4569846498

Multibody systems simulation software 83
{ZG} 1
Z
Body n
Z n
{XG} 1
Z G
GRF
XG
O 1 Y G
{QG} 1
01
GROUND
X
LPRF
Q
O n
X n
Y n
Fig. 3.8
method
Orientation of the local part reference frame using the X-point-Z-point
An alternative method of orientating a reference frame is referred to as the
X-point-Z-point method and involves defining the co-ordinates of a point
that lies on the Z-axis of the positioned frame and another point that lies in
the XZ plane of the positioned frame. This is illustrated in Figure 3.8 where
this method is used to orientate the local part reference frame relative to the
ground reference frame. The position of the local part reference frame, O n ,
is defined, as stated earlier, by the vector {QG} 1 . The point Q is coincident
with O n . The position of Z is defined to by {ZG} 1 . The distance of Z from
G along the Z-axis of O n is arbitrary. The position of X is defined by {XG} 1
and may lie anywhere in the XZ plane other than on the Z-axis of O n .
In order to determine the exact orientation of the positioned frame the vector
cross product can be applied to first obtain the new Y-axis. The vector
cross product of the new Y-axis and the new Z-axis can then be used to find
the new X-axis. It will be seen later that if only either the X- or Z-axis is
important then it is only necessary to specify either {XG} 1 or {ZG} 1 .
The X-point-Z-point method can also be used to orientate a marker reference
frame relative to a local part reference frame as illustrated in Figure 3.9.
The notation is changed using QP, XP, ZP instead of the QG, XG, ZG used
to orientate the local part reference frame. It should also be noted that as
with {QP} n the components of {XP} n and {ZP} n would be resolved parallel
to the axes of the local part reference frame O n .
As discussed earlier if the definition of the local part reference frame is
omitted the local part reference frame is taken to be coincident with and
parallel to the ground reference frame when setting up the model. The orientation
of the marker reference frame O m is then defined relative to the ground
reference frame. As shown in Figure 3.9 the position vector {QP} 1 would
define the position of the marker reference frame and similarly {XP} 1 and
{ZP} 1 would now be used to define the orientation. As with {QP} 1 the x, y
and z components of {XP} 1 and {ZP} 1 are now resolved parallel to the
ground reference frame O 1 . It should be noted that the methods described
here have been extended and are more general including the capabilty to
implement parameter-based reference frames.