Connect arduino to beaglebone black
The simplest way is just to plug the Arduino in to the BBB.

The BBB has USB.  The Arduino has USB.  Connect the two together and you have both power and data immediately available.

Depending on the Arduino and its version it will either be there as /dev/ttyAMA0 or /dev/ttyUSB0

You can even use avrdude to upload new software to the Arduino direct from the BBB.