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Geartrains Materials taken from several sources including: Building Robots with LEGO Mindstorms by Ferrari, Ferrari, and Hempel 1

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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." 2

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**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. 3

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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. 4

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**Gear Ratio Gear Ratio = # teeth output gear / # teeth input gear**

You can think of gear ratio as a multiplier on torque and a divider on speed. 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). driven gear driving gear Gear Ratio = # teeth output gear / # teeth input gear = torque out / torque in = speed in / speed out 5

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**Gear Ratio HIGHER Numeric Ratio lower Numeric Ratio = lower Gear**

You can think of gear ratio as a multiplier on torque and a divider on speed. 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 driving gear HIGHER Numeric Ratio = lower Gear lower Numeric Ratio = HIGHER Gear 6

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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. 7

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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. 8

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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. 9

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**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. 10

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**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. 11

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**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. 12

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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. 13

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