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After being located on a machine bed or a fixture, a workpiece will be actuated by gravity, cutting and inertia force during the machining operation. In order to keep the locating precision as well as the production safety, it is necessary to maintain the workpiece stability during the entire machining process. However, insufficient clamping forces cannot prevent the workpiece from translation and rotations whereas excessive clamping forces may cause strongly the improper workpiece deformations. Therefore, analysis and characterization of clamping forces are important in the fixture design task. This paper presents a mechanistic model for optimally determining the clamping forces. The fixture and workpiece are considered to be rigid bodies, and the model solution is proposed as a constrained quadratic optimization by applying the minimum norm principle. In order to efficiently compute the clamping forces, the constrained quadratic optimization is feasibly slacked into the constrained linear programming problem. The presented approach is conceptually simple and computationally efficient. It is particularly useful in the early stages of fixture design and process planning.