Deployable polyhedral mechanisms (DPMs) have witnessed flourishing growth in recent years because of their potential applications in robotics, space exploration, structure engineering, and so forth. 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.

近年来，可展开多面体机构（DPM）因其在机器人、太空探索、结构工程等领域的潜在应用而蓬勃发展。本文首先介绍了一系列受 Sarrus 启发的可展开多面体机构的构造、移动性和运动学。通过进行扩展操作并沿直线运动路径植入Sarrus连杆，分别按照四面体、八面体和二十面体对称性识别和构造可展开的四面体、立方体和十二面体机构。揭示了柏拉图多面体和阿基米德多面体之间具有同步径向运动的三对变换，并且在每种工作配置中都完美地保留了它们显着的对称特性。随后，在等效棱柱关节的辅助下，提出了多环多面体机构运动性的等效分析策略，大大简化了计算过程。因此，本文提出了受 Sarrus 启发的 DPM 的构造方法和等效分析，不仅在理论研究中有价值，而且在机械超材料、可展开架构和空间探索等实际应用中也具有巨大潜力。