Unilateral Fixtures for Sheet Metal Parts with Holes

Kanakasabapathi Gopalakrishnan1, Matthew Zaluzec2, Rama Koganti3, and Patricia Deneszczuk4
(Professor Ken Goldberg)
Ford Motor Co. and (NSF) DMI-0010069

Existing fixtures for holding sheet metal parts are generally bulky, part-specific, and designed by human trial-and-error. In this project, we propose unilateral fixtures, a new class of fixtures that addresses these limitations using modular fixturing elements that lie almost completely on one side of the part, maximizing access on the other side for welding, assembly, or inspection. The primary holding elements are cylindrical jaws with conical grooves that expand between pairs of part hole corners; each grooved jaw provides the equivalent of four point contacts and facilitates part alignment during loading. We present a two-phase algorithm for designing unilateral fixtures. The first phase assumes the part is rigid and uses 2D and 3D kinematic analysis of form-closure to identify all pairs of candidate jaw locations. For this analysis we propose and prove three new grasp properties for 2D and 3D grips at concave vertices, and a new quality metric based on the sensitivity of part orientation to infinitesimal relaxation of jaw position. The first phase also sets bounds on jaw cone angles. The second phase addresses part deformation with a finite element method (FEM) analysis that arranges secondary contacts at part edges and interior surfaces. For a given sheet-metal part, given as a 2D surface embedded in 3D with n concavities and m mesh nodes, the kinematic algorithm takes O(n2) time to compute a list of all unilateral fixtures ranked by quality, or a report that none exist for that part. The FEM deformation analysis arranges r secondary contacts considering m part elements in O(m(sup>3r). We have implemented both phases of the algorithm and report alignment data from experiments with two physical parts.

Figure 1: Unilateral fixture used to hold sheet metal parts

Figure 2: Addition of secondary jaws to minimize deformation as calculated using a FEM mesh
1Graduate Student (non-EECS)
2Professor, Ford Motor Co.
3Outside Adviser (non-EECS), Ford Motor Co.
4Outside Adviser (non-EECS), Ford Moror Co.

More information (http://alpha.ieor.berkeley.edu/vggrip/) or

Send mail to the author : (gopal@ieor.berkeley.edu)

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