Hi Pierre,
I noticed the same wiring error as you have while I've been reviewing the manual for the AR3, as I prepare for my own build.
I also searched these forums for a possible answer but I did not find one. The following posts remained unanswered:
https://www.anninrobotics.com/forum/robot-builds/ar3-building-wiring-completed
https://www.anninrobotics.com/forum/questions/5v-psu
Here's my understanding:
The pictures from page #238 to #241 shows two pairs each of black and red wires coming from the 4th pair (black) and 5th pair (red) of the DIN rail terminals. This is where the manual is missing the instructions to add this second pair of wires, including the instructions to solder said wires to the GX16-2 plug on the enclosure door even though the pictures show the installed wires.
If you then jump to page #265, this is when you solder another pair of 22awg wires (black and red) to the GX16-2 plug on the enclosure door. The other end of these wires need to be soldered, with heat shrink, to a pair of jumper wires, which are then connected to the Teensy 3.5 appropriate pins as instructed on page #265 (bottom image). This is how the Teensy 3.5 derives it's power. From 5V power supply unit, to the DIN rail, to the GX16-2 plug, to the Teensy 3.5. Please note, that it is my opinion that the red jumper wire mentioned on page #258, is the same red jumper wire that will be soldered and connected to the Teensy 3.5 Vin pin on page #265. We're missing the follow through on that instruction, including the making of the black wire.
As you can tell, there are missing steps in the manual. Perhaps the community will help with the next revision?
So to answer you're question, from what I can tell, yes to either of your methods asked. The power for the Teensy 3.5 is ultimately derived from the 5V connection point on the DIN rail, which as you know, is sourced from the 5V power supply unit. What's the best method regarding common grounding techniques is another question I choose to side-step for now ;)
Hope that helps Pierre so you can continue with your build.
Would you mind sharing whether you're building the aluminum or 3D printed version?
Separate but related to your post, I'm confused by where the missing +V side of power for the Arduino Mega 2560 is coming from. I can only assume the power will then be derived from a direct connection via the USB cable to a PC and the -V side for establishing a common ground. According to the datasheet, "The board can operate on an external supply of 6 to 20 volts. If supplied with less than 7V, however, the 5V pin may supply less than five volts and the board may be unstable."
As instructed in the manual, we're not using 5V from the Arduino for the relay module, however, it's the "board may be unstable" part that leaves me uncomfortable. Are they referring again the stability of the 5V output from the Arduino, or the boards ability to function properly? I'm thinking the latter but I would like to hear other's opinion on the matter.
Regards,
D.D.