Tag: mechanics

Compound Gears

As I mentioned in my previous post, “Gears & Torque: Crash Course,” using the available VEX gears, you can achieve a 7x increase in speed (or increase in torque) by combining a 12-tooth gear and an 84-tooth gear in between your motor and your moving part. But what if you need more than 7x faster? Or what if you need a really strong moving part? You can achieve this by stacking the gears in a certain way, called compound gears.

Below is a slightly-modified diagram of our Nothing But Net flywheel, which used compound gears to get the flywheel spinning fast enough to launch the NBN balls:

Compound Gears

The drive axle on the left had 2 motors, top and bottom, with a 60-tooth gear; the output axle on the right has a 12-tooth gear and the flywheel. The magic happens on the axle(s) in the middle of the sandwich. The key to compound gears is putting 2 gears of different sizes on the same axle, as shown above (a 12-tooth gear on top, being driven by the 60-tooth gear, and an 84-tooth gear below it, driving the 12-tooth gear on the flywheel axle). The formula is explained below, but it’s easiest to think about how things are turning, as described in the colored labels in the diagram.

The formula for simple gears, from my previous post, is:

Gear Ratio  =  Teeth on Driven Gear
(gear connected to moving part)
Teeth on Driving Gear
(gear connected to motor)

For compound gears, we just calculate this same gear ratio for each pair of gears (however many pairs you have), and then multiply them together, achieving the same answer as shown in the example above:

Gear Ratio  =  12
(connected to middle axle)
 x  12
(connected to flywheel axle)
 =  1  x  1  =  1
(connected to motor)
(connected to middle axle)
5 7 35

The nifty thing about compound gears is that you can stack them up in many different combinations, and by using even more than 3 axles, you can achieve very high speed or very high torque.

Notice I said high speed OR high torque. Just because we’re using compound gears doesn’t mean we get to break the laws of physics (sad face). And, as I mentioned in my previous post about how motors work, even when you pick one of these, there is a limit to how far you can go. Compound gears don’t come with magic unicorns included in the box (again, sad face). What will happen if you try to push the motors too far? Motor Overload (aka Motor Stall). They will just stop, or they will work for a short period of time, and then fail. My next post is going to be about motor overload, so stay tuned!


Gears & Torque: Crash Course

If you’re like me, you’ve probably heard the word “torque” in car advertisements on the radio all your life and never really knew what they were talking about, but they made it sound mighty impressive. When I jumped in to being a coach for VEX, I had to do a lot of mechanical learning very quickly, and I started with gears (and finally learned what torque is). Here’s a little summary of that first wave of learning.

Strength vs. Speed (and what Torque is)

Strength vs. SpeedIn VEX, you can think of strength and speed as a husband and wife sharing a not-large-enough blanket at night; if one spouse gets more blanket, the other spouse gets colder. There’s no other way about it. With VEX motors, you can either have more strength or more speed, but not both. These are your choices, illustrated at right. You’ll have to decide what your best balance of speed and strength is, for each instance where you are using a motor. Usually it comes down to something like, “What’s the fastest speed we can get for the strength we require?” or, “How strong does it need to be to lift the heaviest thing we need to move?”

So what is torque? The technical definition is:

a measure of the rotational influence that a force has on an object

Huh? Not that helpful. Well, in our case, since we’re talking about VEX motors (things that rotate), we can say it’s a measure of the motor’s force, or, basically, “strength” in the diagram above.

Use Gears to Get What You Want

OK, so you’ve decided what your priorities are for your motor use (strength, speed, or [usually] a combination of the two). How do you achieve that from a VEX motor? With gears! Putting gears in between the motor and your wheel (or moving part) will make the wheel go faster or slower than the motor itself. Looking again at the diagram above, you can also think about this the other way around: the gears will make your wheel/moving part stronger or weaker than the motor by itself.

Side Note About VEX Gear Types

A tangent about VEX gears. They come in 2 types: standard/normal strength and high-strength. In our rookie season, we were, well, rookies. About a lot of things, including VEX parts. On our NBN robot, we started with standard, normal-strength gears on our flywheel, and the week before the first competition, we started loosing speed and it got slower and slower and slower. Once we took apart the flywheel (no small task), we saw that the shaft had turned the square in the center of the gear into something of a circle — yes, our gears were stripped, from the inside.

That’s when we learned about VEX high-strength gears, and we never looked back. As shown in the diagram below, high-strength gears have number of features that make them an improvement.

Normal vs. High-Strength Gears

  • First, they are about twice as thick as standard gears, meaning they are really unlikely to crack, and the teeth are unlikely to break, even when treated rather harshly (we have proven this empirically).
  • The center of the high-strength gear, when you take them out of the box, is just a big square hole, and you can put one of 2 inserts into it:
    • one (not shown) makes it a round hole in which a shaft can spin freely;
    • the other, shown above, is a metal insert that has a square hole that the shaft fits through. These metal inserts are really snug; sometimes we’ve had to wedge them in with screwdrivers, pliers, etc., but once they’re in, they’re not going anywhere, and they’re not going to strip. One insert goes on each face of the gear.
  • The smallest gear, the 12-tooth, is solid metal, and is obviously not going to break, ever.

There is theoretically more friction with the high-strength gears, since there is larger surface area where the gears mesh, but we have never noticed any decrease in performance. At this point, the ONLY time I would consider using standard gears on a robot is if there were not enough space to fit the thicker, high-strength gears in the structural design, and if that were the case, I might encourage my kids to reconsider their design. Seriously. For a competition robot, there is no reason to go with the less-reliable standard VEX gears.


Gear Ratios

The phrase “gear ratio” refers to the difference (up or down) in speed between the motor and the end point in your chain of gears (a wheel or other moving part). Going back to the diagram of the scales at the top of this post, you can also think of the gear ratio as describing the difference in strength (torque) between your motor and your moving part.

VEX gears come in only 4 sizes (thankfully): 12-tooth, 36-tooth, 60-tooth, and 84-tooth. Notice that these numbers are all divisible by 12? That’s not an accident, as we shall see in a moment.

To cut to the chase, to calculate a gear ratio, you simply count the teeth on the respective gears, place them in a fraction, and simplify the fraction to lowest terms:

Gear Ratio  =  Teeth on Driven Gear
(gear connected to moving part)
Teeth on Driving Gear
(gear connected to motor)

So what does this mean really? Here’s some examples:
Gear Ratio 3-to-1If we have a motor connected to a 12-tooth gear, and a moving part connected to a 36-tooth gear, as shown at left, then the 12-tooth gear will go around 3 times before the bigger gear goes around 1 time.

Gear Ratio  =  36  =  3
12 1

So the gear connected to my moving part is moving much more slowly than my motor. What does this get me? More strength, or torque. My moving part can lift more, push more, etc. than if it were connected to the motor directly. How much more? 3x more! What does it cost me? Speed! My moving part is only going 1/3 the speed that it would go if it were connected to the motor directly. (See husband-and-wife sharing too-small-blanket above.) That’s your tradeoff.

One more example, in the other direction:

Gear Ratio, 3-to-5Here my motor is connected to a 60 tooth gear, and my moving part is connected to a 36-tooth gear. When my motor turns its gear around once, the gear connected to my moving part goes around almost 2 times. So my moving part is going almost twice as fast as if it were connected to the motor directly. And what do I give up in the process? Yes, torque. I can’t lift as much, throw as far, push as strongly, etc. But presumably in this case I’ve chosen this gear ratio because I don’t need those things.

Gear Ratio  =  36  =  3
60 5

Did I mention that all of these numbers are divisible by 12? It makes for nice, simple gear ratio calculations—all of them, in every possible combination. How nice!

But wait! If the biggest gear is 84 teeth, and the smallest one is 12 teeth, then the fastest I can make my wheel spin is 7x the original motor speed (84/12 = 7). What if I want MORE than 7x the speed??

Next Time: Compound Gears

Whew! That’s all I have time to type and graphic-ize today. Next time I’ll find some pictures that show compound gears and what you can achieve by using them (we did this last year with our NBN robot to achieve the high speeds needed for our flywheel).


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