http://www.mapleprimes.com/posts/204684-Lever-Mechanisms-  

Planar slider-crank mechanism.  

(x+0.125sin(10y))^4+(y+0.125sin(10x))^4 - 0.4^4=0 

     It was proposed for members of the department  http://malplab.ru/ and their colleagues from other departments that they to make the calculation of the kinematics of almost classical crank mechanism. Example  performed  in analogy to the examples in the description of the method in the first message.
     The crank rotates uniformly variable length, its point is fixed at the origin, the movable point moves along the curve defined by the equation (x + sin (1.5y)) ^ 4 + y ^ 4 - 0.25 ^ 4 = 0, the conrod length is equal to 1, the second conrod point moves along the axis oX.
     The same proposal I want to make here in the forum for all those wishing to try their hand.

From a certain point in time I began to think about moving to Kazan.

@shadi1386 Basically, if alpha = const, then try  solve ([f1, f2], [x, y, beta]);

But this, I think, you will not be happy much. Maple 15

>restart:
f1 := (1/2)*x+2*alpha*beta*(x^2+3*y^2)^beta*x^2/(x^2+3*y^2)-(3/2)*y-(1/2)*alpha*(x^2+3*y^2)^beta = kappa*rho*c0^2;
f2 := -(1/2)*y+2*alpha*beta*(x^2+3*y^2)^beta*y^2/(x^2+3*y^2)-(1/2)*x-(1/2)*alpha*(x^2+3*y^2)^beta = 0;
solve([f1, f2], [x, y, beta]);

The approach to the solution is possible only numerically.

@Markiyan Hirnyk I did not apply to you in any way, and answered ThU message in its proposed form.

@ThU  I do not know what makes Markyan and I do not want to know.  To You I will answer. I downloaded your file equidistant_curve_MP_2.mw  and checked. Everything is working. I checked on Mapl 15 and on Maple 17. Looks like one in one in my file in the first message.
 I bad user of Maple  (and do not speak English), but I can describe to you algorithm in detail if  you want made it yourself, if you are interested, but does not work text.

@Alsu Thank you.

@Markiyan Hirnyk This is the next provocation. The flag was marked and sent to the administration.

 @vv 

    I would be glad if someone would do this. This is especially true underdetermined systems of equations in general and especially the linkage. Only my Maple knowledge will not allow that.
    I think this is a task for a professional programmers.
?
 

    And one more example here
http://www.mapleprimes.com/questions/219995-Finding-A-Convinient-Parametrization-Of-Surfaces#comment234126

@Bryon  And another, it seems to me, is very urgent question: what would happen if, by virtue of his health one of the moderators will delete all forum?

The same example. Only we have the cylinder instead of the plane. The red curve.

ВЫПУКЛОСТЬ_EXAM.mw     
   Another easier way. Intersects  the surface by the plane. Is obtained red curve. We are building a plane perpendicular to the red curve at every point of red curve. These planes  intersects  the surface. Obtained blue curves. At the points of blue curves we construct equidistant surface (previous examples).
   If we consider that the solution is very accurate, and the number of points is not particularly limited, such an approach is applicable for practical purposes.