A flat rigid plate is a universal planar manipulator

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 horizontally-vibrating flat plate. We show that a closed rigid motion of the plate, involving its 3 DOF, can be computed which produces desired average forces at a finite 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.

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