Arduino USB is connected to PC.hi Jopee.
Where is the Arduino +V supply? on that image
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The stepper motor may be driven by a bridge connection, which doesn't require a ground connection for the motor.Stepper motor works the same without that ground connection.

But usually isolated from grounded mains supply by transformer(s).The stepper motor may be driven by a bridge connection, which doesn't require a ground connection for the motor.
There is no connection between PS module and USB ground.hi J,
If that lower left PSU module is not connected to 0v/Gnd on its input, then the control signals from the Arduino would not have a 0v/Gnd reference and would be floating.
The fact that the project works without that link shows that the 9Vdc power source is connected somehow to the USB ground.
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Note: the link is to ensure that project would work even if the 9V PSU being used was isolated from ground/floating
Better image.
View attachment 338822
hi
What PSU is driving that PCB power supply?
Can you show the power connections and power supply type?
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For example: the circuit I posted showing no link and an isolated PSU driving power PCB will not work.
There is no common ground 0V for the Arduino logic signals.
Although this means of supply is connected to Earth GND on a typical MOBO, I agree the best term to describe it in this application is Power Common.Arduino USB is connected to PC.