Characterization of the stability of a flexible fixture that uses three-point frictional constraint for assembly applications
Abstract
Flexible assembly systems require flexible fixtures to constrain parts in a stable fashion in order to perform assembly operations. A fixtured part is either unstable or stable depending on whether or not it moves when the clamping force is applied. The frictional constraint is well suited for fixturing within the assembly environment; however, methods of predicting the stability of parts under frictional constraint are few. This dissertation gives a systematic strategy that uses graphical techniques to characterize the stability of parts fixtured under a particular type of three-point frictional constraint. This stability characterization scheme can aid a fixture designer in the synthesis of fixture configurations. The three inputs into this method are the location of the center of gravity of the part and the geometrical and frictional properties of the fixturing system. No information about the applied clamping force is necessary for the method to characterize stability. The method first determines if it is possible that static equilibrium will not occur when the clamping force is applied. If this possibility exists, then corresponding kinematically possible motions are determined and are tested for consistency with dynamics to determine if any of them are a possible unstable mode. Finally, the method classifies a part into one of three classifications: stable, unstable, or indeterminate. If it is determined that there are no possible unstable modes then the part is stable. But if it is determined that the part will move in an unstable motion then it is unstable. If it is discovered that the part has possible unstable motions and yet can also be stable under either a purely two-point frictional constraint or the three-point frictional constraint, then it is indeterminate. Several examples of using the method are given. Unlike parts within the stable and unstable classifications, the stability of indeterminate parts is significantly influenced by the following: the deformation of the part, the solution of the dynamic equations of motion of the part, and the surface friction upon the part. Since the influences of deformation and surface friction are, using the current knowledge in the literature, indeterminate in themselves, they cause indeterminacies of stability to exist. In spite of these stability indeterminacies, the method can determine all possible unstable motions of both unstable and indeterminate parts. The method gives a characterization of stability which goes beyond its determination and hence provides useful feedback to the fixture designer as to how a fixture configuration can be modified in order to either make it stable or improve its stability properties.
Degree
Ph.D.
Advisors
Cipra, Purdue University.
Subject Area
Mechanical engineering
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