Sixteen healthy male subjects who did not have neuromuscular disorders or injuries were recruited. The subjects were divided into two groups based on their maximal jump height: the trained group (TG; n = 8, age: 25.1 ± 1.9 years, height: 178.6 ± 3.5 cm, weight: 78.1 ± 6.1 kg) and the untrained group (UG; n = 8, age: 25.1 ± 1.5 years, height: 174.4 ± 5.9 cm, weight: 75.8 ± 10.2 kg). Previous studies have reported that healthy male individuals can jump less than 50 cm (B. W. Hoffman et al., 2022) and elite athletes can jump around 50 cm (Tauchi et al., 2008). Therefore, we grouped the subjects based on whether they could jump over 50 cm or not. The untrained group consisted of individuals who did not exercise regularly and could not jump over 50 cm. All participants provided informed consent and participated in the experiments approved by the institutional review board (7001988-202204-HR-1139-03).

All the CMJs were performed with the participants’ hands on their hips. Two different types of CMJ jumps were performed: a jump to 20% of their height (CMJ₂₀) and the maximum effort jump (CMJ_Max) (Kim et al., 2014). Before data collection, participants performed a warm-up jump to 10% of their height and received jump height feedback using a laser marker for CMJ₂₀. Each task was performed twice, with at least a 1-minute rest period provided between trials. Jump height was measured using the position of the C7 marker.

The CMJs were captured using eight 3D motion capture cameras (VICON MX-F20, Oxford Metric Ltd., Oxford, UK) with a sampling rate of 200 Hz and two force plates (AMTI, OR6-7, Watertown, MA) with a sampling rate of 1000 Hz. A modified Helen Hayes marker set (Kadaba et al., 1990) with 30 reflective markers and two cluster markers were used (Farris et al., 2016). Lower extremity joint kinematics and kinetics were calculated using an open-source program (OpenSim 4.1) (Delp et al., 2007). Joint power and force were normalized by each participant’s weight. To accommodate the fast jumping movement used in this study. We modified the Lai Arnold 2017 model’s ankle dorsal range and contraction velocity to 30 degrees and 15 m/s, respectively, based on a previous running study (Arnold et al., 2013; Thelen et al., 2005). The model was scaled using each participant’s anthropometric information.

Ground reaction force (GRF) data and marker data were filtered using a fourth-order low-pass filter with a cut-off frequency of 15 Hz and 30 Hz, respectively. The initiation of the jump was defined as the point when the velocity of the C7 marker exceeded 0.05 m/s, and the propulsion phase was defined as the time when the upward velocity of the center of mass (CoM) exceeded 0.05 m/s. The takeoff phase was set when the GRF was <10 N during a CMJ (Farris et al., 2016). Time was normalized with 101 from the initial phase to takeoff and was represented as a percentage. Relative time of propulsion, peak joint angle, moment and power was calculated.

A portable real-time ultrasound imaging system (LogicScan 128 EXT-12 kit, TELEMED UAD, Vilnius, Lithuania) was used to measure the medial gastrocnemius (MG). A linear probe (LV7.5/60/96Z, Samsung Medison, Seoul, Korea) was placed on the muscular belly, where the superficial and deep aponeurosis were parallel. The architecture was captured during CMJs and collected at a sampling rate of 80 Hz.

The fascicle length (FL) which is the distance between superficial and deep aponeurosis, and the fascicle pennation angle, which is the angle between the FL and deep aponeurosis, were measured using Image-J software (National Institute of Health, MD, USA). To establish the reliability, four participants from each group were randomly analyzed (FL during CMJ; intraclass correlation coefficients between days [ICC] = 0.835-0.997 for CMJ₂₀, 0.945-0.998 for CMJ_Max). MTU length was used from the OpenSim program and the tendon length was calculated using the fascicle length and the MTU length (Bobbert et al., 1986a). Fascicle and tendon force were also calculated from the previous equation (Kubo et al., 2000). The physiological cross-sectional area was set at 15.4% (Fukunaga et al., 1996), and the moment arm length was adopted from OpenSim program. The lower limb length, which is the distance between the lateral malleolus and the lateral epicondyle, was measured to normalize the length of the MTU, fascicle, and tendon.

Fascicle shortening velocity was calculated directly using the fascicle length, and was measured as the rate of change in fascicle length. The rate of change in tendon length was measured from the onset of propulsion to just before the peak MG tendon length, and from after the peak MG tendon length to take-off.

Repeated measures ANOVA with Bonferroni post-hoc was conducted using IBM SPSS Statistics 25.0 (Chicago, IL, USA) to examine the interaction effect between the group (TG and UG) and the task (CMJ₂₀ and CMJ_Max). All data were presented as the mean ± s.d. to identify the difference based on tasks and groups and significance was set at p < 0.05.

For CMJ_Max, the TG jumped higher than the UG (p < 0.05) (Table 1). The CMJ₂₀ jump height between the groups was not different (Table 1).

Regardless of groups, the peak mechanical power and positive and negative work increased significantly in CMJ_Max (p < 0.05) (Table 1). In both groups, the peak ankle joint angle did not change during the task, the peak hip and knee joint angles were increased in CMJ_Max compared to in CMJ₂₀ (p < 0.05) (Figure 1A). When compared to CMJ₂₀, CMJ_Max had faster hip, knee, and ankle joint velocities in both groups (p < .05) (Figure 1B). A greater hip joint moment was observed in CMJ_Max (UG; 1.8 ± 0.5 Nm/kg, TG; 2.1 ± 0.5 Nm/kg) compared with CMJ₂₀ (UG; 1.3 ± 0.4 Nm/kg, TG; 1.6 ± 0.4 Nm/kg), but the peak moment of other joints was not different between tasks. However, the power of all joints was significantly increased at all joints during the CMJ_Max compared to CMJ₂₀ (p < 0.05) (Figure 1C).

Regardless of grouping, the onset of the propulsion phase started relatively earlier in CMJ_Max compared to CMJ₂₀ (Table 2). During a CMJ_Max, the initiation of the hip and knee joint extension appeared earlier than CMJ₂₀ (Table 2). However, the peak power at the knee joint occurred relatively later in CMJ_Max.

Both groups showed greater negative work during CMJ_Max (UG: -3.6 ± 0.9 J/kg, TG: -4.2 ± 0.9 J/kg) compared to CMJ₂₀ (UG: -3.0 ± 0.3 J/kg, TG: -2.7 ± 0.6 J/kg). However, there were no differences between groups in joint kinematics and kinetics (Figure 2). The TG group showed relatively delayed extension of the ankle joint and the peak hip joint moment and power compared to the UG group (Table 2). However, the change in the length of the MTU and tendon did not differ between groups.

The magnitude of the MTU shortening of the MG did not differ between the tasks, but, the MTU lengthening of the MG was increased during CMJ_Max (16.9 ± 4.9 mm) compared to CMJ₂₀ (10.9 ± 5.2 mm). Although the MTU length was changed, the changes in the length of the fascicle and tendon were not observed.

Regardless of the groups, fascicle force (CMJ₂₀: 631.92 ± 82.30 N, CMJ_Max: 721.3 ± 147.3 N) and tendon force (CMJ₂₀: 552.5 ± 62.9 N, CMJ_Max: 620.09 ± 92.02 N) increased as task intensity increased (p < 0.05). The rate of change in tendon length after the maximum tendon length was greater during CMJ_Max compared to CMJ₂₀ (Figure 3F) (p < 0.05).

Before the propulsive phase, the rate of change in fascicle length was smaller in the TG group than in the UG group (Figure 3B) (p < 0.05). Similarly, the fascicle shortening velocity did differ between groups (UG: -0.3 ± 0.1 m/s, TG: -0.2 ± 0.1 m/s, average values for a CMJ) (p < 0.05). However, the rate of change in tendon length did not differ between the groups.

The total work critical to achieving jump height was determined by the power generated at each joint during the propulsion phase (Vanezis and Lees, 2005; Vanrenterghem et al., 2004). Similar to previous studies that emphasized the use of proximal joints (Bobbert et al., 1996; Fukashiro and Komi, 1987; Nikolaidou et al., 2017), TG and UG accentuated the negative work, which was enhanced by about 38% during CMJ_Max compared to CMJ₂₀. Both groups were also propelled with fast joint velocity, indicating that they employed a joint strategy aimed at increasing the power by maximizing the magnitude and the velocity of force production.

When performing a low-effort task without MTU interaction, the performance is achieved effectively. However, as the task intensity increases, the behavior becomes more crucial for enhancing the SSC effect as previous studies have shown (Vanrenterghem et al., 2004). In terms of joints strategy, greater countermoves and fast-extending proximal joints were favorable to generating greater force by activating muscles and storing elastic energy (Astley and Roberts, 2014; Salles et al., 2011). Performance at the optimum length or velocity, which increases the potential for force and power production according to the force-length or velocity relationship, is enhanced by MTU interaction (Kawakami et al., 2002). However, our study found that the velocity is more dedicated to using elastic energy rather than changing the length. The faster recoil velocity at CMJ_Max could maximize the ankle joint power at CMJ_Max, which increased by about 9.9% compared to CMJ₂₀. Therefore, TG and UG jumped with coordinated use of joints and MTU to increase the usage of elastic energy.

Both TG and UG groups used joints and elastic energy to attempt to jump higher, in line with previous research (McErlain-Naylor et al., 2014). However, the difference in jump height between the group could not be fully explained by the magnitude of these factors alone. According to Cormie et al. (2009), not only the peak value of variables but also its timing was important for achieving height. Our results suggest that the jumping strategy in TG was similar to the efficient dynamic catapult mechanism.

To further lengthen the tendon length and optimize force production, TG utilized a strategy of extending the ankle joint as late as possible and early extension of proximal joints. This resulted in the tendon being stretched further, allowing the fascicle to produce force around the optimal length with low velocity (Kawakami et al., 2002). The almost isometrical shortening during the force generation phase in TG suggested that they had a neuro-mechanical advantage in generating higher force than UG for a given level of muscle activation. However, when the muscle shortening velocity was low, the power potential was diminished by the power-velocity relationship. Nevertheless, the tendon still enabled the muscle to generate greater force at the optimal fascicle length states and amplified the power (Farris et al., 2016; Kawakami et al., 2002; Roberts and Azizi, 2011).

In addition, it is important to note that producing greater force in the concentric phase is highly dependent on the rapid force development at the eccentric phase in the early propulsion phase (Krzyszkowski et al., 2022; Sole et al., 2018). Our study showed that the GRF in TG was higher at the end of propulsion compared to the beginning, whereas in UG, the concentric force appeared to slightly decrease despite high GRF at the early propulsion. This suggests that even with consecutively transferred power, the power generated in the hip joint may not fully transmit to the ankle joint in UG (Prilutsky and Zatsiorsky, 1994). Consequently, additional muscle work might be required in UG to generate large joint force and power. Additionally, the delayed ankle joint extension and instantaneous recoiled elastic energy in TG might have contributed to slightly increased concentric force, but, further researches is needed to investigate this.