Qualitative analysis and quantitative evaluation of fixturing

Abstract Form-closure is considered as a purely geometric property of a set of unilateral contact constraints such as those applied on a workpiece by a mechanical fixture. This paper provided qualitative analysis of form-closure fixturing. The necessary and sufficient condition for form-closure fixturing is derived. Some fundamental problems related to form-closure are solved such as minimum number of frictionless contact points and the way to arrange them to achieve form-closure. On the basis of qualitative analysis, the quantitative evaluation of form-closure is investigated. To assess quantitatively the form-closure fixturing, two quantitative indices, one to minimize the sum of all normal contact forces and the other to minimize the maximum normal contact force, are presented. Finally, the given example verifies the analysis method and evaluating indices.

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