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This paper examines the grasps attainable by mechanical hands with two opposing articulated fingers. Such grasps are called planar, since all forces lie in plane defined by the contact points and the center of mass of the object. Assuming the contact interaction can be modeled by point contact with friction we obtain the equilibrium equations parametrized by the magnitude of one of the applied normal forces. Thus a curve of possible grasps in friction angle space is obtained from which an optimum may be chosen. Three examples are discussed in detail.