From Shear Centre to Eigenwrenches

In the field of mechanism design, the behaviour of compliant shell mechanisms is commonly characterised via the eigenscrew decomposition of their spatial stiffness matrix. Recent developments have included the design of compliant shell mechanisms made with anisotropic materials. Conceptually, these compliant mechanisms are very similar to morphing composite structures that are typically designed using structural mechanics approaches. Eigenscrew decomposition could, therefore, provide additional insight to designers. To bridge the gap between the two communities, we present the equivalence of eigenscrews (eigenwrench and eigentwist) and familiar structural concepts such as shear centre and centre of twist for the special case of a cantilevered beam. It is hoped that this explicit link will help bridge these disparate fields, and encourage cross-fertilisation of ideas.