Advanced the software side quite a bit. Waiting for some new parts rn so I used the time to finish the gui for now and calculate everything i need to to send to the arduino! You can now input the three values making up the target point and hit calculate. Then the angles of the three joints relative to their home position as well as the delta of the angles, which is the value which the joints need to move in order to reach the target position, are displayed below. These are the values which are going to be send to the arduino. I also added the function to ignore physically impossible positions of the arm and only show the possible ones. In theory I only have to add some kind of interface to send data to the arduino and the software would be done!