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


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 multicylinder 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..



