Polyhedral Zig-Zag Linkages

Abstract

In this paper new overconstrained mechanisms are described which are synthesized by inserting equal basic mechanisms known as Nuremberg scissors into the edges of a Platonian polyhedron and interconnecting them at their ends by different kinds of articulations. The basic mechanism is a planar mechanism and can be inserted into an edge of a Platonian polyhedron in two different ways: either its plane becomes identical with the plane given by the edge line and the center of the polyhedron or orthogonal to this plane. For each of these two insertions two different kinds of articulation (located at the apexes of the polyhedron) are proposed in the paper. Four different kinds of new polyhedral linkages are thus obtained whose syntheses are decribed in detail. A corkscrew on the market under the commercial name Zig-Zag is based on Nuremberg scissors. As the common parts in the newly designed linkages are Nuremberg scissors we adopt this name for the whole family of new polyhedral linkages which are, though highly overconstrained, movable with one degree of freedom.