Grasp Functions

When manipulating parts, it is important to determine the orientation of the part with respect to thegripper. This orientation may not be known precisely or may be disturbed by the act of grasping. It isin some cases possible to use mechanical compliance to orient parts during grasping. It was recentlyshown [14] that any part with polygonal boundary can be oriented and grasped in this manner using aparallel-jaw gripper.Many of the curves currently used in engineering design are algebraic but non-linear. Although thesecurves can be approximated as polygons for the purpose of visualization, such approximations can leadto false conclusions about mechanical behavior. In this paper we consider the class of parts whose planarprojection has a piecewise algebraic convex hull.Our primary result is a proof that a grasp plan exists for any such part. We give a planning algorithmthat produces the shortest plan and runs in time O(n2 logn+ N ), where n is the number of transitionsin the grasp function and N is the length of the plan produced. We believe this to be the first paper toaddress the problem of manipulating algebraic parts when their initial orientation is unknown.