1. 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

2. 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
DrivenDriver
idler

3. 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.

4. 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

5. 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