Re: Determining the curve
- From: "Philippe 92" <nospam@xxxxxxxxxxxx>
- Date: Fri, 10 Mar 2006 21:17:25 +0100
Randy Poe wrote :
google@xxxxxxxxxxxxxxxxxxxx wrote:
Hi, I hope someone can help me here.
Where I work I use a roller to role a flat plate of metal into a curve.
The roller consists of three cylinders, A, B and C. A sits on top of B
and both are fixed. Cylinder C sits to the right of A and B and can
move vertically. The distance between the centre points of A/B and C is
80mm. The diameter of each cylinder is 74 mm.
So, a flat plate is fed in between A and B. It hits C at an angle
relative to the position of C along the vertical axis. This then rolls
the plate into a curve which in the end curves to form a circle.
What I want to do is put a scale along side the cylinder C so that I
can set it to the correct vertical position to create the circle I
want.
So, my question is, can anyone think of a formular with one variable
'd' that I can plug the desired diameter in and get the value 'Y' (the
vertical position of cylinder C)
If I understand the mechanics right, the circle formed is one
which can be drawn tangent to B and C.
The metal bends on radius R forming an arc from A/B to C
of angular length theta. The horizontal length of this
arc is R sin(theta) = 80 mm. The vertical rise of this arc
is R (1 - cos(theta)) = Y
R - Y = R cos(theta)
R sin(theta) = 80 mm
R^2 sin^(theta) + R^2 cos^2(theta) = R^2 = (80 mm)^2 + (R-Y)^2
R^2 = (80 mm)^2 + R^2 + Y^2 - 2RY
Y^2 - 2RY + (80 mm)^2 = 0
Solving the quadratic equation and making the approximation that
R >> 80 mm (the bending radius is a lot larger than 80 mm), I get
Y = 80 mm * (80 mm/2R) or
Y = 80 mm / (D/80 mm)
Take the ratio of D to 80 mm, and divide 80 mm by that amount.
If you want a diameter of D = 1 meter, the ratio is 1m/0.08 m = 12.5,
and Y = (80/12.5) mm = 6.4 mm.
Does that number seem correct according to your experience?
I discounted the metal thickness and the radius of the rollers.
- Randy
There was a thread here on this topic.
From: "Lee" <m...@xxxxxxxxxxxxxxxx>
Newsgroups: sci.math
Subject: Defining an arc by contact with three circles
Date: 10 Jun 2005 01:44:09 -0700
Message-ID:
<1118393049.260172.299580@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
Discounting metal resilience, the curve is a circle tangent to the
three given circles A B C (Apollonius' problem)
With metal thickness = 2e, you could just consider increasing all three
radii by e.
The method to calculate the radius of Apollonius circles is explained
in
http://mathworld.wolfram.com/ApolloniusProblem.html
At the time I designed a Javascript to do the calculation
(but different parameters from yours, corresponds to above mentioned
thread)
Regards.
--
philippe
mail : chephip at free dot fr
site : http://chephip.free.fr/
.
- References:
- Determining the curve
- From: google
- Re: Determining the curve
- From: Randy Poe
- Determining the curve
- Prev by Date: Re: Simple proof of FLT: Why is it impossible?
- Next by Date: Number of connected regions in an image, viewed as a graph
- Previous by thread: Re: Determining the curve
- Next by thread: Re: Well Ordering the Reals
- Index(es):
Relevant Pages
|
