A Flat Rigid Plate is a Universal Planar Manipulator

Dan Reznik John Canny EECS Dept., UC-Berkeley, CA 94720-1776 USA Abstract We consider the problem of parallel part manipulation, i.e., the simultaneous position and orientation control of one or more parts in a bounded region of the plane. We propose a novel, minimalist device, based on a single horizontallyvibrating at plate. We show that a closed rigid motion of the plate, involving its 3 dofs, can be computed which produces desired average forces at a nite number of points, e.g., parts' locations. This implies that one or more parts can follow independent trajectories simultaneously, as they interact with a single vibrating plate. This is in sharp contrast with more complex designs such as massively-parallel actuator arrays and/or prehensile manipulation. Dynamic simulation is used to test the current method in two parallel part manipulation examples. A prototype of the device has been built with inexpensive parts; physical implementation of the proposed method is currently underway.