I am making a room automation system for a school project. Here's the basics. When the piezo registers 3 knocks in a short amount of time, the knob will be opened by the servo attached with a belt.(Any suggestions on this part would be great too). Then the wooden 90 degree piece will fit around the door and be able to push it open. then the transistor will turn on the lights. I will also have a (not pictured) simple contact switch on my door so I know when it's closed. (Don't know what to do with that yet). Once I get this part down I will have a separate arduino on my bedside table controlling my bedside lamp and my radio. I have an old light controller that you just plug into an outlet and then you can control that outlet with a remote. That shouldn't be too hard to hack to be controlled with the arduino. I will also have the arduino turn on my lights when the alarm goes off. I may have it use a microphone or a light sensor for when the alarm light goes off. When I knock once on my bedside table, it will turn my bedside light on. When I knock twice, It will turn my radio on and off, three times and both my bedside and my overhead lights will turn off. Here is a picture of the door part. After that is my main problem.
I can't find a transistor powerful enough to control 2 60 - 75w 120v AC lightbulbs. My lightswitch will be replaced by this transistor and will be controlled by the arduino instead. Could somebody please give me a link to a suitable transistor on digikey? Thanks!
I can't find a transistor powerful enough to control 2 60 - 75w 120v AC lightbulbs
If you have to ask this question, I would suggest you shouldn't be trying to do it.
Try looking at solid-state relays (SSRs) or even mechanical relays instead.
I think you will probably need a relay for that, such as:
Match or slightly exceed the specifications for your voltage and current for your location to be safe. (Mine is 120V 5A, and the relay that I linked to in the above URL above is rated at 15A. There is no way my light will draw 5A, but if the light is ever shorted out for some reason, the breaker should trip first - before the current draw of a short melts my relay down.)
Do I need to say playing with that kind of voltage is dangerous? You probably want the advice of an electrician, too. (how's that for a sneaky "cover-my-ass" move?) 
that is a nice move. So would I probably be better off just buying another servo to flip the light switch?
You could do something like purchase an IR-capable dimmer and then just have your arduino flash an IR pulse at the thing.. They aren't that expensive (relatively speaking). You could also put in an X10 switch and communicate that way.
Remotely Dimmable switch:
http://www.homedepot.com/webapp/wcs/stores/servlet/ProductDisplay?langId=-1&storeId=10051&catalogId=10053&N=5yc1vZ1xr5&R=100652556
I'd recommend using a servo to flip the switch.
X10 is a good option, but it can often be difficult to make it work reliably. If you want to be able to demonstrate the system a servo is going to be much easier to deal with.
Thanks everyone! Now what would be the best way to turn a doorknob. Mine only needs a 90 degree turn to open, but all I have is a cheap standard 180 degree servo from adafruit.
It's a servo - it'll turn as much or as little as you want it to! (within reason)
But how do you think I should connect the servo to the knob? I was thinking a belt but that may slip.
Rubber belt is probably the only thing you're going to be able to use. Maybe some elastic rubber tubing, like from a bicycle tire, so that you can stretch it tightly over the door knob.
How about replacing the door knob with a door lever similar to: http://tinyurl.com/nx5t82. A servo-mounted arm could then actuate the door lever and it could still be easily opened by hand.
Mike
I would expect a conventional door latch would require more torque than a servo can muster. Perhaps you could use something like an electric cabinet latch:
http://cgi.ebay.com/Latch-Electric-Cabinet-Lock_W0QQitemZ260300750967QQcmdZViewItemQQptZLH_DefaultDomain_0?hash=item3c9b224077&_trksid=p3286.c0.m14
Thanks mem! I think I have got it now!