Sainsmart Omron 12V optocoupled 2 channel relay problem I know that there are plenty of questions related to relays, but I have to ask. I am trying to sort out the issue and spend hours reading but cannot make progress. 

I have SainSmart 2-Channel 12V Relay Module for Arduino and wired it according to picture. 



Arduino UNO R3 board is powered from 12V plug external power supply. I take that 12V to power JD-VCC on relay (from VIN). Arduino 5V is used to power optocoupler circuitry.

I want to use to power 12/24/220V devices (on picture I wired 6V battery for troubleshooting). 

So, when I set PIN7 to LOW i would expect that fan spins up. LED on relay goes RED, so I expect it is sign that relay is activated. However, fan does not power on. 
When I bring PIN7 to HIGH, I hear click; LED goes OFF. I assume it deactivated relay. All the time I have 6V on voltmeter. 

What I am doing wrong?
I really tried to find answer around, but either I do not see or it is not so obvious. 

Thank you,
Lets troubleshoot this circuit:


The circuit diagram you put in your question shows a wire creating a short across the relay coil. Check this, as this will definitely stop your fan from spinning. However, I assume this is an error in the diagram.
The picture on the website shows a jumper link between VCC and JD-VCC. Make sure this is removed.
Check that the fan works when you power it directly from the 6V battery. The fan may work only at a higher voltage or run off of AC voltage. Also, the battery could be flat - measure its voltage when it is under a small load.
Drive the input circuitry directly off of 5V. That is connect VCC to 5V and then directly connect IN1 to GND. Open circuit the IN1 input to turn it off. Check that this direct driving opens and closes the relay contacts.
Check the 12V supply. Does the voltage drop significantly when the relay pulls in or out? Does it have enough current? "Each [relay] needs 15-20mA Driver Current" Measure it using your DMM in ammeter mode.
Check your wiring is correct. It sounds simple, but you will be surprised by how many times the wiring is the cause of the problem.
Measure the resistance of the relay contacts in both the open and closed states. Arcing or poor manufacturing can be causes for the contacts to not function as intended.