Kinematic graspability of a 2D multifingered hand

We describe a solution to the problem of determining the kinematic feasibility of a dextrous hand to grasp a given object at a desired configuration in the two dimensional space. We refer to this problem as kinematic graspability. The kinematic configuration of a grasp is defined in terms of a set of contact pairs between the topological features of the hand and the object. We derive the sufficient conditions in order for the hand to make the desired contact and avoid collision. These conditions are then formulated as a constrained nonlinear global optimization problem, whose solution yields a definitive answer to kinematic graspability for a grasp configuration. Numerical examples are provided to illustrate the method.