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Under a whole hand grasp, it may not be possible to generate grasping forces in all directions. Thus, the traditional techniques developed based on fingertip contacts is inadequate. In this paper, we decompose the contact force space into four orthogonal subspaces, each with a clear physical interpretation. Based on linear matrix inequalities (LMI's) representations of grasping constraints, we address and formulate the active force closure and the active grasp feasibility problems as LMI feasibility problems. Combining the effects of both active and passive forces, we propose a new cost index for the whole hand grasping force optimization problem. We further simply the force optimization problem for a whole hand grasp, which is active force closure.