  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.
