Kinematics and Dynamics of the Fulleroid

Abstract

This paper presents, besides a new synthesis, the kinematic and dynamic analysis of a complex spatial mechanism, called Fulleroid, which initially has been synthesized on the basis of the generalized Heureka Oktahedron. This mechanism consists of 24 equal triangular bodies interconcected by simple or double rotary joints. It is a highly overconstrained linkage which is, however, movable with one global degree of freedom due to its special dimensions. The six symmetry planes of the Fulleroid clearly define a center and allow introducing a central co-ordinate system in relation to which all of its rigid bodies perform Schoenfließ motions. With these special (relative) motions it becomes possible to determine the (absolute) motion of each link within a second (absolute) co-ordinate system fixed to one of these bodies. Knowing the positions of the bodies within this co-ordinate system and knowing the (absolute) velocities of all points of the Fulleroid as functions of the input parameter and its time derivative, the ruling differential equation can be established for a given input force or moment.