| he problem of immobilizing an object by placing "fingers" (or points) on its boundary occurs in the field of dexterous manipulation, manufacturing and geometry. In this dissertation, we consider the purely static problems of good grasp and fixture set synthesis, and explore their connection to problems in computational and combinatorial geometry. Two efficient randomized approximation algorithms are proposed for finding the smallest cover for a given convex set and for finding the largest scale by which a convex set can be scaled and still be covered by a cover of a given size. These algorithms have applications to finding a good grasp or fixture set. An... |
