#002 Reduction Gears
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Definition

A Gear is a rotating round mechanical part with "teeth" that mesh to transmit rotational power. They can be made of plastic or wood, but the most common material is metal, due to the wearing effect on the teeth.

Teeth on gears offer several advantages over friction wheels.

  • Teeth prevent slippage, so gears are always synchronized exactly with one another.
  • Teeth design make it so that slight imperfections in the diameter or spacing of two gears can be a a bit off, for example if dirt gets in the machine.
  • Teeth make it easy to determine exact gear ratios. You just count the number of teeth on the two gears and divide by the smaller one. So if one gear has 100 teeth and another has 10, the gear ratio is 10:1.

The Circular Pitch is the diameter of the circle where a gear meshes at. It is not immediately obvious by looking at the teeth, .

Mechanical Gear Circular Pitch
The green line shows the Circular Pitch, the effective diameter of the gear
Source: Mechanical-Library.org

Module is the circular pitch divided by the number of teeth, usually written in millimeters. Gears will only mesh if the teeth have the same module.

Mechanical Gear Module
Size comparison of Module 0.8 teeth (left) and Module 2 teeth (right)
Source: khkgears.net

Diametral Pitch The number of teeth divided by the circle diameter, e.g. 2 teeth per inch . (This measuement is used mainly where feet and inches are used.) Gears will only mesh if the teeth have the same Diametral Pitch.

Pressure Angle defines how the gears contact each other, and thus how the force is distributed along the tooth. Standard pressure angles are 14.5, 20, and 25 degrees. Gears must have the same pressure angle to mesh well.

Frequency is how often a gear rotates in a set time. Typically written as RPM (Revolutions per Minute)

Period is the time for a rotation. To calculate, divide 1 by frequency.

Backlash is the slip that occurs when gears change direction, because of the spacing between teeth. Highly efficient gear trains have a small amount of backlash, but must be carefully engineered and consturcted.

Torque is the measure of the rotational force applied to an object..

Key Facts

To find the Gear Ratio, count the number of teeth on the “driven” gear, and divide it by the number of teeth on the “driving” gear. If the following gear has 100 teeth and the driving gear has 10, the ratio is 100:10 or 10:1. This is also expressed as a ratio of 10. The gear ratio can also be computed using the pitch diameter (or even the radius) using the same equation: Ratio = Output Gear Diameter / Input Gear Diameter

Gear Trains are created when two or more gears are made to interfere with each other in order to transmit power from one shaft to another. This is useful as one can get complex gear ratios by combining different gear pairs. In theory, one could create a 1,000,000,000:1 gear pair. but the first gear would be enormous!

Speed vs. Torque The key concept for gears is that speed and torque are directly related, and that gears of different sizes can control them.

If the "driving" gear is the same size as the "following" gear, the rotation rate and torque of the second remains the same. However, if the driving gear is twice as big as the following gear (2:1), the following gear will spin twice as fast and have half the torque.

In machinery, it is common to have a less powerful but fast spinning motor use a small gear to drive a larger gear with great torque. In other cases, because a motor can only turn so fast, a large to small gear ratio can make the output much faster, but with less torque

The transmission in a car is a device that switches different output gears so a motor can drive both slowly (first gear), or on highways (4th gear), or even in reverse. This is more obvious in a Manual transmission, but the same principle happens in "automatic" transmissions. See below for an animations

Engineering Rules of Thumb

View in 3D

These models use Apple "Quick Look AR" (Augmented Reality).

To use on iPhone: click link below, then click the model's image again. Hold phone over flat surface such as a table, and model should appear. One can move the phone around to inspect the model, even the insides. It can be scaled up by pinching with two finger tips, and rotated by rotating with two finger tips.

To use on Mac: click link below, then open the downloaded USDZ file in Preview app. It can be rotated by dragging the cursor.

Usage on other devices will be supported as time and resources permit.

Mechanical Library Gear Reduction Model
Gear Reduction
Source:mechanical-library.org

Display

This model has a "Gear Train" of 10 gears. The driving gear (in the top left) spins at approximately 1000 Rotations Per Minute (RPM). It drives a larger gear with 100 teeth, so the ratio is written as 1:10. There are 9 other 1:10 gear pairs, so the final gear spins at .000001 RPM, which takes 1 year and 329 days of continuous operation to spin once around.

Reduction Gear display in Mechanical Library
Reduction Gear display in Mechanical Library
Source: mechanical-library.org
Video of Reduction Gear display in Mechanical Library
Source: mechanical-library.org
reduction gear model
Mechanical Library Reduction Gear Model
Source: mechanical-library.org

Images

ManualTransmissionAnimation
Manual transmission in a typical car
Source: Jahobr, CC0, via Wikimedia Commons
G01 Compound Gear Train
G01 Compound Gear Train

Videos

Arthur Ganson - Machine with Concrete -A scultpture with so much gear reduction that the end gear is simply embedded in concrete
Spinning Levers - How A Transmission Works (Classic video from 1936)

3D Printing

3d Printed GEARBOX speed record - (500,000:1 gear ratio) STL file available for free at 3dprinteracademy.com
3D Printed GEARBOX STL file available for free at thingverse.com

Mechanism in Legos

Legos have long supported gears in their models.
a universal joint 'spider', with one cap off, showing needle bearings
Lego Technic, Universal Joint 4L Item No: 9244c01
Gear Ratio Basics | How To Calculate Gear Ratios | Lego Technic
Every LEGO Gear Ratio is Possible
Gear Ratios, Torque, and Horsepower explained
A crazy 1 to 10^102 LEGO Gear Ratio

History

Early gears were made from wood with cylindrical pegs for cogs and were often lubricated with grease from animal fat. Gears were used to change the rotational speed from water wheels or wind mills to power pumps or grain mills. The speed of a horse was typically too slow to use, so wooden gears increased the speed.

The industrial revolution of the 1800's saw an explosion in the use of metal gearing. A science of gear design and manufacture rapidly developed through the century.

A horse-powered wooden gear mill
A traditional wooden Cog wheel and Spindle
A traditional wooden Cog wheel and Spindle
Wooden gears in a mill in Steenmeulen, Terdeghem.
Complex and very large mechanisms were made with wooden gears, such as this mill in Steenmeulen, Terdeghem.
South Pointing Chariot
An ancient Chinese "South Pointing Chariot" used gears to point in a direction, accounting for wheel movement.
Source: WMR Kinematic Control Using Underactuated Mechanisms for Goal Direction and Evasion by Jorge U. Reyes-Muñoz, Edgar A. Martínez-García, Ricardo Rodríguez-Jorge and Rafael Torres-Córdoba

Reconstructing the Library Display

The Mechnical Library Gear Reduction display is composed of

Research