Self-posture changeability (SPC) for 3-D link system

The authors discuss the self-posture changeability (SPC) for a general 3-D link system. The series of motions brought about by SPC is called self-posture changing motions (SPCM). SPC and SPCM are considered assuming that the link system moves slowly enough to suppress any dynamic effects. It is shown that, according to a particular combination of link posture, joint assignment, and object shape, there exist a deadlock state, where no further angular displacement can be imparted to the position-controlled joint. It is also shown that there are two different types of deadlock states which never result in any SPCM. The authors introduce (w, ω)-posture changeability, the characteristic with which a link can change posture for every possible force within a cone of a prime axis w and a solid angle, ω. The necessary and sufficient conditions leading to (w, ω)-posture changeability are shown, for a given contact point and frictional conditions. a sufficient condition is included required to realize SPCM under the assumption that the contact point moves continuously over the object and the link-object system never results in a deadlock state