1. Gears Transmit rotary motion and torque Gears have positive engagement
(belts are driven by friction)

2. Gear Types
Spur Gear
Rack and Pinion Gear
Internal Gear
Helical Gear

3. Gear Types
Bevel Gear
Herringbone Gear
Miter Gear
Worm Gear

4. Power Transmission

5. Size of equivalent friction rollers
Gear Geometry
Pitch Diameter
Size of equivalent friction rollers
Pitch circle
Line of Centers
Number of Teeth
Must be an integer value

6. Gear Kinematics
Velocity Ratio
Gear Ratio
Pitch Circles d2 w2 d1 w1

7. Gear Trains
Gear trains are used to achieve high ratios with moderate size gears.
Train Value (TV)
TV = (VR)1 (VR)2 (VR)3 …

8. Example
The gear train shown is used with an input speed of 1200 rpm, cw. Determine the output velocity :
N1=24
N2= 36
N3=20
N4= 40
N5=16
N6= 64
win
wout 1 2 3 4 5 6
wout =1200rpm*(24/36)*(20/40)*(16/64)=1200*(1/12)=100rpm
But, since power is conserved, the output Torque is increased
by a factor of 12

9. Questions
If you design a vehicle which you would like to drive at a slower rate, you are better off to use a gear train rather than simply reducing the power level to the motor. Why?
What happens if you increase the diameter of the driving wheels?

10. A Three- Wheeled Vehicle with a Free Front Wheel
Wheel radius= r
Rear wheels differentially powered. l b 2 r
(1) r2 = (R-b)(velocity hub axle 2) R
(2) rl = (R+b) (velocity hub axle 1)
Dividing (1) by (2)
Center of Rotation
2/l = (R-b) / (R+b)
Angular velocity 
Note: 1=2 R =
1=R =b
2=R =b
Solving for R
R = b(1+ 2) / (1- 2)