Force Closure Grasps of High Quality

We study grasps of multiinger dexterous hands under the point contact model. Speciically, we are interested in high-quality force closure grasps. We abstract the problem into the space of force/torque wrenches where the quality is proportional to the magnitude of the largest wrench expressed as a non-negative combination of the grasp wrenches. This abstraction enables us to solve the problem by application of quantitative versions of Steinitz's theorem. We prove such a version by a geometric construction and specify an algorithm to select d(d + 3)=2 wrenches (or points) in d dimensions that guarantee quality 1=d. This is the rst general solution, with practical signiicance, to the grasping problem. We also modify the problem by letting the quality be part of the input and show a lower bound as well as a heuristic solution for determining the number of wrenches required. The extension of the antipodal algorithm leads to interesting observations but fails to generalize. Lastly, we impose some structure on the wrench space, which is more realistically viewed as a generalized cylinder. This suggests satisfactory solutions for certain speciic cases.