4569846498

Modelling and analysis of suspension systems 135
Z 1
GRF
O 1
X 1
Y 1
{R DG } 1
D
{F D } 1
{R CG } 1
G
C
{F B } 1
{R AG } 1
{R BG } 1
m 2 {g} 1
{F A } 1
B
A
{F C } 1
Fig. 4.4
The wheel load reaction problem
F Az F Bz F Cz F Dz m 2 g 0 (4.4)
If we continue now to take moments about the mass centre G of Body 2 we
have
∑{M G } 1 {0} 1 (4.5)
{R AG } {F A } 1 {R BG } 1 {F B } 1 {R CG } 1 {F C } 1
{R DG } 1 {F D } 1 {0} 1 (4.6)
If we expand the vector moment terms for the force acting at A only we get
⎡ 0 AGz
AGy
⎤ ⎡ 0
⎢
⎥
AG 0 AG
⎢
⎢ z
x⎥
⎢
0
⎢
⎣
AG AG 0 ⎥
⎦ ⎣⎢
F
y x Az
⎤ ⎡ AGyF
⎥
⎢
⎥
AGxF
⎢
⎦⎥
⎣⎢
0
Az
Az
⎤
⎥
⎥
⎦⎥
(4.7)
From (4.7) it is clear that we can now write equation (4.6) as
AG y F Az BG y F Bz CG y F Cz DG y F Dz 0 (4.8)
AG x F Az BG x F ABz CG x F Cz DG x F Dz 0 (4.9)
It can now be seen that we have the classical case of an indeterminate problem
where there are insufficient equations available to solve for the
unknowns. The four unknowns here are F Az , F Bz , F Cz and F Dz . There are,
however, only the three equations (4.4), (4.8) and (4.9) available to effect a
solution. Trying to arrange the equations in matrix form for solution
demonstrates the futility of the problem.