BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-87-1153
       ENTRY:: April 24, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Optimum Grip of a Polygon
        TYPE:: Technical Report
      AUTHOR:: Markenscoff, Xanthippi
      AUTHOR:: Papadimitriou, Christos
        DATE:: April 1987
       PAGES:: 24
    ABSTRACT:: It has been shown by Baker, Fortune and Grosse that any
               two-dimensional polygonal object can be prehended stably with
               three fingers, so that its weight (along the third dimension)
               is balanced. Besides, in this paper we show that form closure
               of a polygon object can be achieved by four fingers (previous
               proofs were not complete). We formulate and solve the problem
               of finding the optimum stable grip or form closure of any
               given polygon. For stable grip it is most natural to minimize
               the forces needed to balance through friction the object's
               weight along the third dimension. For form closure, we
               minimize the worst-case forces needed to balance any unit
               force acting on the center of gravity of the object. The
               mathematical techniques used in the two instances are an
               interesting mix of Optimization and Euclidean geometry. Our
               results lead to algorithms for the efficient computation of
               the optimum grip in each case.
       NOTES:: [Adminitrivia V1/Prg/19950424]
         END:: STAN//CS-TR-87-1153