A System for Automated Fixture Planning with Modular Fixtures

3.2. Interference Checking
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The location of every fixture component in a fixtllre plan should be determined so that they do not
interfere with part geometry, cum paths, and odw fixture compa0entF. Currently, when determining the
location of a fixture component, a tool designer relies on visual inspection to duect any interference. Since
swept volumes of cutter paths are not explicitly displayed on a typical CAD-based fixtllre planning system,
the visual inspection of the tool designer is imprecise in nature; behhe tends m determine the location of
fixture components futher away from any cutter paths than necessary in order to avoid any interference
with cutter paths. A precise analytic tool for inrerference checking would not only speed up the process,
but also help demmh !matbn%.of fLm compcnents withoat h g . too consa~ave even under
complex cutting operarioas.
F’art geometry and future components’ geomeay can be explicitly stored in a data- and displayed on a
graphics terminal. Ihe swept volume of a cutter path can be cooshucted in the spce as a polyhedral object
using the cutter’s diameter and the cutter path specified in the, pan coordioares. The details used m
consrmcf the swept volumes will be disc& in chapter 4.
Although algarithms exist which detect interference between LWO objects in space, tbese algorithms ax
computationally intensiva Ihm, the possibility of interference seeds to be checked first by simpler
schemes m speea up the analysis. One simple sheme is to check interfenacc by comparing the minimal
and maximal x, y, and z cmxdmam . of two objects dcsaibad Wim respect to an arbitrary Cartesian
A A A A A A
coordinate system. Let &, y-. k, &, y-, and & be the minimal and maximal x, y, z
coordinates of an ob* k Also, let L, yk, &, Cu, yL be the minimai and maximal x. y, z
coordinates of an object B. Then, if any of the following sufficiear mndirioas are Wed. there is no
interference between objects A and B
A B
when x- > x,,,~, or
A B
when y- > ymu. or
A B
when > q-, or
A B
when xnux < h, or
A B
when ym < y-, or
A B
when m, < L.
Figure 3-1 shows three objects in the Carresian coordinate system (For brevity, only x and y coordinates
are shown in 2D). While. the mordiaate cMnplnison ~eognizes that objects (A and B) and (A and C) do
not interfere at ail, it detects the pospibility of imaferenm between objects B and C. Thns, an intersection
checking algorithm should be used to refine the wwez at &is point
Another simple scheme to check the possibility of interference between two objects is to bound each
object by a sphere oracylinderand check the sum of two radii and the distance between sphere centers
(Figure 3-2) [Kim 851.