ComputerAided_Design_Engineering_amp_Manufactur.pdf

Using the above equation, the following expressions may be written describing the robot TCP position
during the placement of horizontal clamps with respect to the fixture bed coordinate frame.
© 2001 by CRC Press LLC
(3.27)
(3.28)
(3.29)
where the �RHCP is the translation in the X-direction from the coordinate frame describing the reference
fixture position to that of the pick/place position, and �RHCCF is the initial (i.e., unclamped) clearance
between the contact surfaces of the horizontal clamp and the workpiece. As an example, Figure 3.15
shows various locations at which the manipulator is required to interact with the horizontal clamp in
order to perform pick/place and height adjustment operations. Therefore, functional locations on the
fixture module and robot TCP poses may be obtained using the above formulation in a similar manner.
Calculation of Interference
Collision avoidance requires magnitude and direction information; it is generally used for path planning
of robots providing alternative robot position. Thus, collision avoidance is not appropriate for application
in fixture planning. This is mainly due to the fact that the fixture modules must be at locations where
they would be in contact with the workpiece. The technique appropriate for fixture construction is
interference detection requiring only a true or false result. Therefore, we are only interested in interference
detection at critical locations during fixture construction.
The proposed approach utilizes three tests to predict if any interference occurs between the fixture
modules during the construction of the fixture. These tests include minimum separation, maximum
separation, and model boundary. The underlying reason for minimum and maximum separation tests
is to create a minimum region in which interference will occur, and a maximum region in which
interference will not occur, regardless of the orientation of the fixture modules (Figure 3.16). The model
boundary test is performed if the condition for minimum separation is met and the condition for
maximum separation is not, thus taking into account the orientation of the fixture modules. The strategy
and mathematical formulations for each test will be outlined using examples of cases involving interference
between horizontal supports. Cases of interference detection involving other fixture modules follow
similar hierarchical structure and formulations.
Minimum Separation
The test for minimum separation determines if the distance between the axes of the pick�place�adjustment
coordinate frames of the two horizontal supports is smaller than the minimum distance required such
that the bases of the two horizontal supports would not interfere with each other. Thus, if this condition
is not satisfied, regardless of the orientation of the fixture modules, the two horizontal supports will
collide during fixture setup. Figure 3.17 shows the schematic diagram of two horizontal supports located
so that the shortest distance between the base centers is obtained. The geometrical constraint may be
formulated mathematically as follows:
or
HC PXj
HC PYj
HC PZj
�
�
HC FXj
HC FYj
� ( �RHCP � �RHCCF) cos(
HCF�j) � ( �RHCP � �RHCCF) sin(
HCF�j) � Z � �ZHCP where Z � 0 @ fixture bed coordinate frame
�CC �HS ��HS ��
�min �
�CC � 2�HS � � 0
(3.30)
(3.31)