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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.

Thanks ahead,

János


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