Do some chess players actively train moving the pieces on the board quickly? Having spent the last couple of days watching the Rapid and Blitz World Championships I became, once again curious about the following subject.  

In some circumstances, especially in blitz games, it can be a slight but significant advantage to be able to perform the move as quickly as possible in a physical or mechanical sense. Now, playing a lot certainly gives confidence and ease, and there are some simple principles (such as short moves cost less time), but I was wondering if some players actively and in a structured way train this aspect of the game. To make this question answerable let me ask specifically: 

Are there any  books or other sources that discuss ways to train and to improve carrying out moves quickly (in a physical or mechanical sense)?

However, I would also be interested in slightly more anecdotal answers on this subject. My primary intent was to ask this for over the board games, but I aspects specific to online games are also welcome.
I'm a FIDE master and in my experience I've never come across any material on how to physically move pieces faster. There's not a lot you have to do: pick up the piece, move your arm to where you want to move the piece, and let go. As you play more this becomes second nature, to the point where training wouldn't make much sense.

As for short moves costing less time, this usually isn't a factor in blitz/bullet games; the exception is when you're about to flag and just need to make moves quickly. Then moving a piece 1-2 squares can be better than moving it across the board. Also, if you move pieces that are physically closer to the clock, you can save very small (but possibly precious) amounts of time. So for Black it would be moving pieces on the right side of the board, and for White the left side. Again, such strategies would only be implemented when you're down to literally a few seconds.