# How to turn direction of 4 planar wheels into up/down motion?

For the head in a 2D plotter I have 4 gears in an X configuration in the same plane. The gears are driven by belts from the outside in different combinations. The top and bottom gear can be turned in opposite direction as indicated by green arrows. Or the left and right wheels can be turned in opposite directions as indicated by the red arrows. Both of those can happen simultaneously. The gears can also be driven all in the same direction as indicated by the blue arrows. Or all directions can be reversed. This is part of a larger construct and the belt movement already has effects there so they can't be changed.

Now what I want to build is some mechanical contraption that turns the blue arrow movement into an upward (or downward if reversed) movement to rise (or lower) the pen of the plotter.

If all wheels turn anti clockwise the pen should rise. If all wheels turn clockwise the pen should lower (or vice versa).

• belt movement already has effects ... do the belts move the head? – jsotola Apr 13 '18 at 7:11
• yes, the belt (it's actually one loop) moves the head – Goswin von Brederlow Apr 16 '18 at 9:06
• please draw the belt arrangement – jsotola Apr 17 '18 at 2:52
• Not that it matters for the question but here you go: ksr-ugc.imgix.net/assets/020/588/881/… – Goswin von Brederlow Apr 17 '18 at 8:11
• note: the pen elevating mechanism needs only two gears to operate (either two diagonally from each other) – jsotola Apr 17 '18 at 18:47

A- Imagine a hollow cylinder with the following design,

1. The outside surface of the cylinder can mesh with the four gears in the image and it will be placed among them.
2. the inside of the cylinder has a helical groove spanning the length of the cylinder (from top to bottom)
3. the cylinder can only rotate (no upward or downward motion)
4. the cylinder is open from top and bottom.

B- Now for the part that would hold the pen,

1. this part will be placed inside the cylinder.
2. this part will have pins that are meshing the inside grooves of the cylinder.
3. this part cannot rotate. it can only move up or down.

When the gears rotate according to the blue arrows >>> the cylinder will rotate (meaning that the groves will rotate) >>> and since the pen holder cannot rotate, the groves will force it to move up or down. The below figure shown the same idea but with a cylinder that has an outside groove.

• But when the gears rotate like the green or red arrows the cylinder will block movement or break apart – Goswin von Brederlow Apr 16 '18 at 9:04
• In this case, the cylinder can be meshed with only one of the gears and it will provide the same motion. Because it is either having the rotate clockwise or anti-clockwise (cylinder can be meshed to all gears) or having the gears rotate according to red-green arrows (cylinder will be meshed to only one gear) – Hussein Fawzy Apr 16 '18 at 11:07
• It can't. Because then it would always move the pen even when moving the head. The pen must only move when all gears turn in the same direction. – Goswin von Brederlow Apr 16 '18 at 11:31