ComputerAided_Design_Engineering_amp_Manufactur.pdf

where
where reaction forces at each locating contact point are denoted by F ij, and
or
where r ij are the moment arm of F ij and
© 2001 by CRC Press LLC
R x
(3.7)
(3.8)
(3.9)
(3.10)
(3.11)
(3.12)
Combining equations (3.10) and (3.12) provides a matrix equation in the form of AX � B. In this
formulation the positions of locating fixture modules may have to be reconsidered if the coefficients of
the matrix A are singular.
The analysis can also be carried out using screw pairs. This approach is chosen for this task because
screw representation of displacement and forces emphasizes the underlying representation upon line geometry
and the surface model of the workpiece. Detailed accounts of the screw theory and its development
may be found in Reference 29.
A set of fixture modules in contact with a workpiece can be modeled as a set of zero pitch wrenches
acting on the workpiece. This stems from the fact that any system of forces and couples can be reduced
to a wrench of a given intensity acting on a given screw. Therefore, we are interested in the total freedom
of the workpiece when it is acted upon by a set of wrenches (see Figure 3.11). Once the contact face has
FIGURE 3.11 Schematic diagram of wrenches acting on a workpiece. (From Reference 24. With permission.)
�
F 31
Ry � �(
F21 � F22) Rz � F11 � F12 � F13 3
4�i
��
M � rij � Fij i �1 j �1
M � M1� M2 � M3 3
�
Mi �
Fijai � 3, j
j �1
�i � { 1, 2, 3}