A fixture is a device that holds a part for machining, assembly, inspection, etc. Fixturing is concerned with ``constraining, despite the application of an external wrench, all motions of a rigid body'' [Wentink et al., 1996]. That is, given a rigid body (a part) we wish to hold it firmly (with a fixture) such that the part cannot translate or rotate. In our case, we are concerned with a subset of this general problem where: the part is two dimensional and polygonal, and the points of the fixture are restricted to a discrete set of possible locations.
This problem is known as modular fixturing of planar, polygonal parts. The workspace is a planar surface with holes drilled in some regular lattice, typically in a square-shaped pattern. A fixture is composed of a number of simple fixturing elements (fixels) that are placed in the holes, and can only be located where there is a hole - i.e. discrete set of locations as opposed to a continuum.
Two simple fixels are locators and clamps. A locator is simply a peg or pin that is inserted into a hole in the workspace. A clamp has a peg that fits in a hole, but it also has a piece that extends up to one unit out from the hole. This extension only happens along the axes of the workspace: north, south, east or west; it cannot extend in any arbitrary direction.
In general, we only need three locators and one clamp to fixture a sufficiently large, polygonal part [Wentink et al., 1996]. If a part is too small, it cannot be fixtured. A more thorough treatment of conditions for fixturing can be found in Zhuang et al. [1996].
For our purposes, a fixture is composed of three locators and one clamp. Our problem can then be stated as: given a part, find all fixtures to hold the polygonal part in form closure - i.e. immobilize it. Figure 1 shows an example of a part and a fixture.
Ordinarily, human expertise is required to synthesize a suitable arrangement of these elements to hold a given part [Hoffman, 1987]. Besides being time consuming, if the set of alternatives is not systematically explored, the designer may fail to find an acceptable fixture or may settle upon a sub-optimal fixture.
A complete algorithm to find all modular fixtures was described by Brost and Goldberg [1994]. Because it generates all possible solutions, the fixture design algorithm often generates counter-intuitive solutions that may be overlooked by even an experienced machinist, much as chess machines can play moves that look naïve at first glance but lead the experienced chess player to explore new variations.
The job is not necessarily complete after finding an acceptable fixture for a specified part. In the manufacturing industry, we often have to redesign a product. Usually, a new design requires a completely different fixture design, which costs both money and time. This tempts us to consider the following problem: given a planar polygonal part, and its fixture consisting of three locators and one clamp, is it possible to impose a design rule to specify how much the part shape can be modified such that the redesigned part can still use the same set of locators?
The original FixtureNet brought fixture design to the Web. We have extended FixtureNet to include interactive tools that allow the user to explore qualities of fixtures that are difficult to quantify.