Math Gear(s)

by SSW, published

Math Gear(s) by SSW Nov 18, 2013

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51620Views 17117Downloads Found in Math


At first glance the updates are barely noticeable, but every piece has been revised. The changes make assembly easier with better fit and smoother operation.

This Math manipulative is designed to appear playful from the first look. It lies flat on desk top, so it will also work well with overhead projection systems.

Behind the mechanical fun there are several simple ratio exercises. The eight tooth "Idler" gear is supplied to add reverse rotation without affecting the ratios. Each interchangeable gear has built-in graphics to indicate the number of teeth as well as rotation position. Some gear ratio formulas can be found here: http://en.wikipedia.org/wiki/Gear_ratio.

Rubber bands provide tension to keep the wheels engaged no matter what the combination.

FYI, the "T" on the gears stands for "teeth".


This thing is designed to print on MakerBot Replicator 2 machines, but I'm sure it will have good results on earlier machines as well. All parts fit within 105 mm x 105 mm build area. No support is needed.

Assembly is simple, just look at the photos provided. The rubber bands are just 3/4" or 1" office supplies.

One part that may get a little tricky is the Idler gear. That part is really two parts in one. In my test, it just needed to be broken loose and spun around a few times to free it up. The axle post is now a snap-fit into the center hole in the base unit so that it can be added or taken out as needed.

Be sure to clean out the center holes in the gears after printing so that it is not too difficult to get them on and off of the pins

Have fun learning!

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Would it make sense to use this as a division of fractions exercise? I am trying to think outside the box for a lesson. I know that the quotients of dividing by the fractional amounts of each turn would give you the correct number of turns, but how would I contextualize the reason for doing that?

Hi my name Steel. I am looking at this design and it looks really cool. I cant wate to print!

I'm making these up for my Intro to Engineering Middle School class, and they are wonderful except for one problem I'm having. The gear base pegs keep breaking on me at the slightest touch! I've even tried them at 100% infill with no luck. I'm running a Wanhao Duplicator clone, PLA at various temps up to 215. Any suggestions? I'm brand new to 3-D printing unfortunately, only had the machine for 2 weeks now.

Hello Mrs Montgo,

Sorry for not seeing your message earlier.

This is the first time I've heard anyone have this issue, but it does not surprise me at all. Those pegs are designed to print upright without using support material (I assume that is how you printed them). My guess is that they are breaking between the layers that the printer makes. The slot in the pegs is there to allow them to be squeezed slightly when a gear is pushed onto them. This can put stress on the layers.

A general 3D printing technique is to print with the layers going in a direction similar to the way you would orient wood grain, for strength, in a piece of furniture. I did not take my own advice here, for the sake of making it easier to print. So, I will suggest that you re-orient the pegs 90° for printing (with slot vertical to print plate). By laying them on their side the "grain" of the plastic layers will be going vertical, when stood up. Like a baseball bat. You will probably need to use the support material function, which will involve a bit more cleaning post printing.

I suggest "Simplify3d" for a printing app. Nice control for support.

I hope this helps. Please do reply back to let me know how it works.

-- Bernie (SSW)

Thank you! I will give this a try once I get the stuff off the printer I've got working away right now.

I'm a total rank newbie, we talked about Simplify3d, but I've only worked in Cura so far. I've come a way in 2.5 weeks though.
I will let you know, and put up some pictures of my make when finally all done.



One little thing to watch out for, is that once rotated, be sure the model is sitting flat on virtual build surface (not floating or sunk below zero Z level). I'm not familiar with how Cura works in that regard. Simplify3D has a "drop" function. This lets you spin things around, then pick them up and drop them down to the build surface.

-- SSW

Cura will allow you to rotate 90 degrees, perfect for what I needed Success! Success! Printed 3 sets of them but I did still go with 100% infill, I suspect these parts will get the most stresses put on them. Now I'm going to make 7 more sets for my classroom. Thanks for your help!

What am I supposed to be learning here with the numbers and different configurations?

Hi tvance929,

This gadget was created to help students learn how ratios work, in a hands-on way. The "T" on the gears stands for the number of teeth. So, if you connect the 8 tooth gear with the 16 tooth, the 8 will go around twice for one revolution of the 16. The arrows are just there to help line things up. Additionally, by adding a middle gear you can prove that the ratios stay the same, but the direction changes.

Hope that helps,

Bernie (SSW)

Jun 13, 2016 - Modified Jun 13, 2016
tvance929 - in reply to SSW

Awesome! Thank you sir! Now to assemble this after work and see it in action!

A magnet where the finger supports are and you could also attach this to a whiteboard (rather than an overhead). Would take much to remix it, and disc magnets are dollar-store cheap...

Apr 19, 2016 - Modified Apr 19, 2016

Great, I just printed (PLA). Fit perfectly. Thanks so much.
Chelsea from New Zealand.

Thank you for the comment.


-- SSW

This is a great implementation of a great idea. Super Job!
I assume that you know, at least a bit, about gear design
Do you have any suggestions for where we should look to learn about this?
I have been learning how to build 3D models of gears - but all the lessons that I have encountered so far has been on drawing gears based on pre-defined gear parameters (ie: Tooth Count, OD, PA, etc).
What I have not had much luck finding is a good explanation of how to come up with these numbers to define my own gears that have a specific gear ratio and fit in a targeted space
any suggestions??? thanks!

Thanks for asking this CraigJ.... I have been wondering the same.

Hi tvance929,

As I posted earlier, this is what I use for creating gears: http://www.gearotic.com/Spurtutorial.html

-- SSW

SSW - in reply to craigj

Hi Craig,

I am not an engineer, I just approach things like this from a practical perspective. I found a few resources online to be very helpful. Here are two really good ones:


Have fun!

I tried to print the parts for the base on a printrbot simple metal in PLA, but I couldn't fit the sides onto the center (even after lots and lots of filing) and even after cleanup the pegs were way too tight. I suspect that it might be my filament, though. The thickness varies widely, so one print under-extrudes to the point where there are huge holes and the next probably over-extrudes, causing press-fit parts to not fit.

Will keep running tests and tuning. Not giving up yet!

Trying now with PLA on Simple Metal with heated bed with Prusa PLA and Cura 15.10, will let you know how it turns out!

So far I have only printed with ABS on a Makerbot Replicator 2X.