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Currently, most efficient algorithms for force-closure analysis and dynamic force distribution utilize linear programming, but friction models are nonlinear. Substituting polyhedral cones for circular cones of Coulomb friction realizes the linearization of the frictional point contact constraint. So far, however, there is no approach to soft finger contact. This paper presents such an approach. Then the foregoing algorithms can be extended to grasping with soft finger contact. Herein an optimal force distribution algorithm for soft multifingered grasps is developed with an illustrative example.