Problem with raspberry pi 3 B GPIO there are not working , BrachioGraph project

colporteur has mentioned the reliability concern too. It can't be overstressed how the prototyping needs to change significantly. It's not surprising that things do not work because you have several points of failure on each connection, due to the way you're connecting and chaining things with unreliable items and techniques.

If you really want to continue with breadboard then at least replace it. The one you have is so worn out on the outside, that the chances that all the connections inside it are fine is probably close to zero percent. We are talking from many years of experience. The one in the photo below is low-cost, but should work well. Any cheaper will likely not be very good.

The round-moulded jumper wires you're using are extremely bad. These types are much better (but buy from a good place, because the cheapest ones are sometimes cut inside near the metal crimp, but on the outside look fine).

Replace the breadboard with soldering. Use pin headers (shown highlighted in red. Here is an example). They will connect to your servos and to the jumper wires to the Pi.

Underside of the board can look like this:

or like this:

The photo above is from here:  Circuit Prototyping 

These are all solid reliable connections that are tested with a multimeter if you're unsure.

(or cladboard - unetched PCB, and an exacto knife. Costs virtually nothing, lasts for years. The cheapest impregnated paper board works more reliable than a breadboard)

(impregnated paper is also easier on the knife and lungs than fiber boards)

The paper boards are brilliant for prototyping! Easy to drill too, with the most cheapest of drills, if that is needed (usually doesn't need drilling at all for quick prototyping).

I've not heard of these. I will have to take a look.I normally breadboard and then perf board a CAD PCB design. If it works I'm confident the PCB electrically works. The physical part is where I get into problems.

Action photo:

There's some info here with a short video:

 Copper Clad Prototyping Tools 

In brief, the rotary tool there wasn't useful for this prototyping method (but is _extremely_ useful for cutting fine traces on ready-made PCBs). The "scorper" tool is very handy, but exacto knife would be as effective too. I still have not perfected a technique with the scorper (I recently purchased a second scorper with a slightly different shape, but I think it is possible to do better). 

There's some info here with a short video:

 Copper Clad Prototyping Tools 

In brief, the rotary tool there wasn't useful for this prototyping method (but is _extremely_ useful for cutting fine traces on ready-made PCBs). The "scorper" tool is very handy, but exacto knife would be as effective too. I still have not perfected a technique with the scorper (I recently purchased a second scorper with a slightly different shape, but I think it is possible to do better). 

Very good video. 

Also sometimes tape can be added to the mix, i.e. cut out some parts, and also use tape where it's convenient. Not as rugged though. More pricey too.. conductive adhesive versions of it are crazy expensive now compared to a few years ago (although a reel of the tape could last for years). 

Tape!  I forgot to buy the tape.   Thanks for the reminder.  It will now arrive with the boards.