Gears

• Transmit rotary motion and torque

• Gears have positive engagementfriction drives, belts

Gear Types

Spur Gear Rack and Pinion Gear

Internal Gear Helical Gear

Gear Types

Bevel GearHerringbone Gear

Miter Gear Worm Gear

Power Transmission

Gear Geometry

• Pitch Diameter

Size of equivalent friction rollersPitch circle

Pitch circle

Line of Centers

• Number of Teeth

Must be an integer value

Gear Kinematics

• Velocity RatioGear Ratio

Pitch Circles

d2

2

d1

1 1

2

1

2

2

1

D

D

N

N

VR

=

=

=

• Gear trains are used to achieve high ratios with moderate size gears.

• Train Value (TV)

TV = (VR)1 (VR)2 (VR)3 …

Gear Trains

out

inTV

=

Example

The gear train shown is used with an input speed of 1200 rpm, cw. Determine the output velocity :

in

out

1

2

3

45

6

• N1=24• N2= 36• N3=20 • N4= 40• N5=16 • N6= 64

out =1200rpm*(24/36)*(20/40)*(16/64)=1200*(1/12)=100rpm

But, since power is conserved, the output Torque is increasedby a factor of 12

Questions

1. 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?

2. What happens if you increase the diameter of the driving wheels?

Center of Rotation

R

b

l

2

Wheel radius= r

(1) r2 = (R-b)(velocity hub axle 2)

(2) rl = (R+b) (velocity hub axle 1)

Angular velocity

Dividing (1) by (2)

2/l = (R-b) / (R+b)

Solving for R

R = b(1+ 2) / (1- 2)

A Three- Wheeled Vehicle with a Free Front Wheel

Rear wheels differentially powered.

r

Note: 1=2 R =1=R =b 2=R =b1=2 R=0