Page 95 - Dynamics of Mechanical Systems

0593_C03_fm Page 76 Monday, May 6, 2002 2:03 PM

76 Dynamics of Mechanical Systems

Y n
0 n r

P
r r = a + b sin θ

O θ
X
FIGURE P3.8.1
A fixed cam and follower P.
Determine the velocity and acceleration of P when θ is (a) 0˚; (b) 30˚; (c) 90˚; and (d) 180˚.
θ
˙
P3.8.2: Solve Problem P3.8.1 if , instead of being constant, is:
˙
+
2
θ = 40 10 sin πt rpm
P3.8.3: Suppose in Problem P3.8.1 at t = 0 that the cam is rotating clockwise at a constant
rate of 40 rpm, and that the radial line OP has a fixed inclination of 30˚. Determine the
velocity and acceleration of P relative to the cam when the cam has turned through (a)
0˚; (b) 30˚; (c) 90˚; and (d) 180˚.
P3.8.4: Repeat Problem P3.8.3 for a counterclockwise rotation of the cam at 40 rpm.
P3.8.5: In Problem P3.8.3 and P3.8.4, find the velocity and acceleration of P relative to the
X–Y frame.
P3.8.6: An insect is crawling along a radial line of an old record turntable. If the turntable
rotates clockwise at 33 / 3 rpm and if the insect crawls at 4 in./sec, determine the magnitude
1
of the acceleration of the insect as it crosses the center of the turntable.