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In this paper, we present a novel algorithm for computing three-finger force-closure grasps of 2D and 3D objects. In the case of a robot hand with three hard fingers and point contact with friction, new necessary and sufficient conditions for 2D and 3D equilibrium and force-closure grasps have been deduced, and a corresponding algorithm for computing force-closure grasps has been developed. Based on geometrical analysis, the algorithm is simple and only needs a few algebraic calculations. Finally, the algorithm has been implemented and its effectivity has been demonstrated by two examples.