Functional gears seem irregular

[b139b]

I try a function which I think should define something with mirror symmetry across the x axis, like this:

Code: Select all

t + cos(t * 1.5) * 0.2

using 20 knots it doesn't look very symmetrical, and it looks like there's a knot missing just above the x axis near the other gear.

And, in fact, now that I count the knots drawn on the diagram, it's not showing the one at 342 degrees, even though it is shown in the list. I tried adding another knot there and it shot off into space somewhere on the other side of the diagram. Maybe an off-by-one error somewhere in the handling of that list?

Also, I can't copy-paste into the function box. I want to be able to do that because I'm thinking in terms of the right-hand graph and entering a function for the left-hand graph, so I ask wolfram alpha to integrate my function and then try to paste that in there... but no such luck.


While I'm talking about it, is a planetary pinion planned at any point? Initially I thought I was going to get by with the elliptical gear solution, which does have that option, but I'm now realising I have a more complicated problem with clearances and axle radius. I need a planetary gear arrangement and if my reasoning is correct I might also need to figure out how to arrange a non-integer pinion order (something like 1.1; turning from -200 to +200 degrees).

[ArtF]

>>using 20 knots it doesn't look very symmetrical, and it looks like there's a knot missing just above the x axis near the other gear.

I do see a problem with the last knot not showing up in the knots display, I will look into that. Do you have "Rollover at 360" selected?
With a non 360 degree symmetry of rotation discontinuities will often be seen. The algorithm for this is one that fits the data to a circular
bezier with constraints as to maximum rate of change so some changes will be seen due to bezier conformance, More knots the better
to get tighter resolution in that case.

>>is a planetary pinion planned at any point

I have no plans for functional planetaries, there is so little call for it and so
much development complexity with functional planetaries that I haven't any plans
at the moment.

Regards
Art

[b139b]

I tried it with and without rollover. My intention was to go without but eventually I just started clicking all the buttons to see what changed.

I would have been just as happy with an even simpler approximation, but the asymmetry is what threw me off, so I tried 100 knots as well, and that was more symmetric (but still with a missing point).

I was also kind of groping about a bit trying to get a handle on the shape of the curves and trying to get a feel for working with the integral of the radius rather than the radius itself, so I wouldn't have been confident saying that it should be symmetrical until I tried it with 100 knots and getting a different result.

When I watched the instructional video I wondered if it might be easier to work with a Fourier approximation of the gear profile rather than a Bézier spline. I thought it might help because a DFT is intrinsically periodic, and the functions I was trying would have been exact fits to just one or two bins. But, of course, it would have been challenging to translate that to control points in the user interface, so maybe not such a great idea in that respect.

I have no plans for functional planetaries,

I wonder if maybe I can work out a solution using the elliptical planetary generator to make the external gear and then figure out a function for the internal functional gear which would mesh with that over the arc that I care about -- with a tweaked ratio so that I can get the spacing that I need. I'll have to think about that, I guess.

[Mooselake]

It's been a while since I've watched the updates but I believe that Gearify 2.0 (remember that?) may do functional planetaries

KIrk

[ArtF]

I think Kirk is right, that Gearify may be able to do it for you. I havent seen a formula translator, but its worth a look.

Art