Coin Rotation Paradox Machine

An easy to print tool/toy for demonstrating the coin rotation paradox.

The coin rotation paradox is a math problem that, when one coin is rolled around the rim of another coin of equal size, the moving coin completes not one but two full rotations after going all the way around the stationary coin, when viewed from an external reference frame.

This paradox was at the subject of an error on the 1982 SAT test.  Here is an excellent video that explains the paradox

My toy makes for an easy way to demonstrate the paradox with 4 different size ratios to play with.

This print does not require any supports or use of tools for assembly.  The only thing you will need is a bit of thick or gel CA glue to attach the platters to their corresponding gear.

***Important note on printing*** Make sure that your printer is set so that the seams are not aligned, otherwise your posts and holes will have a bump in one spot that will make the rotation of the parts bind whenever the seams pass each other.

All color changes needed can be accomplished using simple layer color change inside your slicer.  I recommend using 3 different colors for your markers and indicators.  The rings and text on the platters should all be one color.  The mark on the top of the outside post of the gear tray should be a second color.  The mark on the top of the Outside Gear should be a third color.  This makes the visualization of revolutions stand out better than if they were all the same color.

First time assembly instructions.

1. (optional)Attach rubber feet to the bottom of the Base (a).
2. Place Base (a) down with the key slot opening oriented to the right.
3. Place the Gear Tray (b) over the central post of the base so that the tray is oriented to the right.
4. Place the Central Stationary Gear (c) over the central post of the base, align using the key slot and key.
5. Place the Outside Gear (d) over the outermost post of the tray.  Align the orientation marker of the outside gear with the mark on the top of the post.  Both markers should be aligned with the key slot on the central post as well.
6. Place the Middle Gear (e) over the middle post of the tray.  Rotate the middle gear until it meshes with the inner stationary gear and outer gear.
   • Test movement.  The tray should freely rotate around the central hub and the gears should rotate easily.  It may take a few rotations to achieve easy movement due to print imperfections.
     • The marker on the post of the tray should always point towards the center.
     • The marker on the outside gear should always point to the left.
7. (repeat steps 7-12 for each ratio pair) Place the Big Gear (f) on the central hub of the base, align using the key slot and key .  Be sure that the spacer printed as part of the gear is facing down.
8. Place the corresponding Little Gear (g) over the post and shoulder of the outside gear.  Be sure that the spacer printed as part of the gear is facing down.
9. Dry fit the Big Platter (h) for the ratio being used over the central hub of the base.  Orient the radial line so that it lines up with the markers on the tray post and outside gear.  It should also be aligned with the key slot in the hub.
10. Dry fit the Little Platter (i) over the post and shoulder of the outside gear.  Orient the radial line so that all markers are in alignment.
11. Remove the Big Platter (h).  Place small dots of thick CA glue or Gel CA glue around the outside ring of the Big Gear (f) and one or two small dots near the central hub.  Place the big platter back onto the central hub and make sure alignment is correct.  Use the Central Hub Nut (j) to hold the platter in place as the glue hardens.
12. Remove the Little Platter (i).  Place a few small dots of thick CA glue or Gel CA glue on the little gear well away from the shoulder of the outside.  Place the Little Platter (i) back onto the Little Gear (g) and make sure the alignment is correct.  Press down firmly to distribute CA glue.  Let rest for 10-15 minutes to ensure glue is hardened.

Assembly Instructions:

1. Place Base (a) down with the key slot opening oriented to the right.
2. Place the Gear Tray (b) over the central post of the base so that the tray is oriented to the right.
3. Place the inner Stationary Gear (c) over the central post of the base, align using the key slot and key.
4. Place the Outside Gear (d) over the outermost post of the tray.  Align the orientation marker of the outside gear with the mark on the top of the post.  Both markers should be aligned with the key slot on the central post as well.
5. Place the Middle Gear (e) over the middle post of the tray.  Rotate the middle gear until it meshes with the inner stationary gear and outer gear.
   1. Test movement.  The tray should freely rotate around the central hub and the gears should rotate easily.  If this is the first assembly It may take a few rotations to achieve easy movement due to print imperfections.
      1. The marker on the post of the tray should always point towards the center.
      2. The marker on the outside gear should always point to the left.
6. Place the Big Gear and Platter over the central hub.
7. Align the Little Gear and Platter so that the radial line of the Little Platter is lined up with the radial line of the Big Platter and tilt the gear so that you can fit the teeth of the Little gear under the edge of the Big Platter.  Slip the Little Gear and Platter over the shoulder of the Outside Gear.  There should be enough tolerance for the Little Gear to slip over the shoulder with minimal force.
8. Use the Central Hub Nut (j) on the central hub.  Do not over tighten.

Disassembly Instructions:

1. Remove Central Hub Nut (j).
2. Remove the Little Gear and Platter by lifting up on the gear and tilting it as it comes up so that the outermost edge is higher.  There should be enough tolerance for the little gear to slip free with minimal force.
3. Remove the Big Gear and Platter.