Sarrus-inspired Deployable Polyhedral Mechanisms

Deployable polyhedral mechanisms (DPMs) have witnessed flourishing growth in recent years because of their potential applications in robotics, space exploration, structure engineering, etc. This paper firstly presents the construction, mobility and kinematics of a family of Sarrus-inspired deployable polyhedral mechanisms. By carrying out expansion operation and implanting Sarrus linkages along the straight-line motion paths, deployable tetrahedral, cubic and dodecahedral mechanisms are identified and constructed following tetrahedral, octahedral and icosahedral symmetry, respectively. Three paired transformations with synchronized radial motion between Platonic and Archimedean polyhedrons are revealed, and their significant symmetric properties are perfectly remained in each work configuration. Subsequently, with assistant of equivalent prismatic joints, the equivalent analysis strategy for mobility of multiloop polyhedral mechanisms is proposed to significantly simplify the calculation process. This paper hence presents the construction method and equivalent analysis of the Sarrus-inspired DPMs that are not only valuable in theoretical investigation, but also have great potential in practical applications such as mechanical metamaterials, deployable architectures and space exploration.