Abstract
The object of this paper is to develop a procedure that will allow the establishment of necessary and sufficient point contacts on a rigid body to ensure that the body has any desired state of instantaneous motion or restraint. The screw space and its sub-spaces are employed; these are vector spaces but not Euclidean spaces. The states of restraint and instantaneous motion of a body restrained by a system of screws of point contacts are specified by reciprocal sub-spaces of the screw space. This leads to a synthesis procedure for restraint of a rigid body by means of point contacts. The existence and uniqueness of the synthesis solution are discussed, and necessary and sufficient conditions for a realizable surface of a kinematic pair are given. Finally, two quality measures for a feasible set of screws are defined. One represents the uniformity of the distribution of internal forces while the other indicates the restraint's ability to resist external forces.
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