Analysis of two-dimensional fixture clamping with friction

Abstract

Fixtures that constrain the unwanted motion of a workpiece are important tools in automated manufacturing today. In this paper, we analyze the stability of clamping with passive friction force. The concept of the instant center of rotation is applied to transform the stability analysis into a search for a static equilibrium state. Many properties related to the stability analysis are studied. According to these properties, we design an efficient algorithm for searching the static equilibrium state. The maximum allowable cutting force or the minimum normal stress, which are key concerns in automated design of fixtures, can be calculated precisely by using the search operation. The algorithm can also be extended to the case of multiply distributed friction forces with differently configured clamping areas. Several examples are provided to illustrate cutting force design for different fixture conditions.