A Complete Algorithm for Fixture Loading

Abstract

A fixture is a device for locating and holding parts. Since the initial position and orientation of a part may be uncertain, the act of loading the part into the fixture must compensate for this uncertainty. Machinists often refer to the 3-2-1 rule: place the part onto 3-point contact with a horizontal support plane, slide the part along this plane into 2-point contact with the fixture, then translate along this edge until a 1-point contact uniquely locates the part. Finally, apply clamps (Mani and Wilson 1988; Chou, Chandru, and Barash 1989). This rule of thumb implicitly assumes both sensing and compliance: applied forces change as contacts are detected.

In this paper, we geometrically formalize robotic fixture loading as a sensor-based compliant assembly problem and give a complete planning algorithm. We consider the class of modular fixtures that use three locators and one clamp (Brost and Goldberg 1996), and discuss a class of robot commands that cause the part to slide and rotate in the support plane. Sensing is achieved with binary contact sensors on each lo cator ; compliance is achieved with a passive spring-loaded mechanism at the robot end effector. We extend the theory of sensor-based compliant motion planning (Lozano-Perez, Ma son, and Taylor 1984; Erdmann 1986) to generalized polyg onal C-spaces, and give a complete planning algorithm: it is guaranteed to find a loading plan when one exists and to return a negative report otherwise. We report on experiments using the resulting plans. Finally, we use this formalization to prove a sufficient condition for the 3-2-1 rule.