Math Gear(s)

by SSW, published

Math Gear(s) by SSW Nov 18, 2013

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49605Views 16310Downloads Found in Math
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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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49605Views 16310Downloads Found in Math
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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.