A flat rigid plate is a universal planar manipulator

Abstract

We consider the problem of parallel part manipulation, i.e., the simultaneous position and orientation control of one or more p arts in a bounded r egion 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 c omputed which produces desired average forces at a nite number of points, e.g., parts' locations. This implies that one or more p arts can follow independent trajectories simultaneously, as they interact with a single vibrating plate. This is in sharp contrast with more c omplex 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.

A dynamic object manipulation approach to dynamic biped locomotion

“…For instance, we do such a manipulation when manipulating a disc using two simple manipulators. Other, examples include control of an object by rolling it between two plates [2,3], manipulation of objects in a tilting tray [4] or on a vibrating plate [5], manipulation of parts on a conveyor belt with a single-joint robot [6], pushing with point contact [7], dynamic rolling [8], snatching, rolling, and throwing [9], manipulation of planar objects dynamically with simple robots [10], reorientating parts using a manufacturing arm with a passive joint on its end [11] and manipulation of planar shapes using two palms [12] or a series of one degree of freedom arm [34]. Above mentioned robotic systems are much simpler than conventional general purpose manipulators however; they can manipulate a variety of parts without grasping.…”

Friction-Induced Velocity Fields for Point Parts Sliding on a Rigid Oscillated Plate

“…The UPM consists of a single rigid horizontal plate that moves with three degrees-of-freedom (two translational and one rotational). Systems that restrict the plate motion to the horizontal plane, such as the UPM, can only generate frictional force fields with zero divergence [12]. Therefore, position sensing is required to orient and position parts.…”

“…In [17], Lynch and Umbanhowar derived optimal plate motions that maximize part speed on one-and two-DoF translating rigid plates. The three-DoF UPM is capable of generating certain position-dependent force fields [12] including localized ones [18].…”

inFORM

“…While the system can communicate system constraints through graphics and object actuation, it is limited in its ability to manifest mechanical constraints; only the user can create those. Other techniques for moving objects on a 2D surface include vibration [36] and robotics [22].…”