A class of N-sided antiprism deployable polyhedral mechanisms based on an asymmetric eight-bar linkage

Abstract

An asymmetric eight-bar linkage is used as the basic unit to develop a group of N-sided antiprism (N⩾3) mechanisms. First, the geometric properties and kinematics equations of the asymmetric eight-bar linkage are investigated. When the kinematic conditions hold, an asymmetric eight-bar linkage and a single-plane or double-plane symmetric eight-bar linkage can be coupled. Second, the concept of axis groups is proposed, and virtual-center-based method is applied to construct a class of deployable polyhedral mechanisms based on N-sided antiprism polyhedrons; the motion bifurcation characteristics of the mechanisms are revealed by analyzing the singularity of the eight-bar linkages. These mechanisms may perform motion bifurcation in multiple different positions; therefore, these mechanisms are capable of having many different configurations that can increase their application potential for adapting to different tasks and working environments. Finally, the motion unit H is constructed based on the axis group and used as the deployable unit to synthesize a deployable mechanism with 120 loops based on a rhombic triacontahedron. Moreover, H can replace the double-plane symmetrical eight-bar linkage in other deployable polyhedral mechanisms to construct mechanisms with larger work space.