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This paper presents algorithms for optimal grasping forces. The previous work reveals that contact forces with minimal sum or maximum of normal force components can be written as positive combinations of primitive contact forces, to which the corresponding primitive contact wrenches express the required resultant wrench as their positive combination with minimum coefficients in terms of the L1 or L∞ metric. On this basis, we first propose an algorithm to compute such a set of primitive contact forces and the minimum contact forces. Moreover, considering the uncertainty in the actual friction coefficient, we develop another algorithm to determine the minimum required friction coefficient and the corresponding minimum contact forces within a given limit on their magnitude so that such contact forces are more reliable in practice. As our algorithms do not rely on any general optimization technique, they are very efficient and easy to implement. These algorithms can also be used in grasp quality evaluation and optimal grasp planning.