4569846498

210 Multibody Systems Approach to Vehicle Dynamics
Solving equation (4.140) yields the following answers for the 10 unknowns:
f 2 5.333 10 2 rad/mm.s
f 3 6.104 10 2 rad/mm.s
4x 8.774 10 3 rad/s
4y 0.945 rad/s
4z 1.446 10 3 rad/s
5x 14.121 rad/s
5y 3.881 10 2 rad/s
5z 1.106 rad/s
V Px 166.468 mm/s
V Py 108.859 mm/s
It is now possible to use the two scale factors found, f 2 and f 3 , to calculate
the angular velocity vectors { 2 } 1 and { 3 } 1 :
⎡230⎤
⎡12.266⎤
2
2 1
f2
R 5.333 10
⎢
0
⎥
⎢
0
⎥
EF 1
rad/s
⎢ ⎥ ⎢ ⎥
⎣⎢
0 ⎦⎥
⎣⎢
0 ⎦⎥
{ } { }
(4.141)
⎡230⎤
⎡14.039⎤
2
3 1
f3
R 6.1041 10
⎢
0
⎥
⎢
0
⎥
AB 1
rad/s
⎢ ⎥ ⎢ ⎥
⎣⎢
14 ⎦⎥
⎣⎢
0.855 ⎦⎥
{ } { }
(4.142)
In summary the angular velocity vectors for the rigid bodies are as follows:
{ } [ 12. 266 0 0 ] rad/s
{ } [ 14. 039 0 0. 855]
rad/s
{ } [ 8.77410 0.945 1.446 10 ] rad/s
{ } [ 14. 121 3.881 10 1.106 ] rad/s
We can now proceed to calculate the translational velocities at all the moving
points, C, D, G, H and P, within this part of the model:
{V C } 1 {V CA } 1 { 3 } 1 {R CA } 1 (4.143)
⎡V
⎢
⎢
V
⎣⎢
V
T
2 1
T
3 1
T
4 1
T
5 1
Cx
Cy
Cz
3 3
2
⎤ ⎡ 0 0.855 0 ⎤ ⎡115⎤
⎡120.555⎤
⎥ ⎢
⎥ ⎢
⎥
0.855 0 14.039
141
⎥
⎢
435.157
⎥
mm/s
⎢
⎥ ⎢ ⎥ ⎢ ⎥
⎦⎥
⎣⎢
0 14.039 0 ⎦⎥
⎣⎢
38
⎦⎥
⎣⎢
1979.499 ⎦⎥
(4.144)
{V D } 1 {V DA } 1 { 3 } 1 {R DA } 1 (4.145)
⎡V
⎢
⎢
V
⎣⎢
V
Dx
Dy
Dz
⎤ ⎡ 0 0.855 0 ⎤ ⎡115⎤
⎡204.345⎤
⎥ ⎢
⎥ ⎢
⎥
0.855 0 14.039
239
⎥
⎢
112.260
⎥
mm/s
⎢
⎥ ⎢ ⎥ ⎢ ⎥
⎦⎥
⎣⎢
0 14.039 0 ⎦⎥
⎣⎢
15
⎦⎥
⎣⎢
3355.321⎦⎥
(4.146)