The practice of crossing the hands, carrying the left to the acute register and the right to the grave, derives from the harpsichord and dates from the beginning of the Eighteenth century.
For the percussions, the crossover serves to avoid return strokes and, consequently, is used to play with alternate hands (as an alternative to removing them). Nevertheless, it should immediately be said, that the crossover technique must be used with moderation, because it is difficult to achieve equal strokes when one stick obstructs the other.
Obviously, a crossover can be executed from right to left or vice versa.
In the first case, it is the right hand that is placed over the left (Fig.1), while in the second it is the left that is placed over the right (Fig. 2). To execute a crossover properly, in addition to placing one hand over the other, you also need the hand below to the opposite side, creating a space at the level of the wrists.
To facilitate this movement and obtain sounds that are all equal, it is a good idea to practice with ad hoc exercises (pp. 39- 41 and 57- 59 in the "Timpani" method) and to learn to execute the finale (after the impact) by lifting the stick slightly as shown in the picture.