This thesis examines the problems associated with simulating the assembly process using a geometric model of the assembly. In particular, we focus on the mechanics of the process. The parts are modeled as rigid bodies with polyhedral contact surfaces. Using a simple model of contact mechanics, we develop methods to disassemble assemblies addressing mechanical concerns such as stability and fixturing. Starting with the model in its assembled state, contact surfaces are derived. These form the basis to all of the assembly analysis. Non-penetration kinematic constraints are derived from the contact surfaces. Dynamics is modeled using the well known Newton's laws of motion.; As a first step to disassembly, two subassemblies that possess relative degrees-of-freedom are identified. For each of these subassemblies, grasp or fixture plans are synthesized. This thesis presents new results about the complexity of finding minimal grasps for assemblies. Methods to synthesize grasps are also provided. Given a grasp and available directions for motion, parts are moved by analyzing geometric constraints and detecting collisions. During the course of motion, each subassembly is tested for stability due to gravitational forces and changing contact forces. This thesis presents methods for testing stability as well as for synthesizing stable orientations. An exact characterization of the set of all stable orientations for an assembly is provided along with a method to compute the set.; The disassembly process is graphically displayed. This can be used by designers to address assembly concerns up-front during design stages. In order to make more detailed inquiries about the assembly process, this thesis also proposes some computer tools to act as design aids. All these tools use the same input representation of the design, and can be seamlessly invoked at any stage of disassembly.
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