On the Stability of Grasping Three Fingers And a Planar Polygon

Cover On the Stability of Grasping Three Fingers And a Planar Polygon
On the Stability of Grasping Three Fingers And a Planar Polygon
C Marc Bastuscheck
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Note, however, that with friction it is possible for the triangle to rotate about one of the fixed fingers and be pulled away from contact with the other - a motion not possible in the no friction case. For example, suppose that in Fig. 2a there is sufficient friction that the triangle does not slip against finger b. The resulting motion would be rotation about finger b, causing the triangle to move away from finger a. If the force applied by each finger is directed between the other two finger...s this cannot occur, and any slipping results in a grasp closer to the non-friction grasp.
The theory of grasping a triangle is trivially extended to grasping a convex polygon with three fingers in the frictionless case. Three sides are chosen, and extended to make a triangle. (If two parallel sides are chosen, the procedure is not applicable, and it is well known that three fingers cannot grip a rectangle stably without friction. ) The theory is unchanged except that the region P is determined by the actual sides of the polygon, not by their extensions to the triangle.


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