Symmetric Equations for Evaluating Maximum Torsion Stress of Rectangular Beams in Compliant Mechanisms

There are several design equations available for calculating the torsional compliance and the maximum torsion stress of a rectangular cross-section beam, but most depend on the relative magnitude of the two dimensions of the cross-section (i.e., the thickness and the width). After reviewing the available equations, two thickness-to-width ratio independent equations that are symmetric with respect to the two dimensions are obtained for evaluating the maximum torsion stress of rectangular cross-section beams. Based on the resulting equations, outside lamina emergent torsional joints are analyzed and some useful design insights are obtained. These equations, together with the previous work on symmetric equations for calculating torsional compliance, provide a convenient and effective way for designing and optimizing torsional beams in compliant mechanisms.