# Assembly Sequencing and Fixturing

## Overview

The purpose of this project is to develop techniques for performing automatic assembly sequencing and fixturing concurrently. That is, given only a geometric description of a product, we wish to produce:
1. a sequence of part insertions which will assemble the product from its parts, and

2. a fixture to hold the product in place during assembly, such that each intermediate subassembly is stable under gravity and all part-against-part "insertion forces".
Unlike in previous assembly-planning research in the literature, the sequence and fixture are generated concurrently (rather than first one and then the other). This approach, called "sequence/fixture co-design", raises a host of new issues.

The long-term vision for this work is a CAD tool which can provide immediate feedback to a team of product designers about the ease of assembling the proposed product.

# Atlas

Recently-developed techniques for sequence/fixture co-design have been implemented for the case of planar assemblies, in a prototype system called Atlas.

Given a geometric description of an assembly, Atlas will generate an assembly sequence and a fixture for that assembly. The fixture is represented as a continuum of possible fixturing locations, rather than as a finite set of discrete elements.

An example of Atlas' output appears below. The yellow line shows the final (non-minimized) fixture; the corresponding assembly sequence inserts the rightmost part downward, then all other parts from left to right. This assembly and every intermediate subassembly are guaranteed to be stable under gravity and all insertion forces.

Atlas (the Greek mythological one) fixturing the heavens
 ```Assembly Sequence: Starting with the empty fixture, Insert part 6 in direction (0, -1). Insert part 3 in direction (1, 0). Insert part 2 in direction (1, 0). Insert part 1 in direction (1, 0). Insert part 0 in direction (1, 0). Insert part 4 in direction (1, 0). Insert part 5 in direction (1, 0). ```

Although the current implementation of Atlas is restricted to planar assemblies, all of its techniques extend to the three-dimensional case as well.

## Papers

B. Romney,
"Atlas: An Automatic Assembly Sequencing and Fixturing System". Proc. Intl. Conf. on the Theory and Practice of Geometric Modelling, Tübingen, Germany, October 1996. (To appear.)

B. Romney, "Issues in the Co-Design of Assembly Sequences and Fixtures".Manuscript.

## Related Web Sites

The Assembly-Planning Group at Stanford, and its papers and publications.

The STAAT project in assembly sequencing.
This project was in many ways the forerunner of Atlas, and was the subject of an award-winning paper.