Mechanics of form closure (Q759495)

The terms form closure and force closure are well known in the theory of mechanisms. The motion of a rigid body can be partially or completely prevented by contact with fixed surfaces. If such a contact is maintained by virtue of the action of certain forces, such a maintenance of contact is referred to as force closure. If the contact is self-sufficient in maintaining itself without reference to the applied forces, one has form closure. The present paper offers a fundamental clarification of the mechanics of form closure. This necessarily involves the use of point contacts. The requirements are reduced to a conceptually simple and powerful form: the contacts should be applied in the senses in which the equilibrating forces act along the contact normals in the absence of any applied forces. The number of contacts necessary, the number of unloaded contacts and their identification, the case where the problem is solved in stages and the condition for the determinacy of the reactions are effectively dealt with. Examples illustrate the procedure outlined by the authors. Apart from providing the theoretical basis of form closure, the paper may be of practical use in at least one field: the design of work holding devices.