If I have a program written in objective c (written on a mac), how would I use that program to use my robot arm using an arduino mega?
Did you write that program yourself ?
If you did, you know it and how it was built.
If you just "happened to stumble upon" it, you will probably have to guess a lot.
This will have a big impact to the time you would need to convert it.
But how do you know this program will work and do what you want it to do ?
You will see you'll need to do some debugging before your setup will do what you expect it to do.