Transcript Gear Trains

Geartrains
Materials taken from several sources
including: Building Robots with LEGO
Mindstorms by Ferrari, Ferrari, and Hempel
DC motor output characteristics:
Speed
Speed:
Usually specified as the speed in
revolutions 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.
Efficiency = 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
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
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 torque and a divider on
speed.
driving gear
driven gear
You
can calculate the gear ratio by
using the number of teeth of the “driven
gear" (a.k.a. the output gear) divided
by the number of teeth of the “driving
gear” (a.k.a. the input gear).
Gear Ratio = # teeth output gear / # teeth input gear
= torque out / torque in = speed in / speed out
Gear Ratio
You
can think of gear ratio as a
multiplier on torque and a divider on
speed.
driving gear
We gear up when we increase
velocity and decrease torque.
Ratio: 1:3
We gear down when we increase
torque and reduce velocity.
Ratio: 3:1
driven gear
HIGHER Numeric Ratio
= lower Gear
lower Numeric Ratio
= HIGHER Gear
Building Geartrains
The
largest LEGO gear is the
40t, while the smallest is the 8t,
thus, the highest reduction we
can obtain is 40:8, or 5:1. For a
higher ratio use a multistage
reduction system, called a
geartrain.
Idler Gear
What's
the ratio of the geartrain in the
adjoining figure? Starting from the 8t,
the first stage performs an 24:8
reduction, while the second is a 8:24
multiplication. Multiplying the two
fractions, you get 1:1! 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.
Backlash
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 asymmetric
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
24:1 reduction with a single stage.
Special Gears: Clutch Gear
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
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.