TABLE OF CONTENTS Attawith Sudsang, Jean Ponce and Narayan Srinivasa, Beckman Institute, University of Illinois, Urbana, IL, USA
We address the problem of computing immobilizing fixtures and grasps of three-dimensional objects, using simple fixturing devices and grippers with both discrete and continuous degrees of freedom. The proposed approach is based on the notion of second-order immobility introduced by Rimon and Burdick [48, 49, 50], which is used here to derive simple sufficient conditions for immobility and stability in the case of contacts between spherical locators and polyhedral objects. In turn, these conditions are the basis for efficient geometric algorithms that enumerate all of the stable immobilizing fixtures and grasps of polyhedra that can be achieved by various types of fixturing devices and grippers. Preliminary implementations of the proposed algorithms have been constructed, and examples are presented.
We address the problem of immobilizing an object through a few contacts with simple modular fixturing elements, with applications in manufacturing (fixturing) and robotics (grasping). Our approach is based on the notion of second-order immobility introduced by Rimon and Burdick [48, 49, 50], and it is related to recent work in fixture planning by Wallack and Canny [57, 58], Brost and Goldberg [5], and Wagner, Zhuang, and Goldberg [56].
For concreteness, let us consider the fixturing device shown in Figure 1: it consists of two parallel plates with locator holes drilled along a rectangular grid, and of a set of spherical locators with integer height and radius. Four of...
