Multi -rigid -body contact dynamics and haptic interaction for fixture loading planning

The thesis presents an approach to the fixture loading planning problem. That is, to plan the applied forces on the workpiece in order for it to be loaded into a manufacturing fixture.;In our approach, a sequence of applied forces on the mass center of the workpiece is planned. The applied forces will push the workpiece to get in contact with all the locators. For this purpose, we developed a system with two engines, Motion Planning Engine and Dynamics Simulation Engine.;Dynamics Simulation Engine is the foundation of the whole system. The engine maintains a realistic dynamics scene in either automatic planning or haptic guided planning. It serves as an off-line verification of the planned motion so that the generated scheme can be 'played' with the engine. In this thesis, we developed a three-dimensional dynamics simulation engine based on an extension of the explicit time-stepping scheme and an application of the differential inclusion process introduced by J. J. Moreau. In the engine, we developed the contact propagation method for a general three-dimensional rigid-body system with multiple unilateral contacts without any bilateral constraints.;The goal of Motion Planning Engine is to make the workpiece in contact with all the six locators. Here, the workpiece is initially at an arbitrary place with not contact with any locator. The planning follows a simple scheme of monotonously increase the number of contacts with locators. Here we use a two-step scheme. First, finding the velocity of the workpiece that can approach the new locator while maintaining contacts with old locators. This can be formulated as a linear programming problem. Second, finding the applied force to realize such motion. This step is a central issue in the planning because for the rigid-body model, the solution to multiple frictional contacts is generally indeterministic. One possibility is jamming, that is, the applied force cannot move the workpiece even with less than six contacts. In this thesis, we will give criteria to determine whether the jamming will happen, and we will also derive an algorithm to generate the non-jamming applied force.