The purpose of this study was to understand the effect of an arm swing during a CMJ on performance and fDOF. The results confirmed the hypothesis of improved performance with the use of an arm swing during a CMJ through increased external and joint impulses, particularly at the hip and ankle joints, and an increased joint extension proximal-to-distal delay. This study showed that the key characteristics of the movement which had 270 kinetic DOFs and 702 muscle force DOFs at a group level, could be described by a reduced number of fDOF. The CMJArms exhibited four fDOF to define muscle forces and 3D JCFs at a group level, while the CMJNoArms resulted in only three fDOF for both variables. This confirms the second hypothesis that more fDOF are utilized in CMJArms compared to CMJNoArms.
The prolonged countermovement due to the use of an arm swing resulted in increased vertical external impulse, in agreement with previous literature [15, 16, 17, 18], and increased hip and ankle joint impulses, which is in agreement with Chiu et al.[19] and Hara et al.[20] who found a similar pattern in the NJM. However, it was only the hip that exhibited an improved vertical JCF-time profile with an added arm swing, as it was the only joint impulse that remained significantly greater after removing the effect of increased time (by time normalization). This can be explained by the increase in delay in the proximal-to-distal strategy which occurred between peak hip and knee extensor forces, but not between the knee extensors, plantar flexors and take-off. The time between hip and knee extensor peaks increased to allow the forward arm swing to begin the upward acceleration and propulsive phase before the leg begins to extend[16], maximising energy transfer from the elbows and shoulders to the trunk and pelvis creating the ‘pull mechanism’[17]. This resulted in slower hip extension and muscle contraction within an improved region of the force-velocity curve at which the muscles are able to generate more force[26]. Therefore, the inclusion of an arm swing likely improves the hip JCF-time profile by enhancing the proximal-to-distal strategy of the countermovement.
Unlike the increase in time-normalised impulse at the hip, the vertical external and ankle impulses only increased when calculated in real time, indicating that a longer ground contact time was the main factor contributing to increased impulse. However, previous studies have shown an increase in ankle NJM with the use of an arm swing in a CMJ[15, 16, 17, 19, 20]. Even though the average vertical JCF did not increase significantly, the ankle NJM may have increased due to the larger moment arm created about the ankle joint due to the anterior projection of the centre of mass with an arm swing[19].
The vertical impulses at the tibiofemoral and patellofemoral joints did not increase with an added arm swing, even when time was not normalised. As previously discussed, the delay in the proximal-to-distal strategy with the added arm swing occurs just after the breaking phase of the countermovement and prior to leg extension, increasing the forces produced by the biarticulate hamstrings and the gastrocnemius. These muscles generate a flexion moment on the tibia and femur respectively, requiring the knee extensors to be used maximally during the closed chain extension present in jumping[10]. The patellofemoral JCF has been modelled based on the quadriceps tendon and patellar tendon forces while the tibiofemoral JCF was modelled as a result of the opposing posterior cruciate ligament and patellar tendon forces[27]. The maximally used quadriceps during the CMJNoArms and CMJArms, together with their diminished ability to transfer tension to the patellar tendon while in knee flexion[9] (the posture which is prolonged during CMJArms), may explain the similar tibiofemoral and patellofemoral vertical impulses during both jumps.
The results of the participant-level PCA where only one to three fDOF were required to describe the main characteristics of both the CMJNoArms and CMJArms, suggests that a large number of constraints exist in individual CMJ motor control strategies. On average, only one additional fDOF was needed to define the 3D JCF and muscle forces separately for all 18 participants in the CMJNoArms (three total fDOF) and two additional fDOF were needed for CMJArms (four total fDOF). This shows that there was a high degree of similarity between participants in their proximal-to-distal movement pattern, suggesting that underlying mechanical constraints exist within our musculoskeletal system, enforcing this movement pattern[12]. At the maximum depth of the countermovement before the propulsion phase, the quadriceps are able to generate more force about the femur through the quadriceps tendon than about the tibia through the patellar tendon due to the knee flexion and geometry of patella[9]. This enhances the proximal-to-distal strategy in which the femur extends prior to the tibia in vertical jumping[27]. The biarticulate muscles, apart from creating a rotational effect not only on their proximal and distal segments, but also on their intermediate segment[28], are able to transfer energy from their proximal-to-distal segment[10]. Therefore, the biarticulate muscles and the geometry of the patella define additional constraints on the system through mechanical coupling during vertical jumps, reinforcing the proximal-to-distal delay and reducing the load on the central control system[8].
While the lower limb segments exhibit mechanical coupling, the anatomy of the upper limb is not mechanically linked and constrained to that of the lower limb. Thus, the inclusion of an arm swing exhibited greater variability both within (participant-level fDOF) and between (group-level fDOF) participants' movement strategies. The higher variation for CMJArms can also be seen in the stabilization muscles with varying activation and peak timings in CMJArms (Fig. 3, muscle groups 5–7). Theoretically, simply prolonging the proximal-to-distal strategy in CMJArms could have been defined by only three fDOF at a group level, particularly as the peaks in PC2 and PC3 are already delayed in CMJArms compared to CMJNoArms. However, CMJArms required the inclusion of PC4 to describe the force-time curve of the vastus lateralis as some participants exhibited double curves or multiple peaks in the knee extensor force-time curve, while others exhibited a smoother single curve. Similar patterns have been found in knee extensor NJM, where a smoother curve resulted in improved jump performance, compared to knee NJMs consisting of multiple peaks[19]. The CMJArms also required an additional use of PC3 in muscle group 1 (including the biceps femoris), which describes a slight increase in muscle force late in the CMJ propulsion phase. This may have been caused by the delayed peak of the knee extensor requiring additional antagonistic co-contraction of the biarticulate biceps femoris for stability at the knee joint to avoid hyperextension on take-off[8, 9].
The effect of increased variability and number of fDOF on jump performance can be seen more clearly on a participant level. Participants exhibiting two fDOF had a higher vertical external impulse compared to those who only had one fDOF (Table 2) as it would represent the majority of muscles working simultaneously. At a participant level, two fDOF are sufficient to define a proximal-to-distal strategy as the PC score curves are able to follow the individual’s strategy more closely than at a group level and reduces the need for more generic PC curves. The addition of the third fDOF at participant level may indicate excessive variation and reduced coordination within the individual’s motor strategy, resulting in decreased performance. However, the sample size of participants exhibiting one and three fDOFs is too small to make conclusive comparisons between the groups.
Vertical jumping is present in many sports with different demands and constraints. It may not be possible for the potential benefits of a prolonged ground contact time in CMJArms to be fully utilized, such as when fast reaction is required, or when speed is determined by music’s tempo in dance. However, the lack of direct mechanical coupling between the arms and the lower extremity, as described by the additional fDOF, emphasises the importance of training CMJArms to improve the individual’s jump performance. Possible sources of variation in CMJArms which may effect and improve jump height include arm swing timing and technique[16, 18]. Individual’s dynamic core flexion strength has been shown to affect the musculoskeletal ability to transfer the energy generated from the arms to the distal segments[29]. Due to the contribution of shoulder musculature to the vertical energy generated by the arm swing, it has been suggested that shoulder flexor strength may also alter performance in CMJArms[21], although further research is needed. Therefore, training a specific optimal technique, and increasing shoulder and dynamic core flexion strength may be crucial to reduce variation within the individual’s movement strategy and improve jump performance.
As noted by Cleather and Cushion[30], even though the motor strategies used in both CMJs can be described by three or four fDOF, it does not imply that every participant’s motor strategy is the same. In fact, the PC combination for each participant and each muscle can be easily identified from the PCA’s coefficient matrix, resulting in different curve profiles, peak timings and motor strategies from the same PCs. The small number of fDOF present simply indicate that the muscle forces and JCFs are tightly constrained during CMJs and that individual strategies can be defined by a linear combination of the same PCs[30], as can be seen from the multiple curves resulting from different combinations of the CMJ’s PCs (Fig. 3). Future research may explore whether additional constraints are present between the lower extremity, trunk and upper limb segments through a full-body musculoskeletal model and PCA. Jump performance can also be investigated to identify the movement characteristics describing the most effective arm swing technique to improve jump height.
A strength of this study is the inclusion of time normalisation in the vertical impulse analysis. This allowed for a distinction between solely the difference in time or a combined difference of time and vertical force as the main contribution for change in impulse between CMJNoArms and CMJArms. Another strength is the comparison of the muscle group principal component combinations between jumps in real time, clearly indicating the similarities and differences in the timings of the proximal-to-distal strategy. This detail is lost when comparing muscle activity in normalised time[16]. Although Kovács et al.[16] found the same sequence of muscle peak timings using electromyography, no differences were found in muscle peak timings between the jumps. This can be misleading as true differences in peak timing may still exist due to the prolonged CMJArms, while the difference found in the vastus lateralis activation between 38–56% of CMJArms and CMJNoArms may not be significant in real time. The principal impulse for each muscle group also closely represented the sum of the group’s muscle impulses, with a strong positive correlation. This demonstrates further the usefulness of PCA as a data reduction method to simplify the understanding of complex motor control strategies. However, it is important to keep in mind that this technique is based solely on linear relationships between the DOF. Therefore, the number of fDOF may be overestimated as non-linear relationships may still exist in the identified fDOF and thus may not be entirely independent[1]. It should also be noted that the muscle groups categorization and cut-off coefficients for the group’s PC combination were based on the interpretation of the group’s composite muscle force curves. Even though a rigorous method was followed for these steps, muscle group categorization and cut-off coefficients were determined using mainly a qualitative visual inspection of the curves. In addition, individual strategies may have varied and slightly different muscle group categorizations and PC linear combinations may have emerged between participants. There were several possible ways to interpret the results of this study, however the method followed was chosen due to the similarity in movement strategies found previously between participants for CMJArms and CMJNoArms[12], suggesting that an in-depth group analysis was suitable to compare muscle forces between jumps.
In conclusion, jump performance improved with an added arm swing as it increased the ground contact time, resulting in higher vertical impulses. The increased ground contact time to perform the arm swing was mainly used by the lower extremity to decrease the hip extension velocity, allowing the hip muscles to generate higher forces, and to delay knee extension, enhancing the proximal-to-distal strategy. The PCA has shown that muscle activation and joint kinetics in the lower limb exhibit very similar patterns within and between individuals. This suggests that the underlying anatomy, such as biarticulate muscles and the patella, provide mechanical constraints and coupling during a CMJ, reducing the load on the central control system[8]. The inclusion of an arm swing required an additional fDOF (four in total) to describe the main characteristics of the movement, suggesting that the arms are not directly mechanically coupled with the lower extremity, resulting in additional variation within individual motor strategies.