ComputerAided_Design_Engineering_amp_Manufactur.pdf

FIGURE 9.6
FIGURE 9.7
Geometric Interpretation of Spatial Relationships
A spatial relationship can be interpreted as a constraint imposed on the degrees of freedom between mating
or interacting features. In every mating feature (Nnaji, 1990-1; Nnaji, 1990-2), a mating-coordinate frame
is attached. A mating-coordinate frame is derived to represent the coordinate frame needed for expressing
degrees of freedom. The origin and axes of the mating coordinate frame are determined by mating
condition or degrees of freedom of mating.
In plane feature, a mating-coordinate frame is on the plane with Z-axis
point out of the plane (Figure
9.3(a)). In cylindrical feature, the X-axis
of the mating-coordinate frame is coincident with the center line
(Figure 9.3(b)) and, in spherical feature, the origin of the mating frame is coincident with the center of the
sphere (Figure 9.3(c)). The degrees of freedom between mating components can be geometrically represented
and interpreted in accordance with mating geometry. The element of degrees of freedom to describe spatial
relationships can be described as follows:
1. lin_n:
linear translation along n-axis,
where n contains a fixed point and a vector;
2. rot_n:
rotation about n-axis,
where n contains a fixed point and a vector;
3. plane_n,
cyl_n,
sph:
translating along a planar, cylindrical, or spherical surface, etc.
The degrees of freedom of a part can now be expressed as {degrees of freedom of moving along
the feature of relative mating part :: degrees of freedom of moving the part with respect to itself} ,
where the relative mating part is fixed. For example, in Figure 9.3(b), part p1 is against part p2 over
a line. The degree of freedom for p1 with respect to p2 describes the relative motion that maintains
a line contact. p1 may move along the mating planar face of p2 while maintaining fixed orientation.
This can be described as the equation for an infinite plane, Ax+By+Cz�D.
For p1 itself, p1 can rotate
about the z-axis,
which gives a new orientation about the contact line, and p1 can rotate about x-axis
© 2001 by CRC Press LLC
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