ComputerAided_Design_Engineering_amp_Manufactur.pdf

Fixture Module Location
An important objective of a reconfigurable fixturing system is to provide means for a rapidly validating
fixture construction program. 37 The fixture construction program, consisting of the placement, adjustment,
and retrieval operations, is too complex and must be generated automatically. The information
required by the interference detection module consists of the locations of the reference frames of the
fixture modules with respect to the assembly station coordinate frame. All tool center point (TCP)
locations for robot movements are determined by translation and rotation transformations of the reference
frame position on the fixture modules. The positioning and orienting of the fixture module are
performed in four-dimensional space: three to position and one to orient. Therefore, only rotation about
the z-axis is required to orient the fixture module on the fixture bed, in the X-Y plane. The following
expression describes the nomenclature for the location description of fixture modules:
© 2001 by CRC Press LLC
HC Fij
→
Module TypePosition Frame Designation i� ( X, Y, Z��� , , , )
j Station
(3.22)
As an example, the location of reference frame for a horizontal clamp, retrieved from the planning
and verification software modules, is provided to the interference detection software module and is
specified by a six parameter field as below:
HC Fij A
�
HC FXj
, , , , ,
HC FYj
HC FZj
HC F�j
HC F�j
HC F�j
(3.23)
The first three parameters define the position (x, y, and z) and the last three parameters describe the
orientation (roll �, pitch �, and yaw �) of the parent reference frame (F) of the fixture module.
Furthermore, j is the number of fixture modules in any particular category (e.g., HC: horizontal clamp).
It must be noted that the roll and pitch parameters are zero but included only to be consistent for offline
programming purposes. Equation (3.24) describes the pose of the robot TCP during the placement
of the horizontal clamp on the fixture bed.
HC Pij A
�
HC PXj
, HCPYj, �ZHCP, HCF�j, HCF�j, HC F�j
(3.24)
where �ZHCP denotes the height of the robot end-effector with respect to the fixture bed during the
placement of the fixture module on the bed. The transformation from the reference datum on the fixture
module to various critical locations at which the robot is required to interact with the fixture modules
may be given as follows:
[ P]
� [ T]
[ �r]
(3.25)
where P is the pose of the robot TCP, T is the transformation containing the position and orientation
of the fixture module’s reference datum on the fixture bed, and �r is the appropriate distance from the
functional locations on the fixture modules. Thus, the above formulation may be expressed as follows:
cos�
�sin� 0 X 1 0 0 �R
sin� cos � 0 Y 0 1 0 0
0 0 1 Z 0 0 1 �Z
0 0 1 1 0 0 0 1
(3.26)