Chapter 8: Motion and Power Transmission
276
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
lbft 3131
srad 6.751
slbft 2200
output
.T
Input shaft = 350 ft lb
Output shaft = 131 ft lb
Discussion:
The input and output gears rotate the same direction since there is one gear in between
them in the geartrain. The torque on the output shaft is significantly less than the input shaft
because of its higher rotational speed and smaller size.
Chapter 8: Motion and Power Transmission
278
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
s
m
382
Discussion:
This is equivalent to 860 mph, which demonstrates how fast the mechanisms inside hard
Chapter 8: Motion and Power Transmission
281
© 2017 Cengage Learning®. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part.
lb 160
in
ft
08330
s
in
62.8
s
lbft
6837
.
.
.
.
F
160 lb
Discussion:
283
P8.23: The world distance record for riding a standard bicycle in 1 h is 54.526 km, set in
2015 in London. A fixed-gear bike was used, which means that the bike effectively had
only one gear. Assuming that the rider pedaled at a constant speed, how fast did the
rider pedal the front gear/sprocket in rpm to achieve this record?
Approach:
Calculate the speed of the bike using the distance covered in one hour, assuming the bike
Solution:
Calculate the velocity of the bike:
m
hr
m
km
bike 15.15
0001
4.5265
v
Chapter 8: Motion and Power Transmission
Discussion:
At 105.3 rpm, the rider is turning the pedals at a rate of over 1.7 revolutions per second.
Typical rpm values for world record cycling speed attempts are between 90-105 rpm. This
285
P8.26: The geartrain in the transmission for the Segway® Personal Transporter uses helical
gears to reduce noise and vibration. The vehicle’s wheels have a diameter of 48 cm, and
it has a top speed of 12.5 mph. (a) Each gearset was designed to have a noninteger gear
ratio so that the teeth mesh at different points from revolution to revolution, therefore
reducing wear and extending the transmission’s life. What is the velocity ratio at each
mesh point? (b) What is the velocity ratio for the entire geartrain? (c) In the units of
rpm, how fast does the motor’s shaft turn at top speed?
Approach:
The velocity ratios at each mesh point are given by Equation (8.9). For the entire
Solution:
(a) At the first mesh point:
15
N
Chapter 8: Motion and Power Transmission
286
(c) Speed of motor shaft:
Speed of vehicle (Equation (8.2)):
ft
3318
ft
5280
h
mi
12.5 .v
s
s
ft
s
Wheel shaft speed (Table 8.1):
rad
2823
scm 8558
wheel .
.
v
Discussion:
Since the velocity ratios are all < 1, this geartrain is designed to decrease the speed of the
287
P8.27: The mechanism that operates the load/unload tray for holding the disk in a tabletop
Blu-rayTM player uses nylon spur gears, a rack, and a belt drive. The gear that meshes
with the rack has a module of 2.5 mm. The gears have the numbers of teeth indicated,
and the two sheaves have diameters of 7 mm and 17 mm. The rack is connected to the
tray that holds the disk. For the tray to move at 0.1 m/s, how fast must the motor turn?
Approach:
Apply Equation (8.2) to find the speed of the pinion that meshes with the rack. Then use
Solution:
The pitch radius of the small gear that meshes with the rack is (Equation (8.7)):
mm 517
2
mm 5214 .
.
r
In the dimensions of rad/s, the speed of gear 5 is (Equation (8.2)):
srad 7145
m
0175
0
sm 10
5.
.
.
In the units of rpm (Table 8.1):
rpm 5754
srad
rpm
5499srad 7145
5...
Since gears 4 and 5 are on the same shaft, ω4 = ω5. Gears 3 and 4 form a gearset (Equation
(8.8)):
rpm 2309rpm 5754
15
85
4
3
4
3..
N
N
Gear 3 and sheave 2 are on the same shaft, so ω2 = ω3. The speeds of sheaves 1 and 2 are
related by Equation (8.23):
rpm 9750rpm 2309
mm 7
mm 17
2
1
2
1..
d
d
751 rpm
Chapter 8: Motion and Power Transmission
288
289
P8.28: Explain why the number of teeth on the ring gear in a planetary geartrain is related
to the sizes of the sun and planet gears by the equation Nr = Ns + 2Np.
Solution:
With rs, rp, and rr being the pitch radii of the sun, planet and ring gears, the geometry of the