Arduino DUE and optocoupler 4N25
It sounds like the 4N25 opto-coupler on its own can't do what you need because it's not designed to directly make/break a connection between a power source and its load (i.e. it isn't functionally equivalent to a relay).

Internally, the switching functionality is provided by an NPN photo-transistor. A typical open collector usage would be something like this:



(Image copyright Lewis Loflin: http://www.bristolwatch.com/ele/opto_isolated.htm)

The switch (S1) and the power source (Vi) on the left would be your Arduino. All the connections on the right would be part of your device (the actuator).

As you can see, you need 3 connections on the right: voltage source (Vcc), ground, and the output (Vo, which goes to your device). The circuit basically works by pulling the output (Vo) either up to Vcc to turn it on, or down to ground to turn it off.

It looks like all you have is Vcc and Vo, so this kind of configuration won't work. (Don't try to use the ground from your Arduino instead. That could cause various other problems.)

It should be possible to setup additional circuitry to act more like a Solid State Relay, but without a ground reference point it can be harder than it sounds. A mechanical relay might be the easiest option.