"Leroy" <whe### [at] gmailcom> wrote:

> Why did you start this?

Because making parts from CSG can be a big pain, and I figured that I could
model a prism which would give me smooth curves and the proper alignment with
the straight sections.  Not so easy without a good modeler or drawing program.

> I had to try it for my self. Not the prism part but
> getting the belt around a set of pulleys.

I did that ages ago.  I used Friedrich Lohmueller's method, with the angles and
all of that, but doing that for multiple pulleys was a bit overwhelming.
So I found a purely analytical method using the radii and the coordinates of the
centers.

>  I spent the last week working on it. I started with placing a random number of
> pulleys of different sizes around the origin. Then did a simple test to mark
> weather the belt was inside or outside a particular pulley.
>  That test was:: if the vlength of the midpoint of the two pulleys on each side
> of the test pulley was shorter than the vlength of the test then the belt was on
> the outside.
>
>  Then I came the deciding which tangent formula to use and calculating the
> tangent on two adjacent pulleys. There are basic two formulas one for the cross
> over, one for going from Outside to Inside, and the other for Outside to
> Outside. Those formula can also be used for the reversed Inside to Outside and
> Inside to Inside.

Nice - when I was analyzing the possible configurations, I realized that it
could get quite complicated, and there was no good way to automate the process -
and different results might be wanted compared to what an algorithm chose.

> So I had those all 4 tangents that you have shown. But I only needed the one
> tangent for two pulleys.

Correct, unless you only have two pulleys.   ;)
I also knew that one might want to model a system with an idler pulley or
tensioner, so i made everything manually selectable.

>  Then came the curved part of the belt. Each pulley has two tangent points, one
> where the belt comes in and one where the belt goes out. Using the
> Inside/Outside value and those tangent points I make a prism to cut a torus. Did
> I mention the the belt was made of cylinders.

Nice.   The animation I did used a belt made out of truncated cones in order to
simulate a V-belt, and to have an odd-colored cone to mark the belt and give a
better visual cue.


> Now maybe I'll try and animate it;)
> Here a look:

You've done a great job as always   :)

Most belt animations are done with only a short, repeating series of frames, but
with multiple radii, or if marking the pulleys or belt to really show the
rotation, then what constitutes a "single" cycle can be much longer and somewhat
challenging to calculate.

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