Page 179 - Dynamics of Mechanical Systems

0593_C05_fm Page 160 Monday, May 6, 2002 2:15 PM

160 Dynamics of Mechanical Systems

a. Locate or identify the instant center of zero velocity of the crank OA, the con-
necting rod AP, and the piston P.
b. Use the results of (a) to determine the velocities of A and P and the angular
velocity of connecting rod AP.
c. Express the velocities of A and P in terms of the unit vectors n and n of Figure
y
x
P5.4.5.
n
y
A

n
x
9.0 in
3.5 in
300 rpm
FIGURE P5.4.5
A crank, connecting rod, and piston O 60° 10.25 in P
system.

Section 5.7 Instant Center, Analytical Considerations
P5.7.1: A body B having planar motion has a counterclockwise angular velocity of 7 rad/
sec, as represented in Figure P5.7.1. Suppose a point P with coordinates (3, 4) (in meters)
relative to X–Y coordinates in a reference frame R has the velocity:

P
V =−62 n − 62 n m sec
x y
where n and n are the horizontal and vertical unit vectors as in Figure P5.7.1. Determine
x y
the coordinates of the instant center C of B and the velocity of point Q of B whose
coordinates are (2, 4). Express the velocity of Q in terms of n and n .
x y

Y
B
n y
P(3,4) ω = 7 rad/sec

Q(2,4)

FIGURE P5.7.1
A body B in planar motion with R O
known angular velocity and velocity X
of one point. n x

P5.7.2: A body B having planar motion has particle P and Q whose coordinates relative
to the X- and Y-axes are (13, 8) and (25, 13) (in centimeters), as in Figure P5.7.2. Let the
velocities of P and Q be:

P
V =−25 n + 60 n cen sec
x y