|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 onedegree-
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.