Optimal Three Finger Grasps

Cover Optimal Three Finger Grasps
Optimal Three Finger Grasps
James Demmel
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1 If the F^'s are nonzero equilibrium finger forces (i. E. Corresponding to / = and T = in (3)) and two of them are parallel then all three are parallel. We will return to the case of parallel forces later. Now, we look at the problem of finding e from the point of view of finding p which minimizes ^max = majc, |^j(p)|, where 6i{p) is the angle that p — Pi (and hence Fi) makes with the normal n, to the object. To be more precise, 0, (p) is the smaller angle between n, and the line through p and... p, . Notice that I tan(^max)| is the smallest coefficient of friction necessary to achieve the given grasp. The problem is one of minimizing the function max |^i(p)| of two variables (the coordi- nates of p) over a region of the plane. However, because of geometric considerations which will be explained in Section 4 the search for a minimum can be restricted to a finite set, thus yielding a finite algorithm to find the optimal p. The several points p where the minimum might occur will be listed in Theorem 4.

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