Case Studies in Planar Part Feeding and Assembly Based on Design of Limit Sets

Abstract

Vibration is commonly used in industrial parts feeding and alignment processes, and to provide energy to encourage mobility among self-assembling parts. We are studying a simple model of agitation where planar parts are repetitively thrown by a simple one-degree-of-freedom throwing surface, caught and allowed to settle. Throwing actions result in nonlinear discrete-time maps in the parts' configuration space, exhibiting behaviors such as unique fixed points and uncertainty-reducing forward limit sets with large basins of attraction. We show how to shape these maps by choosing the arm geometry, throwing velocity and mass parameters of the parts. In some cases, we can design a single map that is guaranteed to uniquely position and orient a part. In other cases, we can design multiple maps corresponding to different throw velocities such that the composition of the maps can be used to drive multiple parts to a desired assembly. Switching between the throw actions is triggered by simple sensors that recognize when the system has achieved a configuration in the basin of attraction of a subsequent map.