Fortunately, there are a few good examples already out there on how to build this motion rig. For example, here is one using only DC motors. Here is another example using Servo motors which is very impressive. This rig is built with multiple aluminum C-brackets and struts which looks very sturdy but I have no idea where to get the parts. So far I have built a test rig consisting of two RC aircraft 180 degree servo motors connected together, one to shaft of the other as seen in this example I found for sale.
Incidentally, if you are looking for the rubber fixture I am going to use, its a CV-Boot from a car. They can be found in almost any auto supply store. Here is a picture of the one I chose.
It is a close enough match to get the job done. I will end up cutting away the lower half when I mount it to the body. Now back to the test rig. Below is a video of the test rig I built just to see if my two server idea would work. The two servos are joined together with rubber bands so you will see a lot of oscillation as the arm moves around and a hanger is standing in for the antenna but other than that, it is performing the required motions.