| This thesis examines the dynamics of sliding objects (parts) in frictional contact with a flat, rigid, 6-degree-of-freedom (DoF), vibratory support surface (plate). We focus on systems in which the plate is driven periodically with small amplitude displacements, the part is a point mass or a rigid body in three-point contact with the plate, and the frictional forces obey the maximum power inequality (e.g., Coulomb's law). For these systems we show that the part's sliding dynamics are well approximated by a first-order system represented by an asymptotic velocity field mapping part configurations to unique asymptotic velocities. Vectors in the field approximate the part's cycle-averaged velocity at each configuration and are independent of time and the system's initial state. The form of the asymptotic velocity field depends on the plate's motion, the part's inertial properties, the locations of the contact points, and the friction model. Using full dynamic simulations and physical experiments with the Programmable Parts-feeding Oscillatory Device (PPOD2), we show that a wide variety of fields can be generated with a 6-DoF plate, including ones with stable attractors (e.g., sink points and squeeze lines) that automatically reduce uncertainty in the part's configuration.;Assuming point parts and Coulomb friction, we derive closed-form analytic solutions for the set of asymptotic velocity fields generated by a class of plate motions with square wave acceleration profiles. Many fields in this set are well approximated by polynomial functions of the part's position with degree n ≤ 2, and simulations suggest that all fields with degree n ≤ 1 can be generated by slightly more general plate motions. These fields can be used to perform many useful manipulation tasks such as linear conveyance, convergence to/divergence from an arbitrary line, convergence to/divergence from an arbitrary point, rotation about a stationary point, and friction coefficient based sorting.;Finally, we model a general class of flexure-based parallel manipulators with 6-DoF rigid plate end effectors such as the PPOD2. We present an iterative learning controller that drives the acceleration of the plate to a desired periodic trajectory in R6 . We then discuss how to optimally design these manipulators for generating asymptotic velocity fields. |
