Möbius kaleidocycles with adjustable-stiffness joints and the related flat energy landscape

Abstract Möbius kaleidocycles are closed-ring linkages that can undergo smooth and periodic eversion. The original concept includes revolute joints as kinematic pairs between the links, whose rotation axes relative to the centerline of the links are placed at a critical twist angle, meaning the angle below which the chain cannot close congruently for any configuration. Here, the possibility of replacing the revolute joints with flexural-tensegrity joints is proposed and investigated. These joints consist of conjugate profiles in unilateral contact held together by pre-tensioned cables, so that a pure rolling motion is achieved along design pitch profiles. Once the geometry of the pitch profiles is selected, the pre-tension of the cables is the control parameter that governs the stiffness of the joints. As the rotation occurs, the cables are further strained, thus affecting the elastic energy of the system. With specific reference to the simplest case of a Möbius kaleidocycle with seven flexural-tensegrity joints and circular pitch profiles, it is shown that the set of rotations at the joints preserves the properties of a seven-hinged Möbius kaleidocycle, i.e., the algebraic sum of the rotations raised to an even positive integer power remains constant. This means that, for any configuration during the everting motion, the cables do not stretch further and the strain energy of the system is constant. Consequently, the eversion ideally requires a zero driving force once primed.