4569846498

Modelling and analysis of suspension systems 231
Equation 2 F E21y F F21y F G24y 0 (4.273)
Equation 3 F E21z F F21z F G24z 0 (4.274)
Taking moments about point G for the forces acting on Body 2 gives
∑{M G2 } 1 {0} 1 (4.275)
{R EG } 1 {F E21 } 1 {R FG } 1 {F F21 } 1 {0} 1 (4.276)
⎡ 0 9 275⎤
⎡F
⎢
9 0 115
⎥ ⎢
⎢
⎥ ⎢
F
⎣⎢
275 115 0 ⎦⎥
⎣⎢
F
⎤ ⎡0⎤
⎥
⎢
0
⎥
⎥
N mm
⎢ ⎥
⎦⎥
⎣⎢
0⎦⎥
(4.277)
Multiplying out the matrices in (4.277) yields the next set of three equations:
Equation 4 9F E21y 275F E21z 9F F21y 275F F21z 0 (4.278)
Equation 5 9F E21x 115F E21z 9F F21x 115F F21z 0 (4.279)
Equation 6 275F E21x 115F E21y 275F F21x 115F F21y 0 (4.280)
Consider next Body 3 and the equations required for force equilibrium:
∑{F 3 } 1 {0} 1 (4.281)
{F A31 } 1 {F B31 } 1 f S2 {R CI } 1 {F D34 } 1 {0} 1 (4.282)
⎡F
⎢
⎢
F
⎣⎢
F
A31x
A31y
A31z
E21x
E21y
E21z
⎤ ⎡FB31x⎤
⎡ 3 ⎤ ⎡F
⎥
⎥
⎢
F
⎥
⎢ B31y⎥
f
⎢
S2
9
⎥
⎢
F
⎢ ⎥ ⎢
⎦⎥
⎣⎢
FB31z⎦⎥
⎣⎢
436⎦⎥
⎣⎢
F
⎤ ⎡ 0 9 275⎤
⎡F
⎥
⎢
⎥
9 0 115
⎥ ⎢
⎢
⎥ ⎢
F
⎦⎥
⎣⎢
275 115 0 ⎦⎥
⎣⎢
F
D34x
D34y
D34z
⎤ ⎡0⎤
⎥
⎥
⎢
0
⎥
N
⎢ ⎥
⎦⎥
⎣⎢
0⎦⎥
F21x
F21y
F21z
(4.283)
The summation of forces in (4.283) leads to the next set of three equations:
Equation 7 F A31x F B31x 3f S2 F D34x 0 (4.284)
Equation 8 F A31y F B31y 9f S2 F D34y 0 (4.285)
Equation 9 F A31z F B31z 436f S2 F D34z 0 (4.286)
Taking moments about point D for the forces acting on Body 3 gives
∑{M D3 } 1 {0} 1 (4.287)
{R AD } 1 {F A31 } 1 {R BD } 1 {F B31 } 1 {R CD } 1 f S2 {R CI } 1 {0} 1
(4.288)
⎡ 0
⎢
15
⎢
⎣⎢
239
15 239⎤
⎡F
0 115
⎥ ⎢
⎥ ⎢
F
115 0 ⎦⎥
⎣⎢
F
A31x
A31y
A31z
⎤ ⎡ 0
⎥
⎢
⎥
1
⎢
⎦⎥
⎣⎢
239
f
S2
1 239⎤
⎡F
0 115
⎥ ⎢
⎥ ⎢
F
115 0 ⎦⎥
⎣⎢
F
B31x
B31y
B31z
⎡ 0 23 98⎤
⎡ 3 ⎤ ⎡0⎤
⎢
23 0 0
⎥ ⎢
9
⎥
⎢
0
⎥
N mm
⎢
⎥ ⎢ ⎥ ⎢ ⎥
⎣⎢
98 0 0 ⎦⎥
⎣⎢
436⎦⎥
⎣⎢
0⎦⎥
(4.289)
⎤
⎥
⎥
⎦⎥