## 4 Discussion
W4 associates the knee and hip extension to the rectus femoris during the swing phase. Finally, in W5, the hamstring muscles are related to knee and hip extension at the beginning of the early stance and the beginning of the swing phase. Therefore, using kinematic-muscular synergies, it could be clearer to understand the link between muscle activation and biomechanical function. _Incorporating non-linear models._ Preliminary work on muscle synergies [33; 34] showed that synergies combine linearly, and, thus, linear models should effectively capture their combination to produce movement. Most of the available corpus of the scientific literature  
Figure 1: The figure is an original representation created with the data from a study by [PERSON] et al. [32] and [PERSON] et al. [30]. Kinematic–muscular synergies from locomotion in four strides are shown at the top of the figure, and below, the corresponding temporal coefficients are portrayed. In kinematic–muscular synergies, the muscular part is in gray and it highlights the muscle activations, while the kinematic part is red and it shows the corresponding joint acceleration. has built on these bases and NMF has become the reference algorithm for the field [23; 35]. However, the dynamics of the neuromusculoskeletal apparatus contain several levels of non-linearity, and the task space variables might be related to muscle synergies with non-linear models. Thus, future work will have to consider the adoption of non-linear models to capture such relationships, for example, using autoencoder neural networks. _Separating phasic and tonic EMG components._ Phasic and tonic EMG relate to motion-related and postural or anti-gravity EMG components, respectively. Since the first studies from Flanders [36; 37], few studies in motor control have addressed the need to separate such components, especially in upper limb movements [38], and in a recent work, it was demonstrated that the collection of synergies underlying phasic and tonic EMG are in principle different, sharing few synergies only [24]. Thus, separating the two components may shed light on the understanding of sports gestures, especially when the upper limbs are involved in anti-gravity movements. In Figure 2, the two components are shown in a typical reaching movement of the upper limb to reach a target. It can be seen that the phasic EMG shows a typical biphasic burst structure, accounting for the acceleration and deceleration of the limb, while the tonic EMG can be modeled with a linear ramp that connects the baseline EMG level before and after movement onset/offset. The EMG data used to create Figure 2 were derived from a dataset presented in [PERSON] et al. published in 2019 [39]. The separation of the EMG components allows for a more precise analysis of the different roles played by muscles within the movement. Moreover, this separation allows us also to investigate the role of the negative phasic EMG components that may give insight into efficient movement execution during sports movements when exploiting gravity [40]. In particular, for many sports gestures, it becomes possible to divide the movement preparation phase, where tonic EMG plays a major role, from the movement execution phase, in which phasic EMG also comes into play, enabling the acceleration and deceleration of the arm. Postural control is recruited to prepare an efficient movement execution by coordinating the body to counteract gravity; moreover, such tonic EMG components are modulated during movement execution to guarantee support even when the phasic components start to act. There are some sports, such as tennis and basketball, in which maintaining control of posture to assume the correct body position before the execution of the movement is critical to being able to complete the desired movement successfully. Therefore, it is important to study in depth the static position  
Figure 2: Phasic (blue) and tonic (red) EMG of the anterior deltoid during a reaching movement of the upper limb towards a target.