Originally Posted by julian
For maximum control on a groundstroke, the racquet face should remain at a constant angle through the hitting zone. For this to occur, the forward component of the velocity vector of the racquethead must have equal magnitude to the forward component of the velocity vector of the hand. In other words, if the racquethead moves forward faster (or slower) than the hand during the moment of impact, then small errors in timing will result in changes in racquetface angle, leading to less accuracy of the shot. But if the racquethead moves at the same speed as the hand, then small errors in timing are inconsequential and the ball will still go toward the target.
Fig 4 disagrees with your SECOND sentence above
The double-pendulum stroke represented in Fig. 4 of the Cross paper is a reasonable simulation for a golf swing or a tennis serve, but not for a forehand.
For a golf swing (or a tennis serve), the ball is stationary (or almost stationary). This means that small errors in timing will not lead to large errors in direction, as they would if the stroke modeled in Fig 4 was used for a forehand.
The stroke of Fig 4 shows that maximum angular velocity of the clubhead is reached right at impact. This is what you want to achieve when hitting a golf ball, because increased angular velocity leads to more power.
On a tennis serve, the same goal applies - maximum racquethead speed is the ideal. So the stroke of Fig 4 is still a good model.
But for a forehand, whipping the racquet toward the ball with maximum angular velocity at impact is not a good way to hit the ball. If you are a fraction of a second late with your timing, the incoming ball will travel further before making contact with the racquet. And when it does, the racquetface will have a much different angle (because it is rotating at maximum angular velocity), causing a big error in shot direction and the ball to spray off to your right (if you are righthanded).
Instead, for a forehand, ideally you want the racquethead to travel at very high speed through the impact zone, but you want the angular velocity (omega2) to be as small as possible. It might be ok for there to be some angular velocity in the vertical plane (for topspin). But when hitting a return of serve, even vertical velocity is best minimized in order to reduce the sensitivity to timing errors.
If you look at slo-mo forehands on tennisone, you can see that the angular velocity of the racquet (around the vertical axis) slows down to zero just before impact, and stay almost zero well after the ball has left the strings.
I would be interested to see if Cross can set the couples C1 and C2 in his model both to zero (or have C1 increase after the bottom of the swing), and then find values for the weights and lengths of the arm and racquet that permit the hand and racquet to move at the same forward speed through the impact zone.