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THREE SPEED HUB
QUESTIONS OR COMMENTS
smith_eric.jpg (1652 bytes) AUTHOR: Eric Smith
E-MAIL: erics1@mit.edu
COURSE: 2
CLASS/YEAR: 2

MAIN FUNCTIONAL REQUIREMENT:  Provide a bicycle rider with a means of selecting three different gear ratios in the bicycle's drive train

DESIGN PARAMETER:  3 speed hub (this is one possible design parameter)


GEOMETRY/STRUCTURE AND PARTS:

smith-eric-1.gif (25221 bytes)
Components of 3 Speed Hub

EXPLANATION OF HOW IT WORKS/ IS USED:

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Section View of Planetary Gear System

Three speed hubs use a planetary gear system to achieve a gear ratio between the sprocket and the wheel. In this gear system the sun gear is fixed in place while the planet carier is rotated. This causes the planet gears to rotate which in turn causes the ring gear to rotate.

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Cable Lever of Three Speed Hub

The rider selects a speed using a shifter. The shifter pulls on a cable which is connected to the cable lever. This causes the cable lever to rotate.

 

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Animated 2D Cross Section of Three Speed Hub

The cable lever pushes on a pin that goes through the axle. This pin is connected to the planetary gear system and forces it to move side to side when the lever is pulled.

When the planetary gear system shifts from side to side the ring gear and the planet carier are engaged or dissengaged from the wheel and the chain. This is what changes the gear ratio.

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Animated 3D Cross Section of Three Speed Hub

 

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Components of 3 Speed Hub

 

smith-eric-replace.gif (9620 bytes) Speed 1
In a hub with the same number of teeth on the sun and planet gears:

The gear ratio between the sprocket and the wheel is 4:3

(for every 4 rotations of the sprocket the wheel turns 3 times)


 smith-eric-7.gif (19209 bytes) Speed 2



Gear ratio: 1:1




 smith-eric-8.gif (19374 bytes) Speed 3



Gear ratio: 3:4




DOMINANT PHYSICS:

The gear ratio between the planet carrier and ring gear can be calculated based on the number of teeth in the sun and planet gears:

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Components of 3 Speed Hub

 

Variable Descriptioin Units
wr Rotational speed of the ring gear rad/s or rpm
wc Rotational speed of the planet carrier rad/s or rpm
Ns Number of teeth on the sun gear ---
Np Number of teeth on one of the planet gears ---

 

wr = 1 + Ns
wc Ns +2 Np

LIMITING PARAMETERS:

  • Size
The gearing mechanism must be able to fit within the bicycle's hub.
  • Weight
It must be light so it doesn't add too much weight to the rest of the bike
  • Efficiency
Because this is part of the drive train of the bicycle its efficiency greatly effects that of the whole bicycle. Good bearings are a must!
Typical efficencies for internal hubs in good condition are between 94% and 98%.

PLOTS/GRAPHS/TABLES:

None Submitted


WHERE YOU CAN FIND THREE SPEED HUBS:

Three speed hubs are mostly found on bikes built before the 1970s

Modern internal gear hubs are based on this design but use several planetary gear systems chained together to acheive a greater number of speeds.
These are most commonly found on bikes that are used in:

  • stop and go traffic because they can shift gears while the bike is stopped (unlike derailers)
  • harsh enviroments where exposed derailers can get damaged

REFERENCES/MORE INFORMATION:

Internal gear hubs - http://www.sheldonbrown.com/seven_speed.html

Planetary gear trains - http://www.cs.cmu.edu/People/rapidproto/mechanisms/chpt7.html#HDR123

How a 14 speed hub works - http://www.rohloff.de/english/products/speedhub/speedwork.html


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