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98 Mutibody Systems Approach to Vehicle Dynamics
corresponding 5 mm of travel at joint 03. Note again that the ordering and
orientation of the markers defining the coupled joints is critical if the correct
physical representation of the system is to be obtained. At joint 03 the
motion is that of the I marker relative to the J marker in the positive direction
of the z-axes of the markers. At joint 04 the motion is taken to be a positive
rotation of the I marker relative to the J marker about the z-axes of the
markers. The coupler does not take into account mechanical features such
as play in the joints or backlash and as such does not model the reaction
forces within the real mechanism. The coupler also does not consider one
joint to drive the other. This will be a function of other forces defined elsewhere
in the system model. As with the motion statement a degree of freedom
is lost to the system as the coupler has enforced a kinematic relationship
between the motion at joints that cannot be changed by external forces.
3.2.8 Degrees of freedom
Having introduced the modelling of rigid bodies and constraints it is now
possible to describe the determination of the degrees of freedom (DOF) in
a mechanical system. The starting point for this is to consider that any freefloating
rigid body in three-dimensional space will have six degrees of
freedom as shown in Figure 3.18. For the vehicle body shown here and for
the handling simulations that will be discussed later the body will have no
direct constraint connecting it to the ground part. The only contact will be
through the forces and moments generated by a tyre model. For the axis
system shown here the vehicle will have degrees of freedom associated
with translational motion in the longitudinal direction X, the lateral direction
Y and the vertical direction Z. The rotational motions will involve roll
about the x-axis, pitch about the y-axis and yaw about the z-axis. For
vehicles such as ships and aircraft the terms surge, sway and heave are used
to describe the translational motions but these are not commonly used
in vehicle dynamics. It should also be noted that for the examples in this
text the x-axis is taken to point towards the rear of the vehicle where in
other texts discussing vehicle motion this is often forward to be consistent
with the normal direction of travel.
VERTICAL
Z
LONGITUDINAL
X
YAW
Z G
ROLL
X G
Y G
GRF
Y
LATERAL
Fig. 3.18
PITCH
Degrees of freedom associated with an unconstrained rigid body