“Unilateral” Fixturing of Sheet Metal Parts Using Modular Jaws with Plane-Cone Contacts

K. “Gopal” Gopalakrishnan‡, Matthew Zaluzec†, Rama Koganti†, Patricia Deneszczuk† and Ken Goldberg‡ ‡IEOR & EECS, U.C. Berkeley and the †Ford Motor Co.
<Initiated: March, 2002> 
ALPHA Lab, University of California, Berkeley. 
 

Examples of v-grips.

Abstract

To fixture sheet metal parts for welding, we propose “unilateral fixtures” consisting of modular fixturing elements that lie almost completely on one side of the part. These are based on cylindrical jaws with conical grooves which provide the equivalent of 4 point contacts.

We propose a two-phase procedure for designing unilateral fixtures. The first phase is a geometric algorithm that assumes the part is rigid and computes vg-grips (vertex-groove grips). The vg-grip algorithm uses a fast sufficient test for immobility to generate a list of vg-grips and find bounds on jaw cone angles for each. The second phase is a fast heuristic procedure that uses FEM to arrange secondary contacts to reduce part deformation.

For a part described by n concave “virtual vertices”, a list of vg-grips and minimum half cone angles for each vg-grip can be generated in O(n2) time. We also propose a quality metric based on the sensitivity of the part’s orientation to an infinitesimal relaxation of the jaws that can be evaluated in constant time for a given fixture. For an FEM model with m nodes, the second phase takes O(m3r) time to arrange r secondary contacts for each vg-grip.

Introduction

Sheet metal parts are created by stamping and bending planar sheets. To assemble industrial parts such as automotive bodies and large appliances, such sheet metal panels need to be accurately located and held in place by fixtures to permit welding. Existing fixturing methods are usually:

1. Bulky (often larger than the part they are holding).
2. Dedicated to each product model (and hence require a large investment in materials for each model).
3. Designed by human intuition (and hence subject to delays and errors in design).

Our goal is to develop a new approach to fixturing based on fixtures that are:

1. Compact, using a reduced set of contacts (so that the fixture and loading mechanism lie almost completely on one side of the part, to maximize access for welding and inspection).
2. Modular (so that the fixture hardware can be reconfigured quickly and reused for different product models).
3. Designed by CAD/CAM software that can analyze the sheet-metal geometry and automatically design the fixtures based on mathematical models.

This paper is a first step in this direction. We propose fixturing with two types of modular jaws. One type consisting of cylindrical jaws with conical grooves formed by a pair of coaxial frustums joined at their narrow ends. These jaws contact part edges as illustrated. The second type provides point contacts that support the part from the interior. We refer to these as “unilateral fixtures”: the fixturing hardware lies almost entirely on one side of the sheet metal part to maximize access for operations such as welding and inspection.

We present a two-phase design procedure for unilateral fixtures. The first phase is a geometric algorithm that assumes the part is rigid and locates one pair of primary jaws to immobilize the rigid part. This phase is purely geometric. The second phase adds additional secondary jaws using a heuristic Finite Element Method (FEM) procedure to reduce deformation to within specified tolerances. This two-phase approach allows us to reduce the number of FEM iterations in contrast to pure FEM methods.

Implementation for an example part.

Prototype unilateral fixture.

Papers

  • K. “Gopal” Gopalakrishnan, Matthew Zaluzec, Rama Koganti, Patricia Deneszczuk and Ken Goldberg, “Unilateral” Fixturing of Sheet Metal Parts Using Modular Jaws with Plane-Cone Contacts, submitted to IEEE ICRA 2003.[postscript]

Acknowledgements:

    This work was supported in part by the Ford Motor Co. and National Science Foundation under DMI-0010069. Research funding was also provided by Adept Technology, and California State MICRO Grant 00-032.