Most of these robots will use servo motors - that gives you dexterity but means that holding any position requires constant holding torque - which means limited payload and a lot of wasted power.
For a heavy fan (don't forget the reaction force from moving air too), you'd be better off mounting it on a some sort of bearing and just using a motor to turn it. That way the motor isn't trying to fight gravity all the time. The robot arm linked here using Dynamixel servos - you could just use one of them to spin a fan on a lazy susan. Much cheaper and less complicated!
this is why servo-powered robotic arms are not interesting to me at all. I want one with brushless motors and harmonic or planetary drive gearbox. unfortunately you cant build those under $750 as far as I have seen so far. that's putting aside the added complexity. but I will definitely build one some day. there are quite few opensource projects with that setup.
I believe it offers higher torque, better precision and ability to just stick to a position with relatively low/or no power due to gearing-side resistance.
Why not: keep most weight off the arm by using a fan/compressor installed in the base and routing a conduit to the arm? Then it will only have to move the conduit, not the heavy motor.
I’m wanting to manipulate a fan in my home gym with some eye tracking to get it to blow air on my face when I work out, but the fan is a few pounds.
Alternatively: any hardware motor suggestions for such a project?