When does bat speed "happen"?
Many already have a grasp on the concept of the kinetic link. The photo below gives a brief summary:
So the principle really suggests that, in terms of the swing, the bat is going to be the last thing to come around and its velocity is going to be determined by the summation of forces that have been generated by the body and transferred to the bat. Nothing new there...
Here is some more information to illustrate the timing of when the bat actually comes around, or when bat speed "happens":

This graph, from Adair's Physics of Baseball, shows the velocity relationship between the hands and the bat. What you see really is that the hands and bat travel very near the same speed during the time when the body is rotating. From the kinetic chain principle, we know that one segment speeds up when the previous segment slows down, so the bat is going to take off (increase velocity) when the rotation of the body has stopped and the hands change the direction of the know of the bat. You can see that this happens towards the end of the swing process.
Adair's book, along with plenty of other sources (including biomechanics studies in golf) indicate that the wrist uncock passively as the time for contact approaches, which again suggests that the hands are not doing much if anything to apply force to the bat during the early portions of the swing.
It would make sense to think that maximal bat speed should be achieved immediately prior to contact, and this has been shown to be so, with values for maximal linear bat speed occuring around 0.015 seconds before contact. Looks like this:

Of course each segment in the chain is important. Based on the evidence at this point, is appears that the importantce of the lower extremities and torso is to produce the force and the importance of the arms and hands is to be in the right place at the right time to make sure it all gets transferred to the bat just before contact.
Comments