Stable transport of assemblies

Moving assembled parts from place to place is a common task in manufacturing. The general problem is: Given a static 2D or 3D structure and initial and goal states, design the parts, a fixture or end-effector, and a motion to preserve the assembly as it travels between states. This thesis addresses two variations of the stable transport of assemblies problem: stable carrying of assemblies on a fixture and stable pushing of planar assemblies across a horizontal surface. The parts are in frictional contact with one another and their environment. Nonlinearities associated with Coulomb friction give rise to mechanical analysis that is the reverse of the traditional "forces produce motion" analysis. Instead, I use linear constraint satisfaction problems (LC-SPs) to determine whether the contact forces are capable of producing a stable motion of the assembly.; LCSPs are used to determine approximate bounds on the set of stable motions. In the carrying problem, the set of stable motions is bounded by hyperplanes and quadratics. I present an algorithm which uses linear programming to solve for a near time-optimal translation of an assembly. I also present a linear program that computes maximum and minimum feasible accelerations for a position and speed along a given path. These feasible accelerations are then used to compute a near time-optimal trajectory along the path.; Calculating the set of stable motions is similar for the pushing problem. Indeterminacy in the support force for sliding and rotating parts yields a bounded set of possible support friction forces for each part. If the contact forces can balance the entire set of possible support friction forces then the motion is stable. If the contact forces can balance only some of the possible support friction forces then stability of the motion is "undecided." This analysis is verified by an experiment.