2D Motion Structures of N-Fold Rotational Symmetry

Abstract

Kinematic motion structures having a reconfigurable property appear to be a potential candidate for the programmable matter. Motion structures with N-fold rotational symmetry show a reconfigurable pattern transformation, resulting in providing tunable mechanical properties, which deserves to explore more for their unique properties of transformation and the corresponding structural behaviors. The objective of this work is to synthesize motion structures from a bar-and-joint framework, investigating their transformability, linear structural properties - modulus and Poisson’s ratio, and nonlinear structural behaviors with kinematic bifurcation. Two-dimensional (2D) motion structures are synthesized by central scissor links with revolute joints, connected with binary links in the radial direction. They possess an N-fold rotational symmetry (MS-N), and their transformed patterns are investigated. Five 2D motion structures — MS-4, MS-6, MS-8, MS-10, and MS-12, are generated for investigating their mechanical properties together with their transformability. Analytical models of the motion structures are constructed for obtaining relative density, moduli, Poisson’s ratios, volume at each transformed state, and the strain energy required to transform from one state to another. This study integrates kinematics and structural mechanics, expanding the design space of light-weight structural materials with pattern transformation.