Why won't my BJT transistor work as intended?
BC547B:

 

SS8050:



The transistors are interchangeable in this application, but their pinouts are opposite. Rotate your transistor 180 degrees and try again.

The AC you're measuring is probably just interference from mains AC wiring.



Beyond the simple transistor pinout issue, there is a problem with the circuit design. 

Your Arduino is running from a USB power supply. The controller has a battery in it. To switch the transistor on, you apply positive \$V_{BE}\$. The Arduino applies a voltage relative to ground A. However, the emitter is connected to ground B. You need to connect the two grounds together so the Arduino-controller system has a common reference point.







simulate this circuit &ndash; Schematic created using CircuitLab