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In this paper, we present a quantitative measure of multifingered grasps. The measure quantifies the capability of a grasp in firmly holding an object while resisting external loads and/or disturbances. It can also be used for qualitative test of closure properties (form closure and force closure). For planar grasps and frictionless three-dimensional (3-D) grasps, the quantitative measure can be computed efficiently by solving a set of linear programs, while for frictional 3-D grasps, it can be computed by solving nonlinear programs without linearization of the friction cone. By using the proposed quantitative measure, an algorithm for grasp synthesis on polygonal objects is developed. Rather than producing a single grasp configuration, the algorithm computes all grasps on a polygon that satisfy quantitative constraints, i.e., the value of the quantitative measure is greater than a predetermined positive constant. The approach has potential application in grasp planning with multiple optimality criteria.