One-DOF transformation between tetrahedron and truncated tetrahedron

Polyhedrons have great potentials in various engineering fields due to their superior capability of folding in 3D to achieve a large volumetric ratio of packaging. However, their practical applications are limited by the lack of effective folding schemes with minimum degrees of freedom. Here in the paper we created a transformation between a tetrahedron and a truncated tetrahedron with one degree of freedom by properly setting a movable joint at each vertex. Two schemes of joint arrangement were proposed, and their kinematic behaviours were respectively studied analytically and numerically, where mobility calculations are both based on the truss transformation. Finally, the transformation process using the first scheme was demonstrated through a cardboard prototype fabricated with the origami technique.