Lol no one looked at the PDF if you cut the ground from the uno the relays are still hooked to the supply ground and if you turn on one closing the power loop. But the OP should rethink this and read the data sheet the relays are setup to use 20 mA to turn on, and Like I said you don't need a resistor from the uno to turn these on with five volts but your using a resistor and 12 volts that sets it to about 21mA.

That's why it works now but it's not a good idea you forget the 4.7 good by port pin.

So if you left off the resistor and just use 5 volts it should work too and no worries off blowing a port pin.

The way it shows in the pdf you hook the pin from the uC to ground the led of the Optocoupler
it has a built in resistor to limit it to 20 mA.

You didn't add one did you? 

Well if you did what you show in the pic you probably killed your uno you are sinking 12 volts..  
http://elecfreaks.com/store/download/16_Relay.pdf

He is pulling the latch to ground. It's in the datasheet outputs active when E pin is low so you tie it low and just use the data and the clock
 

Its easy he is reading a keypad where you set just one columns high and scan the rows for a press.
Or set one row high and scan the columns which ever way you want to do it.
But he is not reading it as a input.

Try one of these http://www.ftdichip.com/Products/Cables/USBTTLSerial.htm
This one TTL-232RG-VREG1V8-WE

Am I on the right track with the lm334z/nopb?

Nope that's  Voltage Reference

I don't think that's for charging batteries.

At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node, or:

 

That word sum means you added some thing to get a total in this case we are charging 4 cels we only have a set current of 360 and each will charge to that just like a cap 

The op has his charger set to output 360 ma 18/50 = .360 amps divided by  cels 4 is 90ma a cel.
It will take 3.3 hours to charge and he better keep a eye on it there not anything to stop it from over charging.

Once the pack hits 5.6 volts you'll need to stop changing the pack. Thats if it is Ni-MH

 

Yeah but 12 Ohms is little more than a dead short....

Yep and could look like a glowing heater if you used the right wire, or put it in a bulb and make some light.

You don't have to down load it to look at it But the OP is really lazy not to post it.
And what help does he need with the code looks fine and it worked in his video.

So the problem is how you make this work on his uno where to hook what and the like.


https://code.google.com/p/aguaviva-libs/source/browse/arduino/sketches/laserpojector/laserpojector.pde

Yep it looks like a match i just don't see a $100 for a resistor to set that.But who no's Thanks for the math PapaG
I would use hot and cold. And thanks for posting this It sure been fun racking my brain. But maybe we should ask the suppler. LOL just to see whats what.

I been racking my brain about this and I no I seen these things used in some thing just don't no what it was
But I don't think it's to set for 75 F cause it didn't add up on any chart I seen.

Where did you find that a PT100 is 109.3035   It's 109.73 at 25C could you show how you did the math for Fahrenheit

Its not going to work the OP doesn't have the gnd tied on the arduino