This paper explores the role of anisotropic friction properties in vibratory parts manipulation. We show that direction-dependent surface friction properties can be used in conjunction with a vibrating plate to help design friction-induced velocity fields on the surface of the plate. Theoretical, simulation, and experimental results are presented quantifying the anisotropic friction effects of textured surfaces such as micromachined silicon and fabrics.

A position-dependent asymptotic velocity field describes the motion of point parts sliding with friction on the surface of a rigid oscillating plate. These fields can be used to perform manipulation tasks such as sensorless positioning of one or several parts simultaneously. This paper examines the set of fields F generated by periodic plate motions M that combine a single in-plane component and a single out-of-plane component that have square wave accelerations with 50% duty cycles, identical periods, and an arbitrary phase between them. By deconstructing the full map Π : M → F into three simpler maps, we expose the structure of F and its relationship to M. To illustrate, we focus on particular plate motions in M that generate fields well approximated by polynomial functions of position with degree n ≤ 2. Numerical simulations suggest that fields generated from plate motions with more than a single inplane and a single out-of-plane component (all with the same period and square wave accelerations) are well approximated by linear combinations of fields in F.

We show that the frictional forces arising from simultaneous small amplitude periodic translation and rotation of a rigid plate cause parts on the plate to converge to or diverge from a line coinciding with the rotation axis. The relative phase between the translation and rotation determines whether the parts are attracted to or repelled from the rotation axis. Assuming that both the translational and rotational accelerations of the plate are ldquobang-bangrdquo and have identical frequencies, we derive the resultant velocity fields for point parts on the plate. For many choices of phase the speed of the part is approximately proportional to its distance from the rotation axis. The strength of the velocity field can be controlled by modulating the amplitude of the translational acceleration, or modulating the relative phase between the translational and rotational acceleration profiles. We also determine the phases that maximize part speed towards and away from the rotation axis. These optimal phases not only maximize part speed but also generate velocity fields that are nearly independent of the coefficient of friction.

By vibrating a rigid plate with up to six degrees of freedom, we can create a large family of programmable frictional force fields acting on parts resting on the plate. These fields can be used for sensorless part orientation, uncertainty-reducing transport, and simultaneous manipulation of multiple parts. The principle is demonstrated by a plate rotating about an axis below the plate. Simple oscillatory rotation produces a squeeze field that attracts and aligns parts along a center line. This behavior is confirmed in experiment. Motivated by this experimental confirmation, we use a simulation to find plate motions that yield a number of other useful primitive force fields. By sequencing these force fields, we can create any force field that is a convex combination of the primitives.