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

The thesis presents an approach to the fixture loading planni ng problem. That is, to plan the applied forces on the workpiece in order for it to be l oaded into a manufacturing fixture. In our approach, a sequence of applied forces on the mass cent er 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 wit h t o engines, Motion Planning Engine and Dynamics Simulation Engine. Motio n Planning Engine uses the current workpiece position as the input and generat e its new velocity or the applied force on it. Dynamics Simulation Engine is a reverse , it generate the new position of the workpiece from the current position, veloci ty, and applied force on the workpiece. Dynamics Simulation Engine is the foundation of the whole sy stem. The engine maintains a realistic dynamics scene in either automatic pl anning or haptic guided planning. It serves as an off-line verification of the planne d motion so that the generated scheme can be ‘played’ with the engine. In this the sis, we developed a three-dimensional dynamics simulation engine based on an e xte sion of the explicit time-stepping scheme and an application of the differentia l i clusion process introduced by J. J. Moreau. In the engine, we developed the contact propagation method for a general three-dimensional rigid-body system with mul tiple unilateral contacts without any bilateral constraints. We considered the gener al 3-dimensional case of smooth surfaces. We use a differential model of the kinemati cs of surface contact for contact point tracking. While the contact kinematics of general 3-dimensional i surfaces considerably increase the complexity of the dynam ic nalysis, the generalization to 3D would have to deal with the nonlinearity intr oduced by Coulomb’s friction law, compared to the 2D case where the friction forc e is essentially linear. No such a generalization is yet reported in the literature. The goal of Motion Planning Engine is to make the workpiece in co tact with all the six locators. Here, the workpiece is initially at an a rbitrary place with not contact with any locator. The planning follows a simple sche me of monotonously increase the number of contacts with locators. The sequence of locators to be contacted is assigned by the user in the beginning of the plannin g. The major effort is on the fine-motion planning of approaching a new contact wh ile maintaining existed contacts. The difficulty comes when there are multiple contacts. Here we use a two-step scheme. First, finding the velocity of the workpie ce that can approach the new locator while maintaining contacts with old locator s. This can be formulated as a linear programming problem. Second, finding the ap plied force to realize such motion. This step is a central issue in the planning beca use for the rigid-body model, the solution to multiple frictional contacts is gene rally indeterministic. One possibility is jamming, that is, the applied force cannot mo ve the workpiece even with less than six contacts. In this thesis, we will give crit eria to determine whether the jamming will happen, and we will also derive an algorithm to generate the nonjamming applied force. We also developed a haptics guided planning system incorpor ating human interaction and force-feedback with a Phantom. With this system t he user can either edit the automatically planned scheme if it is not satisfactory o r generate the scheme manually in case the automatic planning fails.