A Strategy for Determining the Stability of Parts Fixtured Under Three-Point Frictional Constraint

Abstract

Flexible assembly systems require flexible fixtures to constrain parts in a stable fashion in order to perform assembly operations. This paper gives a systematic strategy that uses graphical techniques to determine the stability of parts fixtured under a particular type of three-point frictional constraint. The two inputs into the analysis method are the geometry and frictional properties of the fixturing system. No information about the applied clamping force is necessary for the method to determine stability. The strategy finds all kinematically possible motions of a part based on the existence of instant centers. Then for subsets of these motions it determines if static equilibrium exists in order to find out which of these motions cannot occur. Finally, the method classifies a part into one of three categories: stable, not stable, or unstable. If it is determined that there are no possible unstable motions, then the part is stable. But if it is determined that the part will move in one-point unstable motion then it is unstable. If any two- or three-point unstable motions are determined to be possible, then the part is classified as not stable. Although some of the parts in the not stable category will be unstable, there are other cases in this classification in which it is not known whether one of the unstable modes will occur. These are indeterminate cases in which the stability of the part cannot be determined. However, the method can determine those cases in which the part is stable which makes it a useful fixture analysis tool.