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ComputerAided_Design_Engineering_amp_Manufactur.pdf

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FIGURE 3.18 Minimum separation test between the horizontal supports.<br />

(view from the above); one of the performing height adjustment operation on one of the horizontal<br />

supports. The following mathematical formulation may be formed as a general constraint for this case.<br />

or<br />

© 2001 by CRC Press LLC<br />

�CC �GHS ��HS ��<br />

�max �<br />

�CC � �GHS � �HS � � 0<br />

(3.33)<br />

(3.34)<br />

where � CC is again the distance between the coordinate frames of the tool application on the two<br />

horizontal supports, � GHS is the diagonal distance from the axis of the end-effector to the corner of the<br />

jaws when the jaws are open, and � HS is the distance from the datum to the corner of the adjustment<br />

lever on the other horizontal support. Again, � is the clearance specified.<br />

However, if the above geometrical constraint is not met, then a model boundary test must be performed.<br />

This is due to the fact that the two horizontal supports may be positioned such that the interferencefree<br />

fixture construction may or may not succeed, depending on the orientation of the fixture modules<br />

with respect to each other. It must be emphasized that the procedure is similar to those for all other<br />

fixture modules.<br />

Interference Formulation Between Convex Polyhedral Objects<br />

This phase of the interference detection again requires the geometrical data of the objects. The models<br />

of the various fixture modules and workstation have been created and are resident in the CAD data base.<br />

The major components of the workstation include the workpiece, the robot, the fixture bed, and the<br />

gripper. However, for the purpose of interference detection of the final fixture configuration, only the<br />

fixture modules and the gripper are used in the analysis. The objects are represented by clusters of convex<br />

polyhedral models. A boundary representation (B-rep) scheme may again be employed to describe each<br />

polyhedral model providing a description of the topology and a specification of dimensions. The topological<br />

representation is hierarchical in structure as shown in Figure 3.19. The representation consists of<br />

a list of:

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