Gears Transmit rotary motion and torque Gears have positive engagement (belts are driven by friction)
Gear Types Spur Gear Rack and Pinion Gear Internal Gear Helical Gear
Gear Types Bevel Gear Herringbone Gear Miter Gear Worm Gear
Power Transmission
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
Gear Kinematics Velocity Ratio Gear Ratio Pitch Circles d2 w2 d1 w1
Gear Trains Gear trains are used to achieve high ratios with moderate size gears. Train Value (TV) TV = (VR)1 (VR)2 (VR)3 …
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
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?
A Three- Wheeled Vehicle with a Free Front Wheel Wheel radius= r Rear wheels differentially powered. l b 2 r (1) r2 = (R-b)(velocity hub axle 2) R (2) rl = (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)