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Can anyone help with this simple geometry problem ? (two circles +
connecting tangents)
Posted:
Oct 7, 2008 11:13 AM
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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..
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