different harmonic permutations of the link arrangement, and there are numerous ways that these six different mechanisms can be grouped together to tile the plane. This paper presents early findings on these groups, some prototypes showing arrays with harmonic motion, and discusses the possible significance of harmonic mechanisms for shape morphing mechanisms.