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An enveloping grasp is one for which the fingers surround the object and hold it securely against the palm. It is the kind of grasp that we use to hold the steering wheel of our car or to hold a wet ice cube. In the case of the ice cube and other slippery objects, we must use an enveloping grasp, because friction forces are small. In this dissertation we are particularly interested in achieving an enveloping grasp of an object by manipulating it away from its supporting surface with an articulated hand. To solve the problem, we make several extensions to the firmly established kinematic equations of grasping and develop a linear program to predict the instantaneous motion of a slippery object during its manipulation. We define the liftability regions for any two-dimensional object and develop a graphical method to determine them. The liftability regions are used to select the initial grasp of the object. Then lift planning strategies determine how to manipulate the object from its initial position into an enveloping grasp in the hand. After achieving envelopment, the grasp is adjusted, maintaining its enveloping character while optimizing an appropriate objective function. These three planning steps, initial grasp selection, lift planning, and grip adjustment are used to determine a grasping plan. The motion linear program is used as the basis of a simulator which solves the equations of motion of the manipulated object. Given a grasp plan, the simulator is used to verify its validity.