Geartrains

1
Geartrains

• Materials taken from several sources including
  Building Robots with LEGO Mindstroms by Ferrari,
  Ferrari, and Hempel

2
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.
  

3
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.
  

4
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

5
Torque, Speed and Power
6
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.
  

7
Characteristics of the LEGO motor

• Lego 9V Technic Motors

8
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."

9
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.
  

10
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.
  

11
Gear Ratio

• You can calculate the "gear ratio" by using the
  number of teeth of the "drive gear" divided by
  the number of teeth of the "driven gear.
  
• We gear up when we increases velocity and reduces
  torque. Ratio 31
  
• We gear down when we reduces velocity and
  increases torque. Ratio 13
  

12
Building Geartrains

• The largest LEGO gear is the 40t, while the
  smallest is the 8t, thus, the highest ratio we
  can obtain is 840, or 15.
  
• If you need an even higher ratio you can use a
  multistage reduction system, called a geartrain.
  
  

13
Idler Gear

• What's the ratio of the geartrain in the
  adjoining figure? Starting from the 8t, the
  first stage performs an 824 reduction, while the
  second is a 2440. Multiplying the two fractions,
  you get 840, or 15, 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.

14
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.

15
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 124
  ratio with a single stage.

16
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.

17
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.

18
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.

19
Special Gears Differential Gear

• The differential gear is used to help cars turn
  corners. The differential gear (placed midway
  between the two wheels) allows one wheel to turn
  at a greater speed than the other. Even though
  the wheels may be turning at different speeds,
  the action of the differential means that the
  torque generated by the motor is distributed
  equally between the half-axles upon which the
  wheels are mounted.