NC State Engineering in Havelock
4 Year Mechanical Engineering Systems BSE
www.engr.ncsu.edu/mes
The Gear Ratio is defined as the input speed relative to the output speed. It is
typically written as:
Gear Ratio = win : wout
The fundamental equations for a gear pair are:
tin win = tout wout
wout / win = rin / rout
wout / win = nin / nout
tout / tin = rout / rin
tout / tin = nout / nin
(power equality)
(velocity relationship in terms of radiuses)
(velocity relationship in terms of number of teeth)
(torque relationship in terms of radiuses)
(torque relationship in terms of number of teeth)
WHERE
t = Torque
w = Angular Speed (rad/sec or RPM)
r = Radius
n = Number Teeth
Small to Large
• Output Speed
• Output Torque
• Input Torque Needed
3∶1
Rev In
For Torque: (Torque In) Times Ratio
Torque On Shaft A = .25 FtLbs
(
.25
. ∗ 3/1
Rev Out
For Speed: (Speed In) Divided By Ratio
Gear “A” going 90 RPM
90
3/1
Large to Small
• Output Speed
• Output Torque
• Input Torque Needed
1: 2
Rev In
For Torque: (Torque In) Times Ratio
Torque On Shaft A = .25 FtLbs
(
.25
.
∗ 1/2
.5: 1
Rev Out
For Speed: (Speed In) Divided By Ratio
Gear “A” going 90 RPM
90
1/2
Complex Gear Machines
Out
20 Teeth
80 Teeth
40 Teeth
In
120 Teeth
IN
30 RPM
.25 FtLbs
∗
∗
….
40 20
80
∗
120 80
9600
1
1: 12 .0833: 1
12
Rev In
Rev Out
Speed: RPM Out = RPM In / Ratio
Speed: 30 RPM In / (1/12) = 360 RPM Out
Torque: .Torque Out = Torque In * Ratio
Torque: .25 FtLbs In * (1/12) = .020833 FtLbs Out
Try this at home for fun
12T
12T
Robot
20T
58T
58T
Motor
58T
The gear on the motor and on the robot are fixed as shown above. You will have 258T gears, 1-12T gear and 1-20T gear. How could you arrange the gears to give a
gear ration like below? We want out robot to turn one time every time the motor turns
about 61.5 times. If our motor turns about 2,000 revolutions per minute, how fast will
our robot turn??
61.588
1
61.588 ∶ 1