
Journal for Geometry and Graphics 16 (2012), No. 1, 019027 Copyright Heldermann Verlag 2012 A FulleroidLike Mechanism Based on the Cube Otto Röschel Institute of Geometry, University of Technology, Kopernikusgasse 24, 8010 Graz, Austria roeschel@tugraz.at We consider one of the Fulleroidlike 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 oneparametric selfmotion ζ_{0}(t) of the mechanism and displayed some of the states of this motion. This mechanism consists of 24 rigid bodies linked via 24 1Rjoints and 12 spherical 2Rjoints. As this Fulleroidlike mechanism admits the selfmotion ζ_{0}(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 selfmotions than ζ_{0}(t) ! In this paper we elucidate this fact and give a list of the possible nontrivial selfmotions of this mechanism: In general there are four different types of oneparametric nontrivial selfmotions of this mechanism: The described type ζ_{0}(t) and 3 further types ζ_{1}(t), ... , ζ_{3}(t). Each type defines eight different oneparametric selfmotions. All these 32 selfmotions share common singular positions where bifurcations are possible. Keywords: Kinematics, robotics, fulleroidlike mechanisms, overconstrained mechanisms, selfmotions, bifurcations of selfmotions. MSC: 53A17 [ Fulltextpdf (493 KB)] for subscribers only. 