Effects of the racket polar moment of inertia on dominant upper limb joint moments during tennis serve

Abstract

This study examined the effect of the polar moment of inertia of a tennis racket on upper limb loading in the serve. Eight amateur competition tennis players performed two sets of 10 serves using two rackets identical in mass, position of center of mass and moments of inertia other than the polar moment of inertia (0.00152 vs 0.00197 kg.m2). An eight-camera motion analysis system collected the 3D trajectories of 16 markers, located on the thorax, upper limbs and racket, from which shoulder, elbow and wrist net joint moments and powers were computed using inverse dynamics. During the cocking phase, increased racket polar moment of inertia was associated with significant increases in the peak shoulder extension and abduction moments, as well the peak elbow extension, valgus and supination moments. During the forward swing phase, peak wrist extension and radial deviation moments significantly increased with polar moment of inertia. During the follow-through phase, the peak shoulder adduction, elbow pronation and wrist external rotation moments displayed a significant inverse relationship with polar moment of inertia. During the forward swing, the magnitudes of negative joint power at the elbow and wrist were significantly larger when players served using the racket with a higher polar moment of inertia. Although a larger polar of inertia allows players to better tolerate off-center impacts, it also appears to place additional loads on the upper extremity when serving and may therefore increase injury risk in tennis players.

Figure 1. The polar moment of inertia of a tennis racket.

Figure 2. Convention for dynamic measurements.

Figure 3. Principal Component 1 (PC1)/Principal Component 2 (PC2) axis system diagram of the peak shoulder extension (E_)/flexion (F_) normalized moments (black markers) during the cocking (C), forward swing (FS) and follow-through (FT) phases.

PC1 explains 54% of the dataset variance and PC2 17%. The individuals are represented by grey markers with PX_I_L and PX_I_H (X ranged from 1 to 8 according to each player), and the supplementary individuals, summarizing the behavior of I_L and I_H, are represented by white markers, I_L being the racket with a low polar moment of inertia and I_H the racket with a high polar moment of inertia. The arrow indicates the main orientation from I_L to I_H.