I don't know what stage of your studies you're at, but if you're going to be an engineer you need to be able to solve problems- that's what engineering is.
To that end, you need to accept that the problem is to move the 5lb mug from A to B. (Unless you simply want to wave it around, as suggested above.)
Assuming your team's hardware guys-n-gals have figured out their side- and sounds like they have since you say you know the dimensions- yours is to provide the intelligence. Inverse kinematics is that intelligence, and you don't dive into code. You understand what inverse kinematics is, look at different ways of implementing it in various algorithms- and then look at ways of coding the algorithm.
It's a fact of life that inverse kinematics is complicated, but you took that complication on when you accepted the job of math guy. You have to understand the math first.... and if that's complicated, well that's tough on you. Get your mind round how to do the math first, then only flowchart the solution (perhaps with pseudo code) and only then figure out the coding.
And of course before all of that, learn to program your Arduinos! There are loads of tutorials on that....
Edit.... sorry if that came across as a bit of a rant, didn't mean it to