@Carl Love  Very grateful to you, especially for the English.

 Another example of different "input links".  Four-bar mechanism.

@Thomas Richard  Thank you very much for such a detailed answer. It seemed better to continue only with Maple.
(As for my Maple drawing(s), of course, it's not modeling, it's simply a visualization of a calculations.)

@Bendesarts Could you briefly tell about the problem in connection with the decision which arose such expressions?

More versions of cam mechanisms

  @tomleslie Example with Isolate: all solutions of a system of polynomial equations.

example_with_isolate.mw 

@tomleslie Root Finding [Isolate] works with Gröbner bases and thus find all the solutions of a polynomial system (when replacing variables for the sum of the real and the imaginary part find all real and all complex solutions. In Mathematica it seems, Nsolve).  On this basis, the system can be examined for compatibility  and an infinite number of solutions. But a polynomial systems only.

For another type of systems is a very powerful tool is DirectSearch [SolveEquations].

If there is a continuous infinite set of solutions recommend Draghilev's method.

@tomleslie  Excuse me, I do not know English, but I realized that this is not a solution, and to the answer to question Muhammad Usman has nothing to do.

tomleslie, check your solution on the value of the discrepancies

Surface type Himmelblau and cylinder

https://vk.com/doc242471809_437007771 
 
 
(x1^2 + x2 - 0.3)^2 + (x1 + x2^2 - 0.7)^2 + x3 - 5 = 0.

 @roya2001 I almost forgot about the intersectplot. As you can see, the other answers in real space are not available.

2DOF_2.mw  

@roya2001 

For example, You can check this by using Direct search optimization package.

http://www.maplesoft.com/applications/view.aspx?SID=87637

One more example with animation

@Bendesarts I do not know how to use Maplesim. Is it impossible to use in Maplesim equations?

I think that the best and universal parameterization would parameterization based on geodesic curves. It is only necessary to have time to do it.