Accession Number:

ADA282724

Title:

Minimal Fixturing of Frictionless Assemblies: Complexity and Algorithms

Descriptive Note:

Corporate Author:

CARNEGIE-MELLON UNIV PITTSBURGH PA ROBOTICS INST

Report Date:

1994-04-01

Pagination or Media Count:

48.0

Abstract:

In many assembly tasks, it is necessary to insure the stability of a subcollection of contacting object. To achieve stability, it is often necessary to introduce fixture elements also called fingers in some work to help hold objects in place. In this paper, the complexity of stabilizing multiple contacting bodies with the fewest number of fixture elements possible is considered. Standard fixture elements of the type explored in previous single- object grasping work are considered, along with two generalized fixture element variants. The types of stability considered are form-closure complete immobility of the assembly stability with respect to a specific external force and torque on each body and stability in the neighborhood of a specific external force and torque on each body. The major result is that for most of the combinations of fixture element varieties, and types of stability considered, achieving an optimal solution that is, finding a smallest set of fixture elements yielding stability is NP-hard. However, for many fixturing problems it seems likely that suboptimal, yet acceptably small solutions can be found in polynomial time, and some candidate algorithms are presented

Subject Categories:

  • Cybernetics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE