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I am looking for help to solve the equation of meshing for helicoids

Posted 11 years ago
Hi, 

 I want to use Mathematica software to solve problem as per the following :
1.  I have equation of a surface represented by x,y,z co-ordinates which is function of two variables u & v - the equations of the same are as given below.
x = 2 r Cos[v + u + \[Gamma]] - r Cos [(2 v) + u + \[Gamma]]
y = 2 r Sin[v + u + \[Gamma]] - r Sin[(2 v) + u + \[Gamma]]
z = p u

2. I need to find the line of contact on this surface with a tool surface generating the same.
3. The equation of meshing of the tool surface and this surface is as given by the formula
{(A - x + p Cot[?c]) z' + A Cot[?c] y' + z x' == 0}
which is a function of u & v.
Solving this should give the values of u & v where there is line contact with the tool, all other variables are constant.
4. The x', y' & z' in the above equation, is used to represent Normal to the original curve represented by x,y,z co-ordinates in the above formula which is nothing but derivative of x,y & z equations w.r.to to u & v.
5. On receipt of values of u & v, they need to be substituted to get the line of contact on the surface of the tool.
6. This is only one such surface - there are many such surfaces of the object being designed.
I hope to have given a brief on the work output desired from the program. When successful, I can be sure of applying this to many different objects having complex surfaces and hence to proceed with procurement of the software.
Look forward for your kind help by guiding me the correct way to apply the program to get the solution.
With Kind Regards

Kamal Agrawal
POSTED BY: Kamal Agrawal
2 Replies
The first step would be to write x, y, z as functions of u and v. If you are not yet familiar with Mathematica's syntax, please take a look at Mathematica's virtual book. You should be able to plot the surface and do a number of things with it.

I'm not sure I understand your questions fully. Calculating the shapes of the intersection of surfaces can be difficult. Sometimes there isn't a symbolic solution. There are a number of techniques you can find online for handling this kind of problem.
POSTED BY: Sean Clarke
Posted 11 years ago
Dear Sean 

Thanks for your suggestion. I am still learning to use Mathematica's syntax. However the stack exchange link you have sent  is very useful. 
POSTED BY: Kamal Agrawal
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