I didn't say they weren't part of the kinetic chain. And yes, I do not perform nor teach any muscle in the hitting arm to fire purposely.
Of course they are because "kinetic energy" means "moving energy". So, when the hitting arm begins to use the energy it receives to go up to the ball, that is part of the kinetic chain.
If there is slight muscle tension in the arm to perform the necessary arm movement, there could be. However, I will not teach it nor mention it. There are enough issues with trying to get the player to completly relax the arm and shoulder to get that "ahhh, haaa" realization. You can throw your arm around with it completely relaxed. That is what I am trying to get a player to do on the serve. the arm just flings in a different direction.
I am sure if we had biomechanics in here they could disect and find which muscles are firing in the slightest sense to let us know that in reality the arm and shoulder might not be completely relaxed even if we thinkk it is, however, for teaching purposes, I don't go there.
thanks for the response - just noticed it now.
I just had another thought. Perhaps if the tricep were to fire, it would actually slow down the extension of the elbow joint.
Consider that the momentum harnessed from previous portions of the kinetic chain allow an extension of the elbow joint that occurs at a faster rate than that possible through simply tricep powered extension. In this case, attempting to actively fire the triceps may cause a bottleneck and a break in the kinetic chain.
A naive intuition is that the tricep powered extension could piggy back onto the extension velocity powered by the transferred momentum from further upstream the kinetic chain, and that the final velocity of elbow extension would be that generated by the sum of the tricep power and that generated by transferred momentum ... but I think this intuition is flawed: I don't think piggybacking can work in this context. A similar notion is running, or cycling, if your body or bike is moving at a certain velocity, then you will only increase your velocity if you push down with your legs (on ground or on pedal) with a force exceeding that required to get to the initial velocity in the first place.
In other words, if someone is pushing your bike from behind (equivalent to the transferred momentum in our kinetic chain example), then it doesn't make sense to pedal unless you can pedal faster than they are pushing you.
Similarly, perhaps it doesn't make sense to actively fire the triceps unless the tricpes could extend your elbow joint faster than that allowed through efficient kinetic linking from the legs, hips, torso, shoulder, etc.
So I think I've answered my own question.