Issues in Dextrous Manipulation Grasping Compliance And Control

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Issues in Dextrous Manipulation Grasping Compliance And Control
Naomi Silver
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Reuleaux and Somoff determined that the form closure of a two dimensional object requires at least four wrenches and of a three dimensional object requires at least seven, where the wrenches are normal to the surface of the object.
[Mishra et. Al. 1987] gave the most general bounds on the number of fingers in the case of a positive grip; they also provided algorithms that find at least one such grip and run in time linear in the complexity of the object. Let d be the dimension of the object, an
...d mj be the degrees of freedom of a free object in c/-dimensional space. (This is three in two dimension and six in three dimension). In summary their results show that the object can be held at equilibrium by a positive grip of m^ + 1 fingers (four fingers in two dimensions and seven fingers 18 Issues in Dextrous Manipulation in three dimensions). If the object has no surfaces of revolution, then the object can be held with a closure gra^p by a positive grip of 2Tnd fingers (six fingers in two dimensions and twelve fingers in three dimensions), and any external wrench acting on the object can be balanced by a positive grip of mj fingers.

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