ComputerAided_Design_Engineering_amp_Manufactur.pdf

FIGURE 3.6
contact point. The geometrical information is then used to determine the components of the normals
for all polygons (i.e., faces) and also to generate views of the workpiece for the purpose of display and
verification. Let the equation of the polygon (i.e., face) be given by:
© 2001 by CRC Press LLC
Schematic diagram of multi-axis fixture modules.
(3.1)
where A,
B,
and C are the components of the normal, and D is a constant. The coefficients A,
B and C
describing the equation of a polygon (i.e., face) are proportional to the areas of the projections of the
polygon onto the YZ,
XZ,
and XY planes, respectively. Thus, the coefficients A,
B,
and C may be easily
determined using the Newell formulation. The next operation in the preprocessor phase is to retrieve
inertial properties (e.g., center of mass, etc.) and store this information for future use. The preprocessor
software must also provide facility for retrieval of the previously generated data, if any.
Fixture Configuration Planning
AX � BY � CZ � D �
0
The planning phase involves specification of the location of the fixture modules by determination of the
contact positions on the workpiece in the CAD environment. There is a total of 12 degrees of freedom,
six linear movements ( �x,
�y,
�z,
�x,
�y,
�z),
and six rotational movements (clockwise or counterclockwise
around each of the three axes) associated with a body that is totally unconstrained as shown
in Figure 3.9(a). The positive location of a workpiece is generally guaranteed if it is in contact with three
points in the first plane, two points in the second plane, and a single point in the third plane, as seen in
Figure 3.9(b). This is the traditional three-two-one rule (i.e., 3-2-1 location rule). 25