In an effort to train my kids to be a nerdy engineer like I am, I have built this gear toy. My 4 year old daughter seems to have figured it out quickly, and she really loves it.

This is made to fit on a pegboard panel available at the Dollar Tree store near my house. If they aren't available in your area, I've included a printable version that should most standard sized FDM printers.

As your kids get older, this could be a great project to help them learn about CAD design. I've included the model files for each of the gears so they can modify them. You'd be amazed at the creative designs your kids will come up with. Maybe they'll even find a cooler way to utilize one of these pegboards to create something fun.

Tips: 

• Mirror the arrow gear in your slicer to have a gear with an arrow pointing the other way. It can help kids visualize how the gears are spinning differently depending on how its set up. 
• The 30 tooth gears only work in certain orientations, but that just adds another level of having to learn and figure things out as you build.
• For building your own gears, I use a module ("m," also known as “pitch” if you're using inches) of 1.25mm. For background on gear design, m=d/z, where d is the diameter of the gears (here is 25mm) and z is the number of teeth. PIay around with the module, diameter, and numbers of teeth and get a real feel of what its like to be an engineer and design, prototype, test, and repeat until it finally works.
• These are much like Legos in the fact that they are very painful to step on with bare feet.