       Surface graphing question

• To: mathgroup at smc.vnet.net
• Subject: [mg64560] Surface graphing question
• From: János <janos.lobb at yale.edu>
• Date: Wed, 22 Feb 2006 05:58:49 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

Thinking about something else, I ran into this problem below.

Let's say I have two concentric circles in a plane with radiuses
rsmall < rbig.  I create a circle involute / see http://
mathworld.wolfram.com/CircleInvolute.html/ using rsmall.  The
involute will turn  1< n  times before it crosses the rbig circle.
Then I erect a cylinder above rsmall and place a cylindrical stick
with radius 0<= rstick << rsmall and length "l" <= (rbig-rsmall)  to
the point where the involute is "coming out" from the bottom of the
cylinder.  The stick is parallel with the cylinder and it is touching
it from the bottom of the stick to the top of the stick at every
point of that line where they touch each-other.  Then I start to move
the bottom of the stick on the involute outwards and I make sure that
the projection of the stick down to the plane of the circles are
always radial.  During the first revolution of the involute the upper
end of the stick is still touching the cylinder.  I do it till the
bottom of the stick gets to the point where the involute crosses the
circle with rbig.  The stick will create a surface in space with
rstick thickness and after one revolution the upper end of the stick
will travel on this surface.

How to graph such a surface and create a cut-out of it with different
planes ?

/Optimally I am looking 3 sticks moving on 3 involutes parallel where
the involutes are 120 degree apart, but I would be happy to start
just with one now :)/

Any good pointer to related web pages would be also appreciated.

János

----------------------------------------------
Trying to argue with a politician is like lifting up the head of a
corpse.
(S. Lem: His Master Voice)

```

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