Page 124 - Dynamics of Mechanical Systems

0593_C04*_fm Page 105 Monday, May 6, 2002 2:06 PM

Kinematics of a Rigid Body 105

n
x
1 rev/sec
n n
y n n z
z x
25 ft
L
W
25 ft n y O
15 mph C
6 in

FIGURE 4.10.2 FIGURE 4.10.3
Sports car C entering a turn to the right. Sports car steering wheel W and left hand L.

*
where L is that point of the car C where L is located at the instant of interest and where,
L
C
as before, S is the fixed road surface. From Figure 4.10.3, V is:
V = ωω × OL = 2π n × 0 433 n + 0 25 n
C L C W x ( z)
.
.
y
(4.10.13)
=−1 571 n + 2 71 n ft sec
.
.
y z
From Figure 4.10.2, V is:
S
L*
V = V + ωω × OL
S L* S O S C
z ( 0
= 22 n + 0 .88 n × .433 n + 0 .25 n z) (4.10.14)
y
x
= 22 .381 n ft sec
x
Therefore, by substituting into Eq. (4.10.12), the velocity of L is:

S L
.
.
V = 22 381 n − 1 571 n + 2 71 n ft sec (4.10.15)
.
x y z
In like manner, from Eq. (4.10.11), the acceleration of L is:
a = a + a +2 ωω × V (4.10.16)
S L C L S L* S C C L
From Figure 4.10.3, a is:
C L
x [ z)]
x (
L
C
C a = ωω W ×( ωω W × OL) = 6 238. n × 6 283. n × 0 433. n + 0 25. n
C
y
(4.10.17)
.
=−17 095 n − 9 87. n ft sec 2
y z