f:=x->((4*x^2-4)^4)^(1/5);
evalf(f(0));

@panke  I type  ?dsolve[events] then press Enter and receive a detailed description.

@panke 
 

restart; 
dsys1 := {x1(0) = 0, x2(0) = 1, diff(x1(t), t) = 1, diff(x2(t), t) = t}; 
dsys11 := dsolve(dsys1, numeric); 
plots[odeplot](dsys11, [t, x1(t)], t = 0 .. 12);
 plots[odeplot](dsys11, [t, x2(t)], t = 0 .. 12); 
dsys := dsolve(dsys1, numeric, events = [[x2(t) = 5, [halt]]]);
plots[odeplot](dsys, [t, x1(t)], t = 0 .. 12); 
plots[odeplot](dsys, [t, x2(t)], t = 0 .. 12);

@nm  Information just in case, perhaps, will be useful. Look at the differences.

Example:
nops(solve([x^2+x*y-1, y+1], [x, y]));
and
nops([allvalues(solve([x^2+x*y-1, y+1], [x, y]))]);

@Adam Ledger You also missed [ ]  in my answer

@nm  You missed [] in my answer.
Maple 17

@Fabio92  Of course, there are fundamental differences in the construction between precision machines and manipulators. But there are materials, for example, wood, plastic, styro foam and the like, where, it seems to me, the use of a manipulator is quite possible as a CNC. That is, yes, the idea is more mathematical than technical.
Thank you for your clarification. My English exists by help a Google  translator only.

I especially thank you for your full understanding of the idea, and it's nice, because I very rarely manage to explain anything even in Russian.
 

@Fabio92  Are you sure you understand the proposed method? The angles are always uniquely determined. Because this is how the model is made-manipulator-trajectory. But this does not mean that there is always only one solution for the same point. It's just that we are able to model this way. Believe me, I would not begin to make messages about inverse problem.

I think that the whole complex of tasks related to the solution of the manipulator's inverse problem can be performed directly in Maple. It will be faster and even more convenient than in specialized CAD. Some known schemes of manipulators are ready for testing; it remains only to perform the formalities associated with the recording of control programs.

Because:
1,  It is clear how to make a mathematical model of a manipulator. And for this there are several examples.
2.  The problem of finding the starting points of motion is conveniently to perform using Maple graphics  and with solve or fsolve functions, for example, in a separate program.
3.  The solution of the direct problem is simply routine programming.

Of course, I may be wrong, but for some reason it so seems to me.

@rlewis  for example  CURVES.mw  Number of system solutions = 2

First we need to finding all the branches of the curve. To do this, we must solve this system of equations for only one t when 0< t <4.

To avoid ambiguity in motion, we impose additional restrictions on the points of the manipulator, thereby reducing the number of degrees of freedom to one.

3d three-link manipulator with four degrees of freedom.  Movement in a spiral.
MAN_4S.mw

An example of an inverse problem for the 3d two-link manipulator with four degrees of freedom. The movement occurs along a straight line between the red and green points. The fourth degree of freedom is formed due to the possibility of the first link to move along the axis oX1 (oX).
The angles of the first link with respect to the coordinate axes are printed by numbers, the angle between the links is represented by an arc, and the change in x1 is simply visible.
Any movement of the extreme point of the manipulator can be specified by a finite set of motions along straight lines, which means that on the basis of such a mathematical model it is possible to calculate any working trajectories.

The inverse problem for a four-link manipulator with five degrees of freedom.

@herclau  If you want a solution for your system of equations, it is very simple, for example:
sistema9_2.mw

If you want to get this picture, then I can tell you where to look for the author, this is the participant  of  https://en.smath.info/forum/  uni.  Believe me, this drawing does not have any relation to the method of Draghilev. It's just a uni's  fantasy.
For example:
picture_of_uni.mw

 this manipulator can not connect points from the first post (here these points are blue) in a straight line. The technical data of the manipulator and its position allow to reach only the black point.

@tomleslie  Thank you very much for your explanations.