[Arm-netbook] python coding help needed (sin, cosine, blah blah)

[Benson Mitchell]

On Sat, Jul 29, 2017 at 8:53 AM, Luke Kenneth Casson Leighton <lkcl at lkcl.net
> wrote:

> http://hands.com/~lkcl/foldable3dsandwich200/belts.py
>
> ok, i could use some algorithm help, here, if anyone's interested.
> the key function is add_bearing in class Belt.
>
I don't really speak python, but I'm happy to put my two cents in.

You've got three of the four cases defined, but to start with I only looked
at the simple one (invert==0, oldinvert==0) which you seem to think is
solved. Unless I'm missing something, it's not really solved at all -- it
looks like it completely ignores any difference in radius when figuring the
contact angles. And I think when you fix that, the hard cases will mostly
explain themselves (you'll basically negate the radius in that calculation,
and maybe also add/subtract the belt thickness).

So, given the old bearing has radius R1 and the new bearing has radius R2,
separated horizontally (or at any other angle) by a distance D, we can find
the deviation from horizontal (or in the general case, the deviation from
the angle connecting their centers):
arcsin((R1-R2)/D)

And of course, negate that if they're both inverted (rather than both
noninverted). (Not entirely clear on your sign convention, so this may be
exactly backwards, but you can figure that out faster than I could puzzle
through it.)

And if you're crossing over, with belt thickness T, that should just become
arcsin((R1+R2+T)/D)
(again, this is going from noninverted to inverted -- negate for inverted
to noninverted, or maybe the opposite.)
But of course in this case, you leave the first bearing at one angle, and
contact the second bearing at the opposite angle; if you actually redefine
R2=-(R2+T), this takes care of itself, so you might not need all the cases.
(Though the part where you wrap the arc around the old bearing will need to
be careful about clockwise/counterclockwise.)

Hope that helps.

Benson Mitchell