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

I am new to Mathematica and not very familiar with the codes. I want to use Mathematica software to solve problem this equation for which I am not getting proper solution and looking for help.

1. I have equation of a surface represented by x,y,z co-ordinates which is function of two variables u & v.
2. I need to find the line of contact on this surface of the tool surface generating the same.
3. The equation of meshing of the tool surface and this surface is as given by the formula denoted by EM 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 Nx, Ny & Nz in the above equation, is used to represent Normal unit vectors to the original curve represented by x,y,z co-ordinates in the above formula.
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.

I hope to have given a brief on the work output desired from the program. Look forward for your kind help by guiding me the correct way to apply the program to get the solution.

 Clear[A, r, v, u, p, γ ]
x[u, v] = 2 r Cos[v + u + γ] - r Cos [(2 v) + u + γ]
Nxu = D[x[u, v], u]
Nxv = D[x[u, v], v]
Nx[u, v] = Nxu Nxv

y[u, v] = 2 r Sin[v + u + γ] - r  Sin[(2 v) + u + γ]
Nyu = D[y[u, v], u]
Nyv = D[y[u, v], v]
Ny[u, v] = Nyu Nyv

z [u] = p u
Nz [u] = D[z[u], u]

EM = NDSolve[(A - x[u, v] + p Cot[γc]) Nz[
u] + (A Cot[γc]) Ny[u, v] + z[u, v] Nx [u, v] == 0, x, y,z, { v, 0, 10} {u, -Pi, Pi}]


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thanks @belisarius –  kamalagrawal Jan 17 at 14:42
“all other variables are constant”, then you should give those variables exact values, NDSolve is a function for solving differential equations numerically, and shouldn't the z[u, v] in EM be z[u]`? What's more, though I can't understand your description very well, according to your code, what you're solving isn't a differential equation at all. You'd better describe your problem in a more understandable way, for example, using some equations (in traditional mathematical expressions)? –  xzczd Jan 18 at 7:29