Le 16/07/2014 17:58, Bald Eagle nous fit lire :
> I'm just going over the details of animating a chain or belt wrapped around 2
> pulleys.  I understand MY math, and the math posted on Wikipedia.
> 
> http://en.wikipedia.org/wiki/Belt_problem
> (Scroll down to the second, related "Pulley Problem"
> 
> The first step to solving the linear length of belt or chain seems to be to
> establish the angle at which the belt is tangent to the pulley, and then from
> that, the linear length can be calculated.
> 
> What is driving me absolutely crazy, is that I'm actually USING FM's code for
> animating a belt, and IT WORKS.  But I look at the known parameters (distance
> between pulleys and difference of the radii) and consistent with the Wikipedia
> math, I use (ARC)COSINE to solve for the angle.  FM uses the SINE.  This doesn't
> seems possible.

You are not measuring the same angle.
Wikipedia computes the covering angle theta on smallest wheel.
FM computes the angle of the belt with the axis of the wheels. (alpha).

The relation is theta = pi - 2 alpha. (or alpha = (pi-theta)/2 ).

When remplacing cos( angle) with an angle2 = pi/2 - angle, cosine become
a sine, and vice-versa.


> 
> Then, when I solve for the linear length, I use the trigonometric relationship
> to derive the length of the remaining side, but FM employs the Pythagorean
> Theorem.  How is this possible when P, the distance between the two pulleys is
> the HYPOTENUSE?!

You have the length hypothenuse, you have the length of the small side,
it is obvious to compute the length of the third side with Pythagore.

( H^2 = S^2 + L^2, hence L = sqrt( H^2 - S^2 ), no problem)

You noticed the subtraction, right ?

> 
> It seems like it ought to turn out oh-so-woefully wrong, but the render and
> animation give one of FM's flawlessly beautiful creations.
> 
> Can someone look at this and explain what Dark Magic is at work here?
>
http://news.povray.org/povray.binaries.misc/thread/<web.53c69f83e73deed5e7df57c0%40news.povray.org>/
> 
> [If posting graphics attachments in another thread, please provide a link in
> this thread]
> 
> 


-- 
IQ of crossposters with FU: 100 / (number of groups)
IQ of crossposters without FU: 100 / (1 + number of groups)
IQ of multiposters: 100 / ( (number of groups) * (number of groups))

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