Of course you can do this, it shouldnt really be that much of a problem from the software point of view. You really need to be getting the correct electronics and hardware set up to be able to do it.
You need a feedback device on each joint that you want to record(usually a potentiometer where the microcontroller can read it and determine where its set to).
If your arm or whatever uses servos, then these do have potentiometers built in for feedback, unfortunately though the servos are quite mean and dont share this information with your microcontroller so you would need to hack the servos and create a connection yourself (I believe this was part of the goal of the "open servo" project if it is still going?).
But yes it is entirely possible, but you need some kind of sensor to create the information before you can use do anything with it.
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if it is servo controlled then this might be of interest
http://www.sparkfun.com/products/9014