Deployable polyhedral mechanisms with radially reciprocating motion based on novel basic units and an additive-then-subtractive design strategy

Abstract

This paper is to deal with the mechanism design problem for constructing deployable polyhedral mechanisms on the basis of novel basic units with an additive-then-subtractive design strategy. The aimed deployable polyhedral mechanisms can be, but are not limited to, Platonic and Archimedean solids. The basic units involved in the type synthesis process refer to one-degree-of-freedom regular polygonal prisms, whose deployable performance has been already proven to be excellent. To show the procedure of the type synthesis method, the case study on a deployable regular-tetrahedron mechanism is presented as a design example. The mobility properties of the proposed deployable regular-tetrahedron mechanism are then confirmed with the combination of screw theory and line geometry. In addition, the kinematic model is presented to study the deployable performance of deployable polyhedral mechanisms. By adopting the proposed type synthesis method, novel deployable Platonic and Archimedean polyhedral mechanisms are proposed with wider-margin radially reciprocating motion. This work not only provides the design and analysis method but also contributes new types of mechanisms, hoping to have a reference for the research of deployable polyhedral mechanisms.