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# Gears: Lego Mindstorms

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### Gears: Lego Mindstorms

1. 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. 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. 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. 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. 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