(solved) I think I do need a geometry program ...

[DiTBho]

I need a program that allows me to build a parallelogram, fix a point on one side, move the upper side of the parallelogram while keeping the lower side still and study the trajectory described by the reference point

What can I use? 

OpenSource, Commercial, whatever, no preference.

edit:
typo.

[IanB]

Desmos?

https://www.desmos.com/geometry

[AndyBeez]

May I ask what a palletogram is?

[DiTBho]

typo, parallelogram

[SiliconWizard]

Not sure what you mean by "study", what does the job really entail?

From the quick description, this reminded me of the copy tool called a pantograph: https://en.wikipedia.org/wiki/Pantograph
The geometry involved is not complicated.

[abeyer]

May I ask what a palletogram is?

I'm pretty sure it's when your old shipping pallet starts losing nails and gets kinda skewed. 

[SiliconWizard]

Not sure what you mean by "study", what does the job really entail?
The geometry involved is not complicated.

Understand how an electromechanical mechanism works, based on a parallelogram that moves in fixed steps, moved by a cable. The fixed steps describe some angles, and I notice that for each corner the cable tension is not constant: at the moment, as first step, I have to reconstruct the function which, given a step, calculates, or in any case extracts, how much tension to give to the cable.

It's a damn job of reverse engineering mixed with industrial espionage. In short, I have to do in 2-3 weeks what an engineering team probably took months to think up.

Anyway, back to the geometry program, I also need to be able to trace points when I operate on a parallelogram creating geometric constraints.

I haven't yet tried geogebra. It looks interesting.

Ouch, while the geometry part is relatively simple (determining the position of the various points), the cinematics are significantly less so.
So you have two different challenges here.
I'm not sure I fully understand what is expected from you. Aren't you mainly designing software? (Maybe not and I've missed part of your activities.) This is more of a mechanical engineering/robotics task, as far as I can tell.
Are you maybe missioned to find or write some software to simulate the above system? Unless it's extremely complicated, analysing it formally would probably make more sense - but would require skills in, as I said, mechanical engineering/cinematics/ultimately robotics.

[jpanhalt]

If you only want 2D, almost any simple CAD program should do that, and they are easy to learn.  I use an ancient 2D called Graphite (Ashlar-Vellum).  It started life in the 90's under a different name.  My version is 2002.

[eutectique]

Try MotionGen https://motiongen.io/

[Someone]

I'm not sure I fully understand what is expected from you. Aren't you mainly designing software? (Maybe not and I've missed part of your activities.) This is more of a mechanical engineering/robotics task, as far as I can tell.
Are you maybe missioned to find or write some software to simulate the above system? Unless it's extremely complicated, analysing it formally would probably make more sense - but would require skills in, as I said, mechanical engineering/cinematics/ultimately robotics.

Having followed the OPs posts, its more tinkering dreaming about adding complexity to bicycles (in this case a derailleur). There is nothing simple or easily modelled about them.

[Someone]

If you only want 2D, almost any simple CAD program should do that, and they are easy to learn.

If you need 3D, many CAD programs do that, and they are hard to use.

[DiTBho]

Having followed the OPs posts, its more tinkering dreaming about adding complexity to bicycles (in this case a derailleur). There is nothing simple or easily modelled about them.

Only you know what the mechanism of a submarine has to do with the derailleur?
They look alike like I look like Johnny Depp, meaning we both have dark hair 

[DiTBho]

If you only want 2D, almost any simple CAD program should do that, and they are easy to learn.  I use an ancient 2D called Graphite (Ashlar-Vellum).  It started life in the 90's under a different name.  My version is 2002.

Found, downloaded, installed.
Solved the problem 

[DiTBho]

would require skills in, as I said, mechanical engineering/cinematics/ultimately robotics.

and you think I'm a plumber? 

[DiTBho]

Try MotionGen

This seems very useful, also for a small puppet animation project (for kids).
Thanks 

[DiTBho]

... talking about puppets, I really like how they animated the ghost-dog in the Ghostbuster Legacy movie; there are a lof of electromeccanical components and micro robotic parts inside that dog, which ultimately weighs around ~250 kg 

Well, I have a friend who models latex and she also knows how to paint on it, maybe we can even make the upper half-back of small latex puppet, and animate it with some RC-servo and nylon cables, paired with ad-hoc 3D-printed meccanisms.

[Nominal Animal]

I need a program that allows me to build a parallelogram, fix a point on one side, move the upper side of the parallelogram while keeping the lower side still and study the trajectory described by the reference point

I use Lego Technic to find out what I need to know, and sketch some images on pen and paper to find out how I want to experiment with that, and finally write an interactive simulation (using HTML+JS or Python3+Qt5).

I always fear that if I stick to a single tool, my solution space will be limited to that of the tool.  Then again, I am slow, taking much more time than "normal people" to develop things (the first time I encounter a problem or need).  So maybe don't listen to me on this? 

[DiTBho]

Lego Technic

I pre-ordered a kit with different parts, gears, axles, electric motors and compressed air pistons!
It will arrive in November

I hadn't thought of it, but it's a brilliant idea! 

[janoc]

If your goal is to design some sort of linkage/mechanism, you likely want to have a look at this sw:

https://blog.rectorsquid.com/linkage-mechanism-designer-and-simulator/

Of course, any decent CAD software (e.g. Onshape, Fusion360, etc) can do that too but the complexity and learning curve is likely much higher.