Gear Trains

A simple gear train is used to transmit rotary motion

A simple gear can change both the magnitude and the line of action of an effort force.

gear trains

The effort force is applied to the "driver" and the load is applied to the "follower".

Transmission Ratio

Transmission or movement ratio can be expressed as

μM = nD / nF = tF / tD         (1)

where

μM = movement ratio

nD = revolutions of driver (rpm)

nF = revolutions of follower (rpm)

tF  = number of teeth on follower

tD = number of teeth on driver

 

When the same direction of rotation is required for both the driver and the follower, an idler wheel is used.

gear trains idler

The movement ratio for a gear with an idler wheel can be expressed as

μM = nD / nF = (tI / tD) (tF / tI) = tF / tD         (2)

where

tI  = number of teeth on idler

 

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Spurs and Gears Spurs and Gears - Use the awesome SketchUp to make 3D models of spurs and gears

Typical Gear Ratios

Typical gear ratios for different types of gear sets are indicated below.

Type of Gear set Typical Gear Ratios
Min Max
Spur gear, external 1 : 1 5 : 1
Spur gear, internal 1.5 : 1 7 : 1
Helical gear, external 1 : 1 10 : 1
Helical gear, internal 1.5 : 1 10 : 1
Straight bevel gear 1 : 1 8 : 1
Spiral bevel gear 1 : 1 8 : 1
Epicyclic planetary gear 3 : 1 12 : 1
Epicyclic star gear 2 : 1 11 : 1

Bicycle Gearing

bicycle gear transmission

The revolutions of a bicycle wheel when pedaling can be calculated by transforming (2) as:

nF = nD  tD / tF   (3)

where

nF = revolutions of the bicycle wheel (rpm)

nDrevolutions of the pedaling (rpm)

tDnumber of teeth in the pedaling sprocket

tFnumber of teeth in wheel sprocket

The distance traveled by the wheel can be calculated by multiplying wheel revolutions with wheel circumference:

l = c nF 

   = c nD tD / tF   

   = π d nD tD / tF    (3b)

where

l = outer wheel traveled length or distance  (m, in)

c = outer wheel circumference (m, in)

d = outer wheel diameter (m, in)

Example - Bicycle Gear

A mountain bike with outer diameter 26 inch wheels has a 42/34/24T chainset and a 7-speed 14-34 cassette in the rear wheel.

The outer circumference of the wheel can be calculated as

c = π (26 in)

  = 81.7 in

The distance traveled by the wheel in the lowest gear - for one pedaling revolution - using the smallest sprocket in the chainset (24T) and the largest sprocket in the cassette (34T) - can be calculated using (3b) as

l = (1) (81.6 in) (24) / (34)

   = 57.7 in

The distance traveled by the wheel in the highest gear - for one pedaling revolution - using the largest sprocket in the chainset (42T) and the smallest sprocket in the cassette (14T) - can be calculated as

l = (1) (81.6 in) (42) / (14)

   = 244.8 in

Bicycle Gearing Calculator

outer wheel diameter - d - (m, mm, in)

number of teeth in chainset sprocket

number of teeth in cassette sprocket

Related Topics

  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects

Related Documents

Key Words

  • en: gear trains spurs teeth circumference driver follower
  • es: trenes de engranajes espuelas seguidor dientes conductor circunferencia
  • de: Getriebe Sporen Zähne Umfang Fahrer Anhänger

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