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Journal for Geometry and Graphics 16 (2012), No. 1, 019--027
Copyright Heldermann Verlag 2012

A Fulleroid-Like Mechanism Based on the Cube

Otto Röschel
Institute of Geometry, University of Technology, Kopernikusgasse 24, 8010 Graz, Austria

We consider one of the Fulleroid-like mechanisms based on a cube described by G. Kiper and K. Wohlhart. 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 1R-joints and 12 spherical 2R-joints. As this Fulleroid-like mechanism 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: 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), ... , ζ3(t). Each type defines eight different one-parametric self-motions. All these 32 self-motions share common singular positions where bifurcations are possible.

Keywords: Kinematics, robotics, fulleroid-like mechanisms, overconstrained mechanisms, self-motions, bifurcations of self-motions.

MSC: 53A17

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