Zero-curvature deformation properties and 3R pseudo-rigid-body model of large-deflection Euler spiral beams

Abstract

Euler spiral beams are curved in their undeflected state but can lay flat (zero-curvature deformed shape) when proper loads are applied at the end of the beams. This zero-curvature deformation property enables deployable compliant mechanisms to deform into compact configurations. However, the condition of zero-curvature deformation is still not clear and Euler spiral beams lack effective models for predicting deformation upon loading. To solve these problems, this paper first describes the shape of Euler spirals by using size-independent quantities. Based on Bernoulli–Euler beam theory, the large-deflection equations of Euler spiral beams are derived. The zero-curvature deformation properties of the Euler spiral beams with different boundary conditions are studied. The conditions for zero-curvature deformation are given. Meanwhile, a 3R pseudo-rigid-body model (PRBM) is proposed for Euler spiral beams. Analysis and design cases are used to verify the proposed model. The results will facilitate the use of the zero-curvature deformation property in developing compact deployable compliant mechanisms and the large-deflection analysis of Euler spiral beams.