Gears: Lego MindStorms: Science

Background Information Gears are wheels with evenly spaced teeth. When gears

of the same or different sizes are connected, they

function like a wheel and axle, allowing for transfer of

force from one to the other. Force requires a push or a

pull. The gears of the teeth can be viewed as a “push.”

Thus 1 push moves 1 tooth. The teeth allow for strong

meshing between gears, reducing slippage and ignoring

minor imperfections in the circumference or diameter of

the two meshing gears.

Figure 1: Image source google images, no attribution available

Gears are identified by the number of teeth and the shape: spur gear, single bevel gear, double bevel

gear, worm gear, and knob wheel.

Spur gears: 40-teeth, 24-teeth, 16-teeth, and 8-teeth respectively.

Double bevel gears: 36-teeth, 20-teeth, and 12-teeth respectively

Special gears: Crown gear, worm gear, single bevel gear, turntable, knob-wheel

Working of a gear

Transfer of force

When effort is applied to a gear (the driving gear), whose teeth mesh with another gear (the driven

or the idler), force from the effort is transferred to the driven gear, causing the driven gear to turn.

In the case of the gear, the teeth “push” to create the force, driver pushes and idler pulls.

Direction of force

A driven gear meshed directly with the driver gear turns in the opposite direction of the driving gear.

An idler gear introduced between the driver and driven gear results in both gears rotating in the

same direction.

Gear ratio

To understand gear ratios, it is useful to think of the gear as a circle and compare the distance 2

gears will travel in 1 rotation.

This is the ratio between the number of rotations of the driven gear to the driver gear. In the above

example, the gear ratio is 40:8 = 5:1

Driver

Driven

Idler

Driver

idler

Total = 5 times (3* 1.67)

The above

is an

example of

a multiple gear-ratio in a compound gearing where

the smaller gear is placed on the same axle as the larger gear.

Speed or force A gear ratio of1:5 indicate that the driving gear is 5-times the size of the driven gear. There is a gain

of speed when the number of teeth on the driver gear is greater than the number of teeth on the

driven gear and an increase in the force when the driver gear is smaller than the driven gear.

Gearing down which is force & gearing up for speed

Worm gear

The worm gear is unique. Each rotation of the worm

results in the rotation of a single tooth of the gear it is

meshed with. The worm gear thus provides for increase

in force and is typically used to lift heavy thing. The

worm gears tend to cause a lot of friction.

Knob wheels

Knob wheels are used to transfer force across axis or

across planes. The amount of effort and work done is

equal, ignoring friction.

Uses of gears

Transfer force typically using a

combination of spur gears, and on

occasion, the knob wheel

Change the axis of rotation, typically by a

combination of bevel or crown gears.

Change in plane of rotation, usually by the

gear box

Increase the speed

Increase the force

To transfer rotational to linear motion

Imperfect gear connections

Some gear combinations do not mesh well, especially at angles.

20-teeth double-bevel and 16-teeth spur

12-teeth double-bevel and 24-teeth spur

12-teeth double bevel and 16-teeth spur

20-teeth double bevel and 24-teeth spur