A Fulleroid - Like Mechanism Based on the Cube

We consider one of the Fulleroid-like mechanisms based on a cube described by G. Kiper [2] and K. Wohlhart [9]. Due to the generation of this mechanism G. Kiper and K.Wohlhart worked out a highly symmetric one-parametric self-motion ζ0(t) of the mechanism and displayed some of the states of this motion. This mechanism consists of 24 rigid bodies linked via 24 rotational linkages (socalled 1R-joints) and 12 linkages, each consisting of two orthogonally intersecting rotational axes (so-called spherical 2R-joints). For the Fulleroid-like mechanism the theoretical degree of freedom takes on the value F = −30. As it admits the self-motion ζ0(t) it is an example of an overconstrained mechanism and as such of high interest. But surprisingly, a physical model of this highly overconstrained mechanism seems to admit more possible self-motions than ζ0(t)! In this paper we elucidate this fact and give a list of the possible non-trivial self-motions of this mechanism: We will demonstrate that in general there are four different types of one-parametric non-trivial self-motions of this mechanism: The described type ζ0(t) and 3 further types ζ1(t), ζ2(t) and ζ3(t). Each type defines eight different one-parametric self-motions. All these 32 self-motions share common singular positions where bifurcations are possible. These singular positions will also be described in the paper.