compound gearing

We tried on a couple of occasions last year to use the VEX turntables as a pivot for an arm mechanism. Although they worked in principle we found the 60 tooth gear to be a limitation as we needed a higher gear ratio for the amount of weight we were trying to lift.

This year one of the teams is working on a design that again uses the small turntable but is flexible in the choice of final gear ratio by simple modifications. Four choices of ratio are available, 5:1, 8.33:1, 11.66:1 and 25:1. The current preferred ratio is 8.33:1 and is able (after preliminary testing) to lift 10 sacks reasonably easily with one 393 on each side of the robot. Here is a partial render showing the compound gearing only, all other structure has been removed.

The position of the motor and also a couple of bearing flat move but otherwise the structure remains the same.

5:1, not actually a compound ratio. 12 tooth gear drives 60 tooth on turntable.

8.33:1, 36 tooth drives 60 tooth, 12 tooth drives turntable 60 tooth.

11.66:1, 36 tooth drives (dual modified) 84 tooth, 12 tooth drives turntable 60 tooth.

25:1, 12 tooth drives 60 tooth, 12 tooth drives turntable 60 tooth.

I was showing 15:1, that was incorrect as it was actually 25:1, however, 15:1 should it also be possible using a 12 driving a 36 for the first stage.

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It’s best to keep as little force on the axles as possible, so you should always use your smallest gears as early as possible in compound gearing. For example, on the 25:3 ratio, if you powered the 12t sprocket into the 60t gear, then ran the 60t gear over to the 36t gear, which powers the arm, the largest force on any teeth would be only 60% of the current configuration.

It’s best to keep as little force on the axles as possible, so you should try to use larger gears when such large forces are present. Compound gearing yields the same resultant force no matter how you rearrange the gears, so the order does not matter in terms of force on gear teeth.

When considering friction, the order does not matter a lot, but it should still be considered. The energy lost due to friction (between the axle and the bearings) is proportional to the force times the angular velocity (RPM). You will not be able to reduce the friction, therefore, assuming the coefficient of friction is constant and you have a fixed number of axles.
But as you put more force on the delrin bearings, the axle can start to dig in (increasing the coefficient of friction and damaging parts), or the whole bearing can slide so it is no longer centered (both of which I have witnessed). To avoid this, force on gears should be reduced where there is less axle support (the gear is further from bearings or there are fewer bearings). Additionally, you can trade force for angular velocity (RPM) by putting the lesser gearing close to the motor so that the intermediate axle has little force on it and instead is turning faster.

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Last year I posted this example that was a design used on the students roundup robot. (full thread)

At that time this was your comment.

That design was notorious for twisting the axle, the students had to swap out one side or the other at almost every competition. So we tried to learn from our mistakes and take that advice.

There were many other design considerations leading to the example I posted yesterday including some that are physical. There was a significant advantage in the 12 tooth gear being smaller than the dimension of the 1x2x1 C channel as it allowed parts to be directly attached to the turntable without further spacing.

Our experience to date suggests that keeping the torque that an axle experiences lower is more important than the forces on individual gear teeth.

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Does the turntable work better than just a high strength 60 tooth gear?

In the application this is designed for it does as the final pivot is cantilevered which the turntable handles much better than a gear. We are trying something a little different from the usual 15lb-20lb monsters that were used the last two years. Total robot weight should be less than 8lb.

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Oh thank you for pointing that out to me. It turns out my previous post on this thread was incorrect (it is fixed now). I can’t recall twisting an axle, because we always screw directly to our arm and don’t use compound ratios. The configuration you posted yesterday is better for preventing axle twisting, and would probably be the best way to do what it’s trying to do (without using larger gears).

Thanks for updating your post, I’m not a mechanical engineer and don’t have the experience with mechanical engineering that I have in other areas, however, the way I always look at this is as follows.

The spec for this design is to run the motor with around 5 in-lb of torque so as to keep the speed of the motor at the optimum point, if we used the 1:5 ratio first then the next stage would be providing 25 in-lb of torque. This torque would have to be transferred through the axle to the gear driving the turntable. With the arrangement I used the 3:5 first stage only places 8.33 in-lb of torque on the axle which therefore has less chance of twisting.

One spec we don’t have is the torsional force needed to twist a VEX 0.125" shaft, I’m sure that’s available with some googling or perhaps experimental measurements, it would be useful to know.

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Nice designs! Thanks for sharing early in the season too.

You may want to look at reinforcing the tower across if possible with either some more standoffs or some metal going across the face of the tower. That nice high torque and load might make it want to move a bit on a twist. You can eliminate some twist with more attachments (but you add weight). You only get one point of attachement per standoff. Adding short sections of aluminum c-channel should do the trick with two screws a piece on each end.

Also using shoulder srews through the bearing blocks on the higer torqued sections will reduce the wiggle room of the axle wanting to move about. A hammer helps get the shoulder screw through the bearing block. There’s just enough room for the nut too.

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We want to reiterate the thanks as the compound gearing certainly helps with issues we had over the weekend with a raised arm backdriving under load. The gearing using high strength gears (25:1) though takes about 2.5-3 seconds to lift to the trough (using 2 393 and heavy elastics. This replaced a 5:1 sprocket which had no problem lifting in 1-2 seconds. We know the sprockets generally are more efficient; but before we rebuild with sprockets either 25:1 or eventually 15:1, is there an opinion on whether it will be as effective on the backdriving issue?

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This is already planned, I stripped all the structure away to show the gearing. The full tower is something like this, how much bracing is added will be determined when the students build it. We are also considering some type of torsion spring to help lift the arm but this is tricky as the arm is designed to be able to make a full 270 deg rotation and pickup sacks from either side.


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What I found out today when playing with the turntables it that the outer piece, the one connected to the gear, is actually held on by the screws. You take the screws out and you can screw in the arm in place of the gray plastic piece.

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Cool, a torsion spring!
From what material will you make your torsion spring? heat-treated axles?
A 12:60 gear on one side, vs a 6:30 HS chain on the other side will give you opposite twists to join with a strong torsion spring twisting only +/- 54 degrees, with a nicely balanced system, rather than a force to a constant anchor.
A competing idea might be a rubberband powered spring cam.

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I honestly have no idea.

Yes, it’s far more likely to end up being some type of rubber band powered device. There is easy access to the central axle and it just seems like there should be a clever way to provide some type of holding power to the arm using the space between the tower supports. Once the students have finished building rev A then we will brainstorm some ideas and revise the design.

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Cool torsion spring idea! Last year one of our teams braided the black tubes to add more strength to a linear motion like inside a steel belted radial tire. I am not sure how well the tubes will do in torsion, but I bet it’ll work just fine.

Also, in addition to the big cross braces you have, the side pieces might need some bracing too as the max force is on the 12 tooth gear going to the turntable.

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Regardless of whether the spring is linear compression, linear expansion, wrapped torsion (US garage door), or linear torsion (car suspension), the force vs displacement curve is unlikely to match what you need to balance the weight of an arm at all arm positions.
I’ve previously posted excel spreadsheets that attempt to calculate the shape of a cam needed lift an arm from -45 to +45 degrees, but it didn’t get any replies in that thread.
While you could form a custom cam for a 1/8" vex rope from allowed plastic, a standard HighStrength sprocket mounted off-center is almost the right shape.

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Well, at this point, your Spreadsheet has 192 Views… Someone must be looking at it… :wink:

I have never been taught this, or really needed to know until today.

How do you calculate the gear ratio for compound gearing?

I would like to make a video tutorial about this at some point, but basically you just multiply the first gear ratio by the second (by the third, ect). So if you have a 1:3 and another 1:3, you will have a 1:9. If you add another 1:3 you will have a 1:27.

To add on to Owen’s response, compound gearing is just putting multiple pairs of gears together in one system. Each pair of gears makes your end gear spin ‘X’ times faster or slower. In a 1:3 + 1:3 compound gearing system, the first pair of gears reduces the speed of the middle axle by a factor of 3. This middle axle feeds into the next pair of gears which reduces the end axle by another factor of 3. Thus the final reduction is 1:9.

OK, that makes sense. Thanks y’all!