A fixture is a critical component of the machining system. Since machining is often characterized by periodic forces and vibration, consideration of dynamic effects in fixture design is crucial. The primary objectives of this thesis are (1) to develop and validate models for quasi-static and dynamic analysis of fixture-workpiece systems, and (2) to develop a fixture synthesis method that considers the fixture-workpiece system dynamics in determining the optimum fixture layout and clamping forces.; In the quasi-static model, the frictional contact between a fixture element and the workpiece surface is modeled as an elastic half-space subjected to distributed normal and tangential loads. The model is experimentally verified and found to yield accurate predictions of the normal and tangential contact forces for different clamping forces. A dynamic fixture-workpiece model is also developed to simulate the workpiece motion in the fixture during machining. The model is capable of simulating stick, slip, and loss of contact conditions at a fixture-workpiece contact. Also, the model includes the effect of interfacial slip damping arising from micro-slip at the fixture-workpiece contacts. For the range investigated, the effect of interfacial slip damping on the workpiece motion is found to be significant.; The quasi-static and dynamic layout optimization algorithms are shown to significantly reduce the workpiece location error induced by the contact deformation. For the quasi-static clamping force optimization, the theoretical minimum clamping force obtained from the algorithm compares favorably with the measured values. In the dynamic synthesis case, an iterative fixture layout and clamping force optimization procedure that yields the "best" improvement in the objective function value is presented.
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