Lego Gear Trains

Power Transfer

General Guidelines

Transmissions

Footnotes

POWER TRANSFER
The motor included in the MIT Lego kits can spin freely at an extremely high rate. If the spin rate could be directly translated to the tires, a very fast car could be built. However, the motor produces a constant power. At these high speeds, the motor cannot provide a significant amount of torque. Since the car will be carrying a large weight, more torque will be needed to make it move. So a tradeoff must be made between torque and angular velocity.
Gears can be used to make this tradeoff. When two gears mesh with each other, the linear velocity of the point of contact is the same for both gears. Since the linear velocity of a gear at the surface is proportional to the radius and the angular velocity of the gear, the smaller gear must spin faster than the larger gear to make up for it's lack of radius. In the process, more torque can be realized from the larger gear.(1)
What you need to know: By connecting a series of gear, the torque can be increased while lowering the spin rate. The only method to know exactly how much of a spin reduction is necessary is to experiment with different gear trains. Remember to slow down the spin, put the smaller gear nearer the motor in the gear train.: The motor included in the MIT Lego kits can spin freely at an extremely high rate. If the spin rate could be directly translated to the tires, a very fast car could be built. However, the motor produces a constant power. At these high speeds, the motor cannot provide a significant amount of torque. Since the car will be carrying a large weight, more torque will be needed to make it move. So a tradeoff must be made between torque and angular velocity.
Gears can be used to make this tradeoff. When two gears mesh with each other, the linear velocity of the point of contact is the same for both gears. Since the linear velocity of a gear at the surface is proportional to the radius and the angular velocity of the gear, the smaller gear must spin faster than the larger gear to make up for it's lack of radius. In the process, more torque can be realized from the larger gear.(1)
What you need to know: By connecting a series of gear, the torque can be increased while lowering the spin rate. The only method to know exactly how much of a spin reduction is necessary is to experiment with different gear trains. Remember to slow down the spin, put the smaller gear nearer the motor in the gear train.

GENERAL GUIDELINES FOR GOOD GEAR TRAINS
Things to Do:

Properly align shafts--Make sure both ends of a rotating shaft are at the same horizontal and vertical position. Otherwise the shafte will not spin freely and it will wear down quickly. (You might even melt the shaft in half.) This not only destroys shafts, but also the supporting pieces gather some of the melted plastic, and no other shaft will fit back into place.
Build from wheels to motor--The position of the motor in the car is less important than the position of the driving wheels. If you try to build a gear train separately and then attach it it to the wheels, you may find that it won't work.
Check spacing between gears--The teeth of contacting gears will be ground away if they barely overlap, thus causing the system to grind. Should the teeth overlap too much, the gears will not turn easily. Either way, power is lost.

Things to Avoid:(2)

Chain drive--As cool as it may seem, the chain does not function well in a gear train. It has a tendency to bind up, especially at high speeds. Also, lining the gears up to have appropriate amounts of slack can be a difficult task at best.
Worm gears--These gears are also pretty cool, but don't be decieved; they are the most inefficient gears available. Worm gears add significantly to friction forces, so try to stay away from them.
Pulleys--Systems incorporate belts generally to allow slippage in the gear train. This means loss of energy, and you want to be as efficient as possible.
Unsupported Gears--Try to have a support on each side of a gear. Otherwise the shaft may become warped or the gear may jump out of alignment with it's meshing gear.
Don't glue right away--Although you may find that gluing gears into place may become necessary (or at least beneficial), don't do it until you are absolutley sure you want the piece there. It's a major pain to pull those suckers back out.: Things to Do:

Properly align shafts--Make sure both ends of a rotating shaft are at the same horizontal and vertical position. Otherwise the shafte will not spin freely and it will wear down quickly. (You might even melt the shaft in half.) This not only destroys shafts, but also the supporting pieces gather some of the melted plastic, and no other shaft will fit back into place.
Build from wheels to motor--The position of the motor in the car is less important than the position of the driving wheels. If you try to build a gear train separately and then attach it it to the wheels, you may find that it won't work.
Check spacing between gears--The teeth of contacting gears will be ground away if they barely overlap, thus causing the system to grind. Should the teeth overlap too much, the gears will not turn easily. Either way, power is lost.; Things to Avoid:(2)

Chain drive--As cool as it may seem, the chain does not function well in a gear train. It has a tendency to bind up, especially at high speeds. Also, lining the gears up to have appropriate amounts of slack can be a difficult task at best.
Worm gears--These gears are also pretty cool, but don't be decieved; they are the most inefficient gears available. Worm gears add significantly to friction forces, so try to stay away from them.
Pulleys--Systems incorporate belts generally to allow slippage in the gear train. This means loss of energy, and you want to be as efficient as possible.
Unsupported Gears--Try to have a support on each side of a gear. Otherwise the shaft may become warped or the gear may jump out of alignment with it's meshing gear.
Don't glue right away--Although you may find that gluing gears into place may become necessary (or at least beneficial), don't do it until you are absolutley sure you want the piece there. It's a major pain to pull those suckers back out.

TRANSMISSIONS
The limiting factor on finishing the track is whether it can climb the hill. The car must be geared with this in mind. However, the car would be capable of moving more quickly if it were geared differently for the straight sections and the downhill. This is the dilemma that you must solve.
A transmission in a car operates in exactly the same fashion. A car needs to go into first gear to gain enough speed so that second gear will not need to supply all the initial power. A similar legoized version of a transmission could also be built to serve the same purpose.
The task involves creating a system of gears which can provide variable spin ratios of the output compared to input spin. A sample transmission is shown to the right which accomplishes this task. A shifting shaft must be created. This shaft has a gear on it that can slide into contact with multiple gears (meshing gear). Depending on which gear the shifter comes into contact with, a different spin ratio is created for the whole system. Each meshing gear connects to the same output gear. The shifter position is then controlled by the servo. The sample transmission shown here will probably not be effective for your car since the change in spin ratio is rather large.
Disclaimer: Don't take the car with a transmission as the only solution to the problem at hand (though certainly a good one). An intelligently built car with only one gear may be competitive with, and actually beat, a multiple gear car. Or, you may choose a totally different alternative. The goal isn't to build a specific design, but to make the fastest vehicle possible. So be creative.: The limiting factor on finishing the track is whether it can climb the hill. The car must be geared with this in mind. However, the car would be capable of moving more quickly if it were geared differently for the straight sections and the downhill. This is the dilemma that you must solve.
A transmission in a car operates in exactly the same fashion. A car needs to go into first gear to gain enough speed so that second gear will not need to supply all the initial power. A similar legoized version of a transmission could also be built to serve the same purpose.
The task involves creating a system of gears which can provide variable spin ratios of the output compared to input spin. A sample transmission is shown to the right which accomplishes this task. A shifting shaft must be created. This shaft has a gear on it that can slide into contact with multiple gears (meshing gear). Depending on which gear the shifter comes into contact with, a different spin ratio is created for the whole system. Each meshing gear connects to the same output gear. The shifter position is then controlled by the servo. The sample transmission shown here will probably not be effective for your car since the change in spin ratio is rather large.
Disclaimer: Don't take the car with a transmission as the only solution to the problem at hand (though certainly a good one). An intelligently built car with only one gear may be competitive with, and actually beat, a multiple gear car. Or, you may choose a totally different alternative. The goal isn't to build a specific design, but to make the fastest vehicle possible. So be creative.

FOOTNOTES

Mechanical Engineering Design, Shigley & Mischke, pp551-558.
MIT handbook, pp96-98