Introducing the Theory of Bonds for Stewart Gough Platforms With Self Motions1

Abstract

We transfer the basic idea of bonds, introduced by Hegedأ¼s, Schicho, and Schrأ¶cker for overconstrained closed chains with rotational joints, to the theory of selfmotions of parallel manipulators of Stewart Gough (SG) type. Moreover, we present some basic facts and results on bonds and demonstrate the potential of this theory on the basis of several examples. As a byproduct we give a geometric characterization of all SG platforms with a pure translational selfmotion and of all spherical threedegrees of freedom (DOF) RPR manipulators with selfmotions.