Re: Stuck on simple circle geometry problem.. Please help!

[Rob P]

On Oct 7, 11:13 am, whatwouldmattdo <Whatwouldmat...@gmail.com> wrote:
> Hello!
> I am an engineering student with a simple geometric relationship
> question I was hoping someone might be able to assist with. I've made
> a dodgy sketch of it available at:
>
> http://img162.imageshack.us/my.php?image=dryergeometryproblemyb8.jpg
>
> Basically, there are two circles, with their own radii r1 and r2, with
> the second circle positioned above the first. The centre points of
> each circle are separated by a total vertical distance Vdiff, and a
> total horizontal distance Hdiff. A tangent runs along the left side of
> circle 2 and touches the right side of circle 1. The tangent touches
> each circle at a bearing of a or b degrees from the vertical,
> depending on the circle radii and separation.
>
> I am interested in finding an expression for Ldraw, which is the
> length of the line touching each circle (thickened in diagram), and an
> expression for Lcont,1 and Lcont,2, which is the length of the arc
> connecting where the tangent touches circle 1 to the bottom most point
> of the circle. Lcont,2 is the length of the arc from the tangent
> touching circle 2 to the top most point of that circle.
>
> Can anyone help me out??
>
> Thanks a million
> Matt
>
> P.S.
> In case you want to know, or if it  helps, there is a point to all
> this... Its for a model of a multi-cylinder paper dryer (viewed side
> on). The cylinders are steam heated and a felt web supports a web of
> paper.
> Basically, when the thick line (web of paper) is touching the
> cylinder, that length of paper (Lcont) will be heating up from
> contacting the cylinder. The length in between them will be cooling
> and evaporating.
>
> I'm making it so with a few given parameters (each cylinder diameter
> or radius, vertical and horizontal distance from each other) each
> length can be calculated. Well, hopefully :P..

Matt,

you may want to look at belt wrap calculations for front end
automotive drives. Belt wrap is an important factor and there may be
a model available out there.

Rob

[rgr]

Note that the tangents and the radii at the tangent points are
vertical to each other. So, by Pythagoras

ldraw = sqrt(d^2+(r1+r2)^2)

where d is the distance of the centers.