Sunday, June 23, 2013

Gearing Up and Down

LEGO Mindstorms NXT hobbyist, do you remember to counting teeth of gear in the past my posting? Now, lets we continue to learning about gearing up and down. Let's start turning the larger gear in our example. It has 24 teeth, each one meshing perfectly between two teeth of the 8t gear. While turning the 24t, every time a new tooth takes the place of the previous one in the contact area of the gears, the 8t gear turns exactly one tooth too. The key point here is that you need to advance only eight teeth of the 24 to make the small gear do a complete turn (360 degrees). After eight teeth more of your 24, the small gear has made a second revolution. With the last eight teeth of your 24, the 8t gear makes its third turn. This is why there is a difference in speed: For every turn of the 24t, the 8t makes three turns! We express this relationship with a ratio that contains the number of teeth in both gears: 24 to 8. We can simplify it, dividing the two terms by the smaller of the two (8), so we get 3 to 1. This makes it very clear in numerical terms that one turn of the first corresponds to three turns of the second.

You have just found a way to get more speed! (To be technically precise, we should call it angular velocity, not speed, but you get the idea.) Before you start imagining mammoth gear ratios for race car robots of LEGO Mindstorms NXT, sorry to disappoint you~there is no free lunch in mechanics; you have to pay for this gained speed.You pay for it with a decrease in torque, or, to keep in simple terms, a decrease in strength.

So, our gearing is able to convert torque to velocity~the more velocity we want the more torque we must sacrifice. The ratio is exactly the same: If you get three times your original angular velocity, you reduce the resulting torque to one-third. One of the nice properties of gears is that this conversion is symmetrical:You can convert torque into velocity or vice versa. And the math you need to manage and understand the process is as simple as doing one division. Along common conventions, we say that we gear up when our system increases velocity and reduces torque, and that we gear down when
it reduces velocity and increases torque. We usually write the ratio 3:1 for the former and 1:3 for the latter.

When should you gear up or down? Experience will tell you. It largely depends on the motor you start with and the robot you want to end up with. The MINDSTORMS NXT servo motors are already geared down significantly within their plastic case, so they turn at a relatively slow velocity and produce quite a bit of torque. Without gearing up or down, they will provide a good match of speed and torque for many robots. If your vehicle will climb steep slopes or your robotic arm will lift some load, you may still want to gear down. If your vehicle will be lightweight and you want more speed, you can gear up. Older LEGO motors have less internal gearing than MINDSTORMS NXT servo
motors. They rotate at a higher velocity but produce less torque. When using them, you will generally want to gear down to reduce speed and increase torque.

LEGO Mindstorms NXT hobbyist, one last thing before you move on to the next topic about The Geartrain. We said that there is no free lunch when it comes to mechanics. This is true for this conversion service as well: We have to pay something to get the conversion done. The price is paid in friction~something you should try to keep as low as possible~but it's unavoidable. Friction will always eat up some of your torque in the conversion process.

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