I developed a generic cycloidal gear builder in OPENJscad. This is a smooth functioning planetary gear set with zero play. This was a test of the software. I wouldn’t go this crazy in an actual machine. This same tech will be used in a few of my new 3D printer builds. I should be able to eliminate a lot of belts.
I am having trouble with a math problem. This arrangement is 2:1:4 sun:planet:ring. Why does it fit 6 planets? This one is weird. Let’s assume we have normal gears. How do I take the 3 tooth counts and turn that into the max number of planets? (Overlapping planets are allowed for this question.) I ask because I have wasted a ton of effort making sure the sun and ring both had a multiple of the number of planets. Apparently that is not the case.
@Gary_Tolley_Grogyan I have been working to make it user friendly. I will upload what I have to github but you will have to really know what you are doing.
Are you asking how to calculate the maximum number of planets? Off the top of my head…
Evenly spaced planets will form a regular n-sided polygon if you draw lines between their centers of rotation. Those centers should fall on the circle that is the average of the sun and ring’s radii. To find the maximum number of planets, take the largest radius of the planet multiplied by two, and see now many sides a polygon with that radius (average of sun and ring) while still having sides longer than that length, calculating side length with side = 2r * sin(180/n).
@Whosa_whatsis that is not quite what I am asking. For a given sun and ring position there are a finite number of possible planet positions. If that number isn’t a multiple of the number of planets you want then you have an issue.
Ah, I see what you’re asking now. The way I would go about thinking about that is to fix the position of the sun and one planet, then find the corresponding rotation of the ring to fit. Then I would imagine rotating the planet around the sun, keeping the teeth meshing, until it again lines up with the ring. I’ll have to sit down with some paper to think about that one later.
@Gary_Tolley_Grogyan I saw on your other post that you need a multiextrusion. This wasn’t printed all at once. The middle piece is printed in two and then bolted. This allows for the pieces to have a slight interference fit. That is critical if you want no backlash or no play.
I haven’t thought all the way through this yet, but I’m suspecting your math is ignoring the fact that you seem to have two kinds of teeth with different action. It may not be valid to expect the same properties as gears with uniform teeth. But I have no experience thinking about cycloidal gears. Interesting.
Now I’m distracted by the idea of gears with high helix angle allowing degenerate planet gears with only one or two teeth.
@Brook_Drumm HELIOS for sure and a 4 axis robot arm printer that is in the work. Anywhere I have been struggling to get the reduction I need. With this tech I can get 100:1 in a super tiny space.
@Ulrich_Baer that is worded bad. I want to know how to use the three different tooth counts in a function to give me the number of possible planets. You are correct on tooth counts.
I assume the two mirrored gears play a role as they can be in the overlaping (with regular gears) position… so 3+ 2×½=4 So 6 Gears can fit into the 4Ring. … so you can get 1.5 Gears into the position. Mathematically. Maybe for this special Gears as they are not symetrical we need to treat them as 2seperated Gears. To each set could hold 4hearts but due to overlap only 6 of the 8 could fit in. If you have a ringgear with 18teeth you will not get in 9 2teeth gears or 6 3teeth?.
So, it looks like the number of positions where a planet will fit for any given position of the sun and ring gears is equal to the sum of the numbers of teeth on the sun and ring gears (or, of course, any factor of that number). These positions are evenly spaced around the sun gear, but of course you’ll need the equation I posted earlier to find the maximum number of those that will actually fit without interfering with one another.
@Whosa_whatsis if i got that right then the described problem of the 6 gears fitting in there is not solved by your equation, as your equation only works for objects without the possible overlapping space.
