Transcript Gear Trains

Geartrains
Materials taken from several sources
including: Building Robots with LEGO
Mindstroms by Ferrari, Ferrari, and Hempel
DC motor output characteristics:
Speed

Speed: Usually specified as the speed in
rotations per minute (RPM) of the motor when
it is unloaded, or running freely, at its
specified operating voltage.
 The speed of the motor is proportional to the
applied voltage. At max speed, the motor
draws relatively little current.
 Typical DC motors run at high speeds up to
twenty thousand RPM or more.
DC motor output characteristics:
Torque

Torque: The rotary force produced on the
output shaft. When a motor is stalled it is
producing the maximum amount of torque
that it can produce. Hence the torque rating is
usually taken when the motor has stalled and
is called the stall torque. The motor torque is
measured in ounce-inches (in the English
system). One ounce-inch means that the
motor is exerting a tangential force of one
ounce at a radius of one inch from the center
of its shaft.
 The torque of the motor is proportional to the
current flowing through it. When stalled, the
motor is drawing near max current.
DC motor output characteristics:
Power
Power: The product of motor speed and
torque. The power output is greatest
somewhere between the unloaded
speed (maximum speed, no torque) and
the stalled state (maximum torque, no
speed).
 PM = T x w
 PMmax ~= ¼ x Tmax x wmax

Torque, Speed and Power
Efficiency

A DC motor is a transducer which changes voltage
and current into speed and torque.
 To calculate a motor's efficiency, you measure its
mechanical output power and divide it by the
electrical input power.
 Effeciency = PM / Pe ~= 50%-60%
 Pe = V x I
 PM = T x w
 Implications:
– Efficiency is highest in the middle of the torque
range so you need to oversize your motor to run
with high efficiency.
– Most robots require relatively low speed and high
torque so motor output is usually geared down.
Characteristics of the LEGO motor

Lego 9V Technic Motors
Gears

A typical DC motor operates at speeds that
are far too high to be useful, and at torques
that are far too low. Gear reduction is the
standard method by which a motor is made
useful.

LEGO gears: Gears are classified by the
number of teeth they have; the description of
which is then shortened to form their name.
For instance, a gear with 24 teeth becomes
"a 24t gear."
Fundamental Properties
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The gears are transferring motion
from one axle to the other.
If their teeth match well, there is
only a small amount of friction.
LEGO parts are designed to match
properly at standard distances.
The two axles turn in opposite
directions: one clockwise and the
other counterclockwise.
The two axles revolve at different
speeds. When you turn the 8t, the
24t turns more slowly, while turning
the 24t makes the 8t turn faster.
Gearing Up and Down
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Gearing is able to convert torque
to velocity. The more velocity
gained, the more torque sacrifice.
The ratio is exactly the same: if
you get three times your original
angular velocity, you reduce the
resulting torque to one third.
This conversion is symmetric: we
can also convert velocity to torque
at the same ratio.
The price of the conversion is
power loss due to friction.
Gear Ratio

You can think of gear ratio as a
multiplier on speed and a divider
on torque.
 You can calculate the gear ratio by
driven gear
using the number of teeth of the
“driving gear" (a.k.a. the input gear)
divided by the number of teeth of the
“driven gear” (a.k.a. the output
gear).
 We gear up when we increase
velocity and decrease torque.
Ratio: 3:1
 We gear down when we increase
torque and reduce velocity.
Ratio: 1:3
driving gear
Gear Ratio = # teeth input gear / # teeth output gear
= torque in / torque out = speed out / speed in
Building Geartrains

The largest LEGO gear is the
40t, while the smallest is the
8t, thus, the highest ratio we
can obtain is 8:40, or 1:5.

If you need an even higher
ratio you can use a
multistage reduction system,
called a geartrain.
Idler Gear

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What's the ratio of the geartrain in the
adjoining figure? Starting from the
8t, the first stage performs an 8:24
reduction, while the second is a
24:40. Multiplying the two fractions,
you get 8:40, or 1:5, the same result
you'd get meshing the 8t directly to
the 40t. The intermediate 24t is an
idler gear, which doesn't affect the
gear ratio.
Idler gears are quite common in
machines, usually to help connect
distant axles. Idler gears have one
very important effect: They change
the direction of rotation.
Blacklash
Backlash is the amount of oscillation a
gear can endure without affecting its
meshing gear.
 Backlash is amplified when gearing up,
and reduced when gearing down. It
generally has a bad effect on a system,
reducing the precision with which you
can control the output axle.

Special Gears: The Worm Gear

The worm gear leads to an assymetric
system; that is, you can use it to turn other
gears, but it can't be turned by other gears.
 For every turn of the worm gear, the mating
gear rotates by exactly one tooth. The worm
gear is a 1t gear. If mated with a 24t, you get
a 1:24 ratio with a single stage.
Special Gears: Clutch Gear
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A thick 24t white gear, which has strange
markings on its face
The clutch gear limits the strength you can
get from a geartrain; this helps to preserve
your motors, and other parts.
The mysterious "2.5-5 Ncm" indicates that
this gear can transmit a maximum torque
of about 2.5 to 5 Ncm.
When exceeding this limit its internal clutch
mechanism starts to slip.
The maximum torque produced by a
system with a clutch gear results from the
maximum torque of the clutch gear
multiplied by the ratio of the gear stages
that follow it.
Special Gears: Bevel and Crown
Gears

There's a class of gears
designed to transfer motion
from one axle to another axle
perpendicular to it, called bevel
gears.

The 24t gear also exists in the
form of a crown gear, a special
gear with front teeth that can be
used like an ordinary 24t, but
can also combine with another
straight gear to transmit motion
in an orthogonal direction.
Pulleys and Belts
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An advantage of pulleys over gear wheels is that their
distance is not as critical. They can be used to
transfer motion to a distant axle.
Pulleys are not very suitable to transmitting high
torque, because the belts tend to slip. The amount of
slippage is not easy to estimate; it depends on many
factors, including the torque and speed, the tension
of the belt, the friction between the belt and the
pulley, and the elasticity of the belt.
The rule with pulleys is that the reduction ratio is
determined by the ratio between their diameters.
Special Gears: Differential Gear

The differential gear is used to help cars turn
corners. The differential gear (placed midway
between the two wheels) allows the wheels to
turn at different speeds while providing the
same torque to both wheels.