LIBRARY ı6ıul 0) - Cranfield University

m23 =z- mi1m32 (3.31)
rn33 = mmu - mum21
(3.32)
It is worth noting that the CAD (workpiece) co-ordinates frame is assumed to
be parallel with the table co-ordinates frame. This was assumed in order to allow
different jigging systems to be used in the table. Hence, the transformation matrix that
describes the CAD (workpiece) co-ordinates frame relative to the table co-ordinates
frame should have the form shown in equation (3.33) which describes a parallel
displacement of the table co-ordinates frame in the direction of the vector po.
MCAD _010
100 pok (3.33)
poyfab'e
table 001 po le
0001
The transformation matrix which transforms the data relative to the CAD
world co-ordinates frame to the robot world co-ordinates frame is then obtained by
pre-multiplying the matrix shown in equation (3.33) by the matrix shown in equation
(3.21). This is shown explicitly in equation (3.34).
MRoC4D
bot = MRtable
obat
xm
(3.3tab 4) )
After applying the transformation of equation (3.34) to the geometrical data
stored in the CAD database all co-ordinated data are referred to the robot world coordinates
frame. This makes it possible to generate the poses necessary for the robot
to carry out the welding operation.
Off-line programming is performed by defining a series of points in space with
co-ordinate frames attached to them, thus providing the positions and orientations
that the robot end tool must achieve. The robot controller calculates the movements
of the robot arm such that a co-ordinates frame attached to the tool (tool co-ordinates
frame) matches the co-ordinates frames defined in the off-line generated program, i. e.
both origins coincide and the co-ordinate axes are parallel.
In the design stage of the weld joints approach vectors are calculated and
stored in the CAD database. These vectors define the orientations with which the
welding torch should approach the joint and carry out the welding operation.
However, only one vector is not enough to define the attitude of the torch, since the
angle of rotation about this approach vector would be undefined. Hence, a second
vector must also be specified to fully define the torch attitude. In order to accomplish
this, a co-ordinates frame will be attached to the welding torch thus defining the
welding torch attitude relative to the robot world co-ordinates frame. This can be
visualised in Figure 3.5 and more specifically, in Figure 3.14, which shows a side view
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