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54 Multibody Systems Approach to Vehicle Dynamics
Suspension strut
D
Body 6
Free-body diagram
D
{F D6G4 } 1
G
Body 4
G
{F G4D6 } 1
Fig. 2.24
Vector notation for line of sight forces
Z 1
M Pz
{M P } 1
M Py
Y P
O 1
1
X 1
M Px
Fig. 2.25
Vector representation of a moment
Considering next the equilibrium of the body shown in Figure 2.26 it can
be seen that a force acting at point P will produce a reaction moment at
point Q. In order to simplify the diagram only the components of the applied
force and the resulting moment are shown here. Since we are looking only
at the derivation of the moment at Q the reaction force at Q is also omitted.
The moment generated at point Q, which is the point where Body 2 is fixed to
the non-moving ground part Body 1, is designated as {M Q21 } 1 . Applying the
same principle as used for a force we would read this as the moment acting
at point Q, on Body 2 due to its connection to Body 1, with components
resolved parallel to the axes of reference frame O 1 . For convenience and to
assist with the interpretation of the derivation that follows the components of
the force {F P } 1 , the moment {M Q21 } 1 and the relative position vector {R PQ } 1
have all been set up in Figure 2.26 to have components that are positive.
Using the traditional approach the three equations of moment equilibrium,
M Qx 0, M Qy 0 and M Qz 0 could be transformed to produce the
following three equations:
M Q21x PQ z F Py PQ y F Pz (2.146)
M Q21y PQ z F Px PQ x F Pz (2.147)
M Q21z PQ x F Py PQ y F Px (2.148)