Theories are presented which describe the grasping of an arbitrary planar object using frictionless point contacts. The theories are based on screw algebra and line geometry, and allow the mapping of the contacts onto an image space, with the study of the necessary relationships between the contacts and the determination of whether these contacts can form a successful grasp. An identical mapping is also used for the relevant surface properties of the shape of the object to be grasped, so that synthesis of grasps can be achieved. Examples of the application of these theories are given.

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