D_Method_12d.mw

      Draghilev’s method and 12d curve.  We solve the system of 11 polynomial equations with 12 variables.  This system has infinitely many solutions. One of the subsets of the set of solutions of this system is given curve in the space 12d. For visualization of the curve, we combine arbitrarily xi (i = 1..12) by three, and show them all together like a movie in our 3d. Any point on the curve may be easily checked whether it is solution of the system.
      Someone said  "A", says "B".

@Markiyan Hirnyk 

Edited the first message. It was showed what happens to the original line while minimizing the distance between the points. Other algorithms operate  on the basis of moving of points on the surface too. Movement of points occurs according to a particular task.

The method of calculating of spatial linkage.  Here in the Application Center

(If the link itself does not work, then you can use the clipboard and paste it into the address bar of the browser)
https://www.maplesoft.com/applications/view.aspx?SID=154228

Geometry, velocity and acceleration.

https://vk.com/doc242471809_321893668
https://vk.com/doc242471809_321893668
https://vk.com/doc242471809_324249241

@Carl Love 

This is not the specific device. This is variant of method of calculating the geometry and kinematics of "arrow" by  Maple  tools   for any possible movement of the body in 3d, when its surface is described by a polynomial equation.

Spherical 4-bar linkage

@Preben Alsholm 

Thank you very much. More with your help I found for myself now obvious way to remove an element from array (Array).

@Kitonum 

a := [x+1, x+2, x+3, x+4]:

remove(i -> i=x+2, a);

numelems(a); nops(a); op(2, a);

@Preben Alsholm 

restart;
a := [x+1, x+2, x+3, x+4];
numelems(a);
nops(a);
subs(x+2 = NULL, a);
nops(a); op(2, a);
a;
a := subs(x+2 = NULL, a);
nops(a);
op(2, a);

@Markiyan Hirnyk 

Very interesting, do you know the definition of parallel curves on surface in differential geometry? And yet you probably know the definition of a spiral on the surface?

https://www.google.ru/?gws_rd=ssl#newwindow=1&q=What+are+parallel+curves+on+surface

Parallel curves on the surface (1/6) * x1 ^ 2 + x2 ^ 2 + 10 * x 3 * 4-1 = 0

https://vk.com/doc242471809_320829803
https://vk.com/doc242471809_321212555 

        Initial curve on the surface:

x3-0.1e-1*exp(x1)/(0.1e-1+x1^4+x2^4)=0,

obtained from the intersection of the sphere:

x1^2+(x2-.5)^2+x3^2-2=0.

      Building a geodesic between selected points. Testing shows that the normal to the surface in any point of the our curve lies on the osculating plane. (Show a picture of all the points together with the planes is not possible, so one pointis shown in two positions and two corresponding osculating planes. In the initial positionof the osculating planeis painted in blue, in the end position – green.)
      Not every geodesic curve is the shortest distance between the points, but we can construct a set of geodetic and select from them the shortest. If an initial curve will be on the other side "bulge",  the first geodesic would be the shortest geodesic.

The same algorithm can be used to construct  parallel curves  on surfaces.
For example, three  parallel curves  on the surface:

(x1-sin((x1^2+x2^2+x3^2)^.5)^2)^2+(x2-sin(x1)^2)^2+(x3-sin(x1)^2)^2-9=0;