Performing the vertical jump: Movement adaptations for submaximal jumping

Relationship between jump height and lower limb joint kinetics and kinematics during countermovement jump in elite male athletes

This study aims to identify the relationship between jump height and the kinetic and kinematic parameters of the hip, knee, and ankle joints during countermovement jump (CMJ) in elite male athletes. Sixty-six elite male athletes from various sports (strength and power, winter downhill, combat, ball game, and aquatic) performed maximal effort CMJs with hands and arms crossed against their chests on force platforms. Jumping motion in the sagittal plane was recorded using video analysis and the peak torque, power, and angular velocity of the right hip, knee, and ankle joints were calculated during the propulsive phase. Correlations between the CMJ height and kinetic and kinematic parameters were investigated using Pearson's product-moment coefficient (r) and Spearman's rank correlation coefficient (ρ). CMJ height was highly correlated with peak hip power (ρ = 0.686, p < 0.001) and peak knee angular velocity (r = 0.517, p < 0.001), and moderately correlated with peak hip angular velocity (r = 0.438, p < 0.001) and peak hip torque (r = 0.398, p = 0.001). These results indicate that notable hip torque and power can contribute to increased angular velocity in both the knee and hip joints, ultimately increasing the CMJ height in elite male athletes.

Assessment of countermovement jump with and without arm swing using a single inertial measurement unit

The countermovement vertical jump height, flight time, and jump duration are used to assess athletic performance. Force-plate and motion-capture cameras are used to estimate these parameters, yet, their application is limited to dedicated lab environments. Despite the potential of inertial measurement units (IMU) for estimating the jump height, their accuracy has not been validated. This study investigates the accuracy of our proposed method to estimate the jump height using a sacrum-mounted IMU, during countermovement jumping. Eleven individuals performed four jumps each. To obtain the jump height, we transformed the IMU readouts into anatomical planes, and double-integrated the vertical acceleration after correction for zero velocity and vertical displacement. The accuracy of jump height obtained by IMU was compared to force-plate and motion-capture cameras during jumps without arm swing (mean error (standard deviation) of 0.3(2.2) cm and 1.0(3.0) cm, and correlation coefficient of 0.83 and 0.82, respectively) and during jumps with arm swing (-1.1(2.1) cm and 0.5(1.9) cm, and 0.92 and 0.89). The correlation coefficients were high, and the errors were comparable to the difference between the jump height obtained by force-plate and cameras. Therefore, a sacrum-mounted IMU can be recommended for in-field assessment of countermovement jump with and without arm swing.

A novel computational framework for the estimation of internal musculoskeletal loading and muscle adaptation in hypogravity

Introduction: Spaceflight is associated with substantial and variable musculoskeletal (MSK) adaptations. Characterisation of muscle and joint loading profiles can provide key information to better align exercise prescription to astronaut MSK adaptations upon return-to-Earth. A case-study is presented of single-leg hopping in hypogravity to demonstrate the additional benefit computational MSK modelling has when estimating lower-limb MSK loading. Methods: A single male participant performed single-leg vertical hopping whilst attached to a body weight support system to replicate five gravity conditions (0.17, 0.25, 0.37, 0.50, 1 g). Experimental joint kinematics, joint kinetics and ground reaction forces were tracked in a data-tracking direct collocation simulation framework. Ground reaction forces, sagittal plane hip, knee and ankle net joint moments, quadriceps muscle forces (Rectus Femoris and three Vasti muscles), and hip, knee and ankle joint reaction forces were extracted for analysis. Estimated quadriceps muscle forces were input into a muscle adaptation model to predict a meaningful increase in muscle cross-sectional area, defined in (DeFreitas et al., 2011). Results: Two distinct strategies were observed to cope with the increase in ground reaction forces as gravity increased. Hypogravity was associated with an ankle dominant strategy with increased range of motion and net plantarflexor moment that was not seen at the hip or knee, and the Rectus Femoris being the primary contributor to quadriceps muscle force. At 1 g, all three joints had increased range of motion and net extensor moments relative to 0.50 g, with the Vasti muscles becoming the main muscles contributing to quadriceps muscle force. Additionally, hip joint reaction force did not increase substantially as gravity increased, whereas the other two joints increased monotonically with gravity. The predicted volume of exercise needed to counteract muscle adaptations decreased substantially with gravity. Despite the ankle dominant strategy in hypogravity, the loading on the knee muscles and joint also increased, demonstrating this provided more information about MSK loading. Discussion: This approach, supplemented with muscle-adaptation models, can be used to compare MSK loading between exercises to enhance astronaut exercise prescription.

The effect of fatigue on spike jump biomechanics in view of patellar tendon loading in volleyball

BACKGROUND AND OBJECTIVE

Patellar tendinopathy (PT) is a highly prevalent overuse injury in volleyball and is often linked with overloading of the patellar tendon. Little is known, however, about whether and how patellar tendon loading is affected by fatigue during the most challenging jump activity in volleyball. Therefore, this study investigates the effect of a high-intensity, intermittent fatigue protocol on movement alterations in terms of patellar tendon loading during a volleyball spike jump.

METHODS

Forty-three male volleyball players participated in this study. Three-dimensional full-body kinematics and kinetics were collected when performing a spike jump before and after the fatigue protocol. Sagittal plane joint angles, joint work and patellar tendon loading were calculated and analyzed with curve analyses using paired sample t-tests to investigate fatigue effects (p < 0.05).

RESULTS

Fatigue induced a stiffer lower extremity landing strategy together with prolonged pelvis-trunk flexion compared to baseline (p = 0.001-0.005). Decreased patellar tendon forces (p = 0.001-0.010) and less eccentric knee joint work (-5%, p < 0.001) were observed after the fatigue protocol compared to baseline.

CONCLUSION

Protective strategies seem to be utilized in a fatigued state to avoid additional tensile forces acting on the patellar tendon, including proximal compensations and stiff lower extremity landings. We hypothesize that players might be more prone for developing PT if eccentric patellar tendon loads are high in the non-fatigued state and/or these loads are somehow not decreased after fatigue.

Joint Coordination and Muscle-Tendon Interaction Differ Depending on The Level of Jumping Performance

The countermovement jump is a popular measurement modality to evaluate muscle power in sports and exercise. Muscle power is essential to achieve a high jump, yet the well-coordinated movement of the body segments, which optimizes the stretch-shortening cycle (SSC) effects, is also required. Among the proposed explanations of SSC effects, this study investigated whether the ankle joint kinematics, kinetics, and muscle-tendon interaction depend on the level of jump skill and the jump task. Sixteen healthy males were grouped as a function of their jump height (High jumpers; greater than 50 cm, Low jumpers; less than 50 cm). They were instructed to jump with two intensities; light effort (20 % of their height) and maximal effort. Joint kinematics and kinetics of the lower limbs were analyzed using a 3-dimensional motion analysis system. The muscle-tendon interaction was investigated using B-mode real-time ultrasonography. As the jump intensity increased, all participants jumped with increased joint velocity and power. However, the high jumper shows less fascicle shortening velocity (-0.2 ± 0.1 m/s) than the low jumper group (-0.3 ± 0.1 m/s) and greater tendon velocity, which indicated the capability of elastic energy recoil. In addition, the delayed onset time of ankle extension in the high jumper implies better use of the catapult mechanism. The findings of this study showed that the muscle-tendon interaction differs depending on the jump skill level, suggesting a more efficient neuromuscular control in skilled jumpers.

The Effect of Foot Position and Lean Mass on Jumping and Landing Mechanics in Collegiate Dancers

The purpose of this study was to investigate the effects of foot positioning and lean mass on jumping and landing mechanics in collegiate dancers. Thirteen dancers performed 3 unilateral and bilateral vertical jumps with feet in neutral and turnout positions. Dual-energy x-ray absorptiometry scans, jump height, vertical stiffness, and joint stiffness were assessed for relationships between foot positions. Jump heights were greater in right compared with left limb (P = .029) and neutral compared with turnout (P = .020) during unilateral jumping. In unilateral landing, knee stiffness was greater in turnout compared with neutral (P = .004) during the loading phase. Jump height (P < .001) was significantly increased, and vertical stiffness (P = .003) was significantly decreased during bilateral jumping in neutral compared with turnout. Significantly increased hip stiffness during the attenuation phase was observed in neutral compared with turnout (P = .006). Left-limb lean mass was significantly less than the right limb (P < .05). Adjustments for bilateral jumping were focused on hip stiffness, whereas there was a slight shift to knee strategy for unilateral jump.

Methods of Estimating Foot Power and Work in Standing Vertical Jump

Experimental motion capture studies have commonly considered the foot as a single rigid body even though the foot contains 26 bones and 30 joints. Various methods have been applied to study rigid body deviations of the foot. This study compared 3 methods: distal foot power (DFP), foot power imbalance (FPI), and a 2-segment foot model to study foot power and work in the takeoff phase of standing vertical jumps. Six physically active participants each performed 6 standing vertical jumps from a starting position spanning 2 adjacent force platforms to allow ground reaction forces acting on the foot to be divided at the metatarsophalangeal (MTP) joints. Shortly after movement initiation, DFP showed a power absorption phase followed by a power generation phase. FPI followed a similar pattern with smaller power absorption and a larger power generation compared to DFP. MTP joints primarily generated power in the 2-segment model. The net foot work was -4.0 (1.0) J using DFP, 1.8 (1.1) J using FPI, and 5.1 (0.5) J with MTP. The results suggest that MTP joints are only 1 source of foot power and that differences between DFP and FPI should be further explored in jumping and other movements.

Backward Double Integration is a Valid Method to Calculate Maximal and Sub-Maximal Jump Height

The backward double integration method uses one force plate and could calculate jump height for countermovement jumping, squat jumping and drop jumping by analysing the landing phase instead of the push-off phase. This study compared the accuracy and variability of the forward double integration (FDI), backwards double integration (BDI) and Flight Time + Constant (FT+C) methods, against the marker-based rigid-body modelling method. It was hypothesised that the jump height calculated using the BDI method would be equivalent to the FDI method, while the FT+C method would have reduced accuracy and increased variability during sub-maximal jumping compared to maximal jumping. Twenty-four volunteers performed five maximal and five sub-maximal countermovement jumps, while force plate and motion capture data were collected. The BDI method calculated equivalent mean jump heights compared to the FDI method, with only slightly higher variability (2-3 mm), and therefore can be used in situations where FDI cannot be employed. The FT+C method was able to account for reduced heel-lift distance, despite employing an anthropometrically scaled heel-lift constant. However, across both sub-maximal and maximal jumping, it had increased variability (1.1 cm) compared to FDI and BDI and should not be used when alternate methods are available.

The energetic function of the human foot and its muscles during accelerations and decelerations

The human foot is known to aid propulsion by storing and returning elastic energy during steady-state locomotion. While its function during other tasks is less clear, recent evidence suggests the foot and its intrinsic muscles can also generate or dissipate energy based on the energetic requirements of the center of mass during non-steady-state locomotion. In order to examine contributions of the foot and its muscles to non-steady-state locomotion, we compared the energetics of the foot and ankle joint while jumping and landing before and after the application of a tibial nerve block. Under normal conditions, energetic contributions of the foot rose as work demands increased, while the relative contributions of the foot to center of mass work remained constant with increasing work demands. Under the nerve block, foot contributions to both jumping and landing decreased. Additionally, ankle contributions were also decreased under the influence of the block for both tasks. Our results reinforce findings that foot and ankle function mirror the energetic requirements of the center of mass and provide novel evidence that foot contributions remain relatively constant under increasing energetic demands. Also, while the intrinsic muscles can modulate the energetic capacity of the foot, their removal accounted for only a 3% decrement in total center of mass work. Therefore, the small size of intrinsic muscles appears to limit their capacity to contribute to center of mass work. However, their role in contributing to ankle work capacity is likely important for the energetics of movement.

Age-Related Decline in Vertical Jumping Performance in Masters Track and Field Athletes: Concomitant Influence of Body Composition

Vertical jumping power declines with advancing age, which is theoretically explicable by loss of muscle mass and increases in body fat. However, the results of previous cross-sectional studies remain inconsistent on these relationships. The present study included 256 masters athletes who competed at the 2018 track and field world championships in Málaga, Spain. We assessed body composition with bioelectrical impedance (Inbody S10) and vertical jumping power with a Leonardo ground reaction force platform. Relationships between age, jumping power, and body composition were analyzed by correlation and regression analyses. Hierarchical multiple regression analysis was used to evaluate effects of each factor on vertical jumping power. Age-related rates of decreases in maximal power and jump height were similar between male and female athletes. Percent fat-free mass and percent body fat were negatively and positively, respectively, associated with age in masters athletes and were comparable to those previously observed in the general population. Moreover, these effects in body composition can, to a great extent, explain the age-related decline in jumping power, an effect that seems at least partly independent of age. Finally, the multiple regression model to determine independent predictors of vertical jump performance yielded an overall R² value of 0.75 with the inclusion of (1) athletic specialization in power events, (2) percent fat-free mass, and (3) phase angle. However, partial regression yielded significant effects of age, but not gender, on peak power, even when adjusting for athletic specialization, percent fat-free mass, and phase angle. We concluded that loss of skeletal muscle mass and changes in bio-impedance phase angle are important contributors to the age-related reduction in anaerobic power, even in adults who maintain high levels of physical activity into old age. However, age per se remains a significant predictor of vertical jump performance, further demonstrating deteriorated muscle quality at old age (sarcosthenia).

Knowledge of results during vertical jump testing: an effective method to increase the performance but not the consistency of vertical jumps

This study aimed to determine whether the provision of jump height feedback (knowledge of result; KR) can increase the performance and the consistency of output variables. In a randomised order, sixteen participants performed six squat or countermovement jumps (three from a 90º knee angle and three from a self-preferred knee angle) with or without KR over four sessions. The provision of KR significantly increased peak force (p = 0.046, 1.83%), mean force (p = 0.037, 1.45%), peak velocity (p < 0.001, 3.71%), mean velocity (p = 0.004, 3.44%), peak power (p < 0.001, 4.22%) and mean power (p = 0.001, 4.69%). A high within-session reliability was observed for all variables (coefficient of variation [CV] ≤ 5.62%, intraclass correlation coefficient [ICC] ≥ 0.95). No systematic differences in reliability were detected between the jumps performed without KR (CV = 3.00 ± 1.38%, ICC = 0.97 ± 0.03) and with KR (CV = 3.04 ± 1.49%, ICC = 0.97 ± 0.04). These results suggest that the provision of jump height feedback during vertical jump testing is effective to enhance vertical jump performance but it does not reduce the variability between jumps.

Joint and muscle-tendon coordination strategies during submaximal jumping

Previous research has demonstrated that during submaximal jumping humans prioritize reducing energy consumption by minimizing countermovement depth. However, sometimes movement is constrained to a nonpreferred pattern, and this requires adaptation of neural control that accounts for complex interactions between muscle architecture, muscle properties, and task demands. This study compared submaximal jumping with either a preferred or a deep countermovement depth to examine how joint and muscle mechanics are integrated into the adaptation of coordination strategies in the deep condition. Three-dimensional motion capture, two force plates, electromyography, and ultrasonography were used to examine changes in joint kinetics and kinematics, muscle activation, and muscle kinematics for the lateral gastrocnemius and soleus. Results demonstrated that a decrease in ankle joint work during the deep countermovement depth was due to increased knee flexion, leading to unfavorably short biarticular muscle lengths and reduced active fascicle length change during ankle plantar flexion. Therefore, ankle joint work was likely decreased because of reduced active fascicle length change and operating position on the force-length relationship. Hip joint work was significantly increased as a result of altered muscle activation strategies, likely due to a substantially greater hip extensor muscle activation period compared with plantar flexor muscles during jumping. Therefore, coordination strategies at individual joints are likely influenced by time availability, where a short plantar flexor activation time results in dependence on muscle properties, instead of simply altering muscle activation, while the longer time for contraction of muscles at the hip allows for adjustments to voluntary neural control.

NEW & NOTEWORTHY Using human jumping as a model, we show that adapting movement patterns to altered task demands is achieved differently by muscles across the leg. Because of proximal-to-distal sequencing, distal muscles (i.e., plantar flexors) have reduced activation periods and, as a result, rely on muscle contractile properties (force-length relationship) for adjusting joint kinetics. For proximal muscles that have greater time availability, voluntary activation is modulated to adjust muscle outputs.

Joint- and subject-specific strategies in male basketball players across a range of countermovement jump heights

The purpose of this study was to investigate subject- and joint-specific strategies used by male basketball players as they increase their countermovement jump (CMJ) height from sub-maximal to maximal efforts. Lower extremity joint kinematics and kinetics were recorded as 11 male, NCAA Division I basketball players performed 8-10 CMJ across effort levels of approximately 25%, 50%, 75% and 100%. Simple correlation models were used to investigate the associations between effort levels (i.e., CMJ height) and joint mechanics (i.e., negative (eccentric) and positive (concentric) mechanical work performed at the hip, knee, and ankle joints) for each individual player and the entire group. Group-analyses showed that increases in all joint mechanical variables were associated with increases in CMJ height. In contrast, single-subject analyses revealed that players used individualised strategies, and selectively scaled the magnitude of mechanical work at none (n = 2), one (n = 2), two (n = 5), or all three (n = 2) joints as they increased CMJ efforts. In addition, individual players also appeared to selectively scale different combinations of eccentric or concentric joint work as they increased CMJ height. These results highlight that male basketball players use joint-specific strategies to increase CMJ height when progressively increasing CMJ effort.

Classification of Soccer and Basketball Players' Jumping Performance Characteristics: A Logistic Regression Approach

This study aimed to examine countermovement jump (CMJ) kinetic data using logistic regression, in order to distinguish sports-related mechanical profiles. Eighty-one professional basketball and soccer athletes participated, each performing three CMJs on a force platform. Inferential parametric and nonparametric statistics were performed to explore group differences. Binary logistic regression was used to model the response variable (soccer or not soccer). Statistical significance (p < 0.05) was reached for differences between groups in maximum braking rate of force development (RFD_Dmax, U₇₉ = 1035), mean braking rate of force development (RFD_Davg, U₇₉ = 1038), propulsive impulse (IMP_U, t₇₉ = 2.375), minimum value of vertical displacement for center of mass (S_BCMmin, t₇₉ = 3.135), and time difference (% of impulse time; Δ_Τ) between the peak value of maximum force value (F_Umax) and S_BCMmin (U₇₉ = 1188). Logistic regression showed that RFD_Davg, impulse during the downward phase (IMP_D), IMP_U, and Δ_Τ were all significant predictors. The model showed that soccer group membership could be strongly related to IMP_U, with the odds ratio being 6.48 times higher from the basketball group, whereas RFD_Davg, IMP_D, and Δ_Τ were related to basketball group. The results imply that soccer players execute CMJ differently compared to basketball players, exhibiting increased countermovement depth and impulse generation during the propulsive phase.

Effect of Force Sense to Active Joint Position Sense and Relationships between Active Joint Position Sense, Force Sense, Jumping and Muscle Strength

We aimed to investigate the effect of external load on the joint position sense (JPS) accuracy and its relation to the target jump height. The present study also aimed to explore the relationship between force sense (FS) and maximum voluntary isometric contraction (MVIC). Participants' MVIC levels were determined during the 45-degree knee extension task. Then, participants were asked to execute a knee JPS task with external load (EL-JPS) and with no-load (EL-JPS). To assess jumping accuracy participants were instructed to jump with their 50% of maximum jump height. Results indicated that EL-JPS error values were lower than NL-JPS. EL-JPS was correlated to jumping errors. However, the relationship between NL-JPS and jumping errors was not significant. A significant correlation was found between MVIC and FS errors.

Hip moment and knee power eccentric utilisation ratios determine lower-extremity stretch-shortening cycle performance

The eccentric utilisation ratio (EUR) is calculated as the ratio between countermovement jump (CMJ) and squat jump (SJ) heights, and is an indicator of lower-extremity stretch-shortening cycle (SSC) performance in athletes. Joint-based EUR can also be calculated but have never been reported. The purpose of this study was to investigate whether jump height-based (JH-based) EUR can be predicted by joint-specific EUR. Nine NCAA Division I college athletes (age: 21 ± 1 year, height: 1.75 ± 0.15 m, mass: 71 ± 20 kg) performed three SJ and CMJ. During all jumps, kinematic and kinetic data were obtained and used to calculate hip, knee and ankle net joint moments (NJM) and net joint powers (NJP). JH was calculated from pelvis marker data. EUR (CMJ/SJ [unitless]) were calculated for JH, NJM, and NJP. JH-EUR was 1.11 ± 0.70. NJM-EUR were 1.07 ± 0.17, 1.17 ± 0.25, and 1.07 ± 0.18 for the hip, knee and ankle joint, respectively. NJP-EUR were 1.41 ± 0.12, 1.26 ± 0.28 and 1.06 ± 0.11 for the hip, knee and ankle joint, respectively. Regularised regression showed that Hip-NJM-EUR, Knee-NJP-EUR and Ankle-NJM-EUR were able to predict 83% of the variance in JH-EUR, which suggests that the enhancement of lower-extremity SSC performance during CMJ arises from a combination of these parameters.

Hopping in hypogravity-A rationale for a plyometric exercise countermeasure in planetary exploration missions

Moon and Mars are considered to be future targets for human space explorations. The gravity level on the Moon and Mars amount to 16% and 38%, respectively, of Earth’s gravity. Mechanical loading during the anticipated habitual activities in these hypogravity environments will most likely not be sufficient to maintain physiological integrity of astronauts unless additional exercise countermeasures are performed. Current microgravity exercise countermeasures appear to attenuate but not prevent ‘space deconditioning’. However, plyometric exercises (hopping and whole body vibration) have shown promise in recent analogue bed rest studies and may be options for space exploration missions where resources will be limited compared to the ISS. This paper therefore tests the hypothesis that plyometric hop exercise in hypogravity can generate sufficient mechanical stimuli to prevent musculoskeletal deconditioning. It has been suggested that hypogravity-induced reductions in peak ground reaction force (peak vertical GRF) can be offset by increases in hopping height. Therefore, this study investigated the effects of simulated hypogravity (0.16G, 0.27G, 0.38G, and 0.7G) upon sub-maximal plyometric hopping on the Verticalised Treadmill Facility, simulating different hypogravity levels. Results show that peak vertical GRF are negatively related to simulated gravity level, but positively to hopping height. Contact times decreased with increasing gravity level but were not influenced through hopping height. In contrast, flight time increased with decreasing gravity levels and increasing hopping height (P < 0.001). The present data suggest that the anticipated hypogravity-related reductions of musculoskeletal forces during normal walking can be compensated by performing hops and therefore support the idea of plyometric hopping as a robust and resourceful exercise countermeasure in hypogravity. As maximal hop height was constrained on the VTF further research is needed to determine whether similar relationships are evident during maximal hops and other forms of jumping.

The influence of added mass on muscle activation and contractile mechanics during submaximal and maximal countermovement jumping in humans

Muscle contractile mechanics induced by the changing demands of human movement have the potential to influence our movement strategies. This study examined fascicle length changes of the triceps surae during jumping with added mass or increasing jump height to determine whether the chosen movement strategies were associated with relevant changes in muscle contractile properties. Sixteen participants jumped at sub-maximal and maximal intensities while total net work was matched via two distinct paradigms: (1) adding mass to the participant or (2) increasing jump height. Electromyography (EMG) and ultrasound analyses were performed to examine muscle activation, fascicle length and fascicle velocity changes of the triceps surae during jumping. Integrated EMG was significantly higher in the added mass paradigm with no difference in mean or maximal EMG, indicating that the muscle was activated for a significantly longer period of time but not activated to a greater intensity. Fascicle shortening velocity was slower with added mass compared than with increasing jump height; therefore, intrinsic force–velocity properties probably enabled increased force production. Improved fascicle contractile mechanics paired with a longer activation period probably produced a consistently larger fascicle force, enabling a greater impulse about the ankle joint. This may explain why previous research found that participants used an ankle-centred strategy for work production in the added mass paradigm and not in the jump height paradigm. The varied architecture of muscles within the lower limb may influence which muscles we choose to employ for work production under different task constraints.

The effect of increased shooting distance on energy flow in basketball jump shot

The aim of this study is to clarify the effect of shooting distance on energy flow in basketball jump shot. Ten male right-handed basketball players participated in this study, and three successful shots at three different distances (short condition, equating to a free-throw; long condition, equating to a three-point shot; and mid condition, equating to the mid-point of the short- and long-condition shots) were recorded using a motion capture system and force platforms. Kinetic variables of joints during shooting were analysed using inverse dynamics method. Our results showed that the joint work was not significantly different for short- and mid-condition shots; however, the amount of energy transferred from the torso to the shooting arm by the shoulder joint force increased significantly for the mid-condition shots ([Formula: see text] as opposed to [Formula: see text] J/kg, [Formula: see text]), whereas between the mid- and long-conditions, it was found that the joint work in the lower limbs increased significantly ([Formula: see text] as opposed to [Formula: see text] J/kg, [Formula: see text]). These results suggest that sufficient energy transfer from the lower limbs to the shoot arms is important to keep the motions of the shooting arms approximately constant when shooting from various distances.

Movement Strategies for Countermovement Jumping are Potentially Influenced by Elastic Energy Stored and Released from Tendons

The preferred movement strategies that humans choose to produce work for movement are not fully understood. Previous studies have demonstrated an important contribution of elastic energy stored within the Achilles tendon (AT) during jumping. This study aimed to alter energy available for storage in the AT to examine changes in how jumpers distribute work among lower limb joints. Participants (n = 16) performed maximal and sub-maximal jumps under two paradigms, matched for increasing total work output by manipulating jump height or adding body mass. Motion capture and ground reaction force data were combined in an inverse dynamics analysis to compute ankle, knee and hip joint kinetics. Results demonstrated higher peak moments about the ankle joint with added body mass (+26 Nm), likely resulting in additional energy storage in the AT. Work at the ankle joint increased proportionally with added mass, maintaining a constant contribution (~64%) to total work that was not matched with increasing jump height (-14%). This implies greater energy storage and return by the AT with added mass but not with increased height. When total work during jumping is constant but energy stored in tendons is not, humans prioritise the use of stored elastic energy over muscle work.

Kinetic Contributions of The Upper Limbs During Counter-Movement Verical Jumps With and Without Arm Swing

Mosier, EM, Fry, AC, and Lane, MT. Kinetic contributions of the upper limbs during countermovement. J Strength Cond Res 33(8): 2066-2073, 2019-This study examined the kinetic contributions of the upper extremities during countermovement vertical jumps (CMVJs) while using arm swing (AS) or no arm swing (NAS) conditions. Fourteen healthy men ((Equation is included in full-text article.)± SD; age = 24.1 ± 3.9 years) volunteered for this investigation. Subjects performed in random order a total of 6 jumps consisting of 3 AS and 3 NAS CMVJs. A motion capture system was used to analyze the kinetic data. Paired samples t-tests were used to examine the subjects' mean differences in the AS and NAS CMVJ trials (p<0.05). Results for all subjects were determined for each jump subjects were determined for each jump performed, with statistical analyses performed on mean values for all 3 jumps per subject. The AS significantly increased the vertical jump height (VJH) by an average of 0.07 ± 0.03 m (3.0 ± 1.3 inches). Dual-energy X-ray absorptiometry scans determined that the upper limbs were 12.0% of the total body mass. Movement of the upper limbs during the AS CMVJ produced 32.2 ± 7.0% of the total mean ground reaction force (GRF), and 11.3 ± 2.2% during the NAS CMVJ. The enhancement of performance when jumping using an AS resulted in a 13.6% increase in VJH. The contribution of the upper limbs during the AS CMVJ averaged 31.5% of the peak GRF, which occurred immediately before takeoff. The upper extremities can greatly influence vertical jump performances and the accompanying kinetics. When analyzing jump GRFs, one must be aware of how much the upper limbs contribute to these forces. In addition, proper AS mechanics must be emphasized when instructing correct jump technique.

Can segmental model reductions quantify whole-body balance accurately during dynamic activities?

When investigating whole-body balance in dynamic tasks, adequately tracking the whole-body centre of mass (CoM) or derivatives such as the extrapolated centre of mass (XCoM) can be crucial but add considerable measurement efforts. The aim of this study was to investigate whether reduced kinematic models can still provide adequate CoM and XCoM representations during dynamic sporting tasks. Seventeen healthy recreationally active subjects (14 males and 3 females; age, 24.9±3.2years; height, 177.3±6.9cm; body mass 72.6±7.0kg) participated in this study. Participants completed three dynamic movements, jumping, kicking, and overarm throwing. Marker-based kinematic data were collected with 10 optoelectronic cameras at 250Hz (Oqus Qualisys, Gothenburg, Sweden). The differences between (X)CoM from a full-body model (gold standard) and (X)CoM representations based on six selected model reductions were evaluated using a Bland-Altman approach. A threshold difference was set at ±2cm to help the reader interpret which model can still provide an acceptable (X)CoM representation. Antero-posterior and medio-lateral displacement profiles of the CoM representation based on lower limbs, trunk and upper limbs showed strong agreement, slightly reduced for lower limbs and trunk only. Representations based on lower limbs only showed less strong agreement, particularly for XCoM in kicking. Overall, our results provide justification of the use of certain model reductions for specific needs, saving measurement effort whilst limiting the error of tracking (X)CoM trajectories in the context of whole-body balance investigation.

Manifestations of Proprioception During Vertical Jumps to Specific Heights

Artur, S, Bogdan, P, Kawczyński, A, Winiarski, S, Grzegorz, J, and Andrzej, R. Manifestations of proprioception during vertical jumps to specific heights. J Strength Cond Res 31(6): 1694–1701, 2017—Jumping and proprioception are important abilities in many sports. The efficiency of the proprioceptive system is indirectly related to jumps performed at specified heights. Therefore, this study recorded the ability of young athletes who play team sports to jump to a specific height compared with their maximum ability. A total of 154 male (age: 14.8 ± 0.9 years, body height: 181.8 ± 8.9 cm, body weight: 69.8 ± 11.8 kg, training experience: 3.8 ± 1.7 years) and 151 female (age: 14.1 ± 0.8 years, body height: 170.5 ± 6.5 cm, body weight: 60.3 ± 9.4 kg, training experience: 3.7 ± 1.4 years) team games players were recruited for this study. Each participant performed 2 countermovement jumps with arm swing to 25, 50, 75, and 100% of the maximum height. Measurements were performed using a force plate. Jump height and its accuracy with respect to a specified height were calculated. The results revealed no significant differences in jump height and its accuracy to the specified heights between the groups (stratified by age, sex, and sport). Individuals with a higher jumping accuracy also exhibited greater maximum jump heights. Jumps to 25% of the maximum height were approximately 2 times higher than the target height. The decreased jump accuracy to a specific height when attempting to jump to lower heights should be reduced with training, particularly among athletes who play team sports. These findings provide useful information regarding the proprioceptive system for team sport coaches and may shape guidelines for training routines by working with submaximal loads.

Resolution of low-velocity control in golf putting differentiates professionals from amateurs

It is difficult for humans to apply small amounts of force precisely during motor control. However, experts who have undergone extended training are thought to be able to control low-velocity movement with precision. We investigated the resolution of motor control in golf putting. A total of 10 professional and 10 high-level amateur golfers participated. Putting distances were 0.6-3.3 m, in increments of 0.3 m. We measured the impact velocity and the club-face angle at impact, and the acceleration profile of the downswing. The professionals showed significantly smaller coefficients of variation with respect to impact velocity and smaller root mean square errors in relation to acceleration profiles than did the amateurs. To examine the resolution of motor control for impact velocity, we investigated intra-participant differences in the impact velocity of the club head at two adjacent distances. We found that professionals had higher velocity precision when putting small distance intervals than did amateurs. That is, professionals had higher resolution of low-velocity control than did high-level amateurs. Our results suggest that outstanding performance at a task involves the ability to recognise small distinctions and to produce appropriate movements.

Influence of Familiarization and Competitive Level on the Reliability of Countermovement Vertical Jump Kinetic and Kinematic Variables

Understanding typical variation of vertical jump (VJ) performance and confounding sources of its typical variability (i.e., familiarization and competitive level) is pertinent in the routine monitoring of athletes. We evaluated the presence of systematic error (learning effect) and nonuniformity of error (heteroscedasticity) across VJ performances of athletes that differ in competitive level and quantified the reliability of VJ kinetic and kinematic variables relative to the smallest worthwhile change (SWC). One hundred thirteen high school athletes, 30 college athletes, and 35 professional athletes completed repeat VJ trials. Average eccentric rate of force development (RFD), average concentric (CON) force, CON impulse, and jump height measurements were obtained from vertical ground reaction force (VGRF) data. Systematic error was assessed by evaluating changes in the mean of repeat trials. Heteroscedasticity was evaluated by plotting the difference score (trial 2 - trial 1) against the mean of the trials. Variability of jump variables was calculated as the typical error (TE) and coefficient of variation (%CV). No substantial systematic error (effect size range: -0.07 to 0.11) or heteroscedasticity was present for any of the VJ variables. Vertical jump can be performed without the need for familiarization trials, and the variability can be conveyed as either the raw TE or the %CV. Assessment of VGRF variables is an effective and reliable means of assessing VJ performance. Average CON force and CON impulse are highly reliable (%CV: 2.7% ×/÷ 1.10), although jump height was the only variable to display a %CV ≤SWC. Eccentric RFD is highly variable yet should not be discounted from VJ assessments on this factor alone because it may be sensitive to changes in response to training or fatigue that exceed the TE.

Effects of countermovement depth on kinematic and kinetic patterns of maximum vertical jumps

Although maximum height (H(max)), muscle force (F), and power output (P), have been routinely obtained from maximum vertical jumps for various purposes, a possible role of the countermovement depth (H(cmd)) on the same variables remains largely unexplored. Here we hypothesized that (1) the optimum H(cmd) for maximizing H(max) exists, while (2) an increase in H(cmd) would be associated with a decrease in both F and P. Professional male basketball players (N=11) preformed maximum countermovement jumps with and without arm swing while varying H(cmd)±25 cm from its preferred value. Although regression models revealed a presence of optimum H(cmd) for maximizing H(max), H(max) revealed only small changes within a wide range of H(cmd). The preferred H(cmd) was markedly below its optimum value (p < .05). However, both F and P sharply decreased with H(cmd), while F also revealed a minimum for H(cmd) close to its highest values. Therefore, we conclude that although the optimum H(cmd) should exists, the magnitude of its effect on H(max) should be only minimal within a typical H(cmd) range. Conversely, F and P of leg muscles assessed through maximum vertical jumps should be taken with caution since both of them could be markedly confounded by H(cmd).

Asymmetrical loading demands associated with vertical jump landings in people with unilateral transtibial amputation

Loading symmetry during vertical jump landings between a person with amputation's intact and prosthetic limbs was assessed to determine the role of each limb in controlling the downward momentum of the center of mass during landing. Six participants with unilateral transtibial amputation (TTA) and ten nondisabled participants completed 10 maximal vertical jumps, of which the highest jump was analyzed. Contralateral symmetry was assessed through the Symmetry Index (SI), while symmetry at the group level was assessed through a Mann-Whitney U test. Participants with TTA performed quasi-unilateral landings onto the intact limbs, resulting from either the incapability of the prosthetic ankle to plantar flex or increased residual-limb knee and hip flexion. In the loading phase, the participants with TTA displayed reduced prosthetic-side peak vertical forces (p = 0.04) along with reduced prosthetic-side ankle range of motion (p < 0.001), extensor moments (p = 0.03), and negative work generated (p = 0.00). Individual asymmetries were evident in the peak vertical force magnitudes (SI = 51%-140%), duration from touchdown to peak vertical force (SI = 52%-157%), ankle joint angles at touchdown (SI = 100%-538%), ranges of motion (SI = 147%-200%), knee (SI = 66%-179%) and hip (SI = 87%-132%) extensor moments, and work done at the ankle (SI = 155%-199%) and hip (SI = 83%-204%). High peak forces (25.25 +/- 4.89 N·kg(-1) intact limb and 14.61 +/- 8.28 N·kg(-1) prosthetic limb) from significantly lower (p < 0.001) landing heights than the nondisabled participants indicate a potential injury risk associated with landing for people with TTA.

Asymmetries in joint work during multi-joint movement after anterior cruciate ligament reconstruction: a pilot study

After anterior cruciate ligament reconstruction (ACL-R), many studies have reported a deficit of performance on the injured leg during multi-joint tasks. However, the total mechanical joint work (WTotal ), parameter best related to the vertical displacement of the body mass center during vertical jumping, has not yet been studied. The aim of this research was to compare asymmetries between ACL-R subjects and healthy matched subjects, through the analysis of the kinematics and kinetics during a single-leg squat jump. Asymmetries are defined by the Limb Symmetry Index (LSI). A greater LSI was observed for WTotal in the ACL-R group than in the healthy group. There was no difference in LSI for knee joint work between the two groups, while the LSI for hip and ankle joint work was significantly larger in the ACL-R group. This was explained by greater LSI for the hip and ankle joint range of motion in the ACL-R group than in the healthy group. After ACL-R, patients exhibited greater asymmetries than healthy subjects during single-leg squat jump. Physiotherapists should focus on quality execution of multi-joint movement, especially on hip and ankle joints range of motion in order to reduce asymmetries and to improve vertical jumping performance.

Leg stiffness and joint stiffness while running to and jumping over an obstacle

During running, muscles of the lower limb act like a linear spring bouncing on the ground. When approaching an obstacle, the overall stiffness of this leg-spring system (k(leg)) is modified during the two steps preceding the jump to enhance the movement of the center of mass of the body while leaping the obstacle. The aim of the present study is to understand how k(leg) is modified during the running steps preceding the jump. Since k(leg) depends on the joint torsional stiffness and on the leg geometry, we analyzed the changes in these two parameters in eight subjects approaching and leaping a 0.65 m-high barrier at 15 km h(-1). Ground reaction force (F) was measured during 5-6 steps preceding the obstacle using force platform and the lower limb movements were recorded by camera. From these data, the net muscular moment (M(j)), the angular displacement (θ(j)) and the lever arm of F were evaluated at the hip, knee and ankle. At the level of the hip, the M(j)-θ(j) relation shows that muscles are not acting like torsional springs. At the level of the knee and ankle, the M(j)-θ(j) relation shows that muscles are acting like torsional springs: as compared to steady-state running, the torsional stiffness k(j) decreases from ~1/3 two contacts before the obstacle, and increases from ~2/3 during the last contact. These modifications in k(j) reflect in changes in the magnitude of F but also to changes in the leg geometry, i.e. in the lever arms of F.

Three-Dimensional Gait Analysis Following Achilles Tendon Rupture With Nonsurgical Treatment Reveals Long-Term Deficiencies in Muscle Strength and Function

Background:

Precise long-term assessment of movement and physical function following Achilles tendon rupture is required for the development and evaluation of treatment, including different regimens of physical therapy.

Purpose:

To assess intermediate-term (<10 years by conventional thinking) objective measures of physical function following Achilles tendon rupture treated nonsurgically and to compare these with self-reported measures of physical function.

Study Design:

Cross-sectional study; Level of evidence, 3.

Methods:

Two to 5 years after Achilles tendon rupture, 9 women and 43 men (mean age, 49.2 years; range, 26-68 years) were assessed by physical examination, performance of 1-legged jumps, and 3-dimensional gait analysis (including calculation of muscle work). Self-reported scores for foot function (Achilles tendon rupture score) and level of physical activity were collected. Twenty age- and sex-matched controls were assessed in the same manner.

Results:

Physical examination of patients with the knee extended revealed 11.1° of dorsiflexion on the injured side and 9.2° on the uninjured side (P = .020), indicating gastrocnemius muscle lengthening. The 1-legged jump distance was shorter on the injured side (89.5 vs 96.2 cm; P < .001). Gait analysis showed higher peak dorsiflexion (14.3° vs 13.3°; P = .016) and lower concentric (positive) plantar flexor work (16.6 vs 19.9 J/kg; P = .001) in the ankle on the uninjured side. At the same time, eccentric (negative) dorsiflexor work was higher on the injured side (13.2 vs 11.9 J/kg; P = .010). Self-perceived foot function and physical activity were lower in patients than in healthy controls (mean Achilles tendon rupture score, 78.6 and 99.8, respectively).

Conclusion:

Nonsurgically treated patients with Achilles tendon rupture showed signs of both anatomic and functional lengthening of the tendon. Attenuated muscle strength and function were present during walking as long as 2 to 5 years after rupture, as determined by 3-dimensional gait analysis. More extensive future studies involving patients having both surgical and nonsurgical treatment could provide additional valuable information.

Intersegmental moment analysis characterizes the partial correspondence of jumping and jerking

The aim of this study was to quantify internal joint moments of the lower limb during vertical jumping and the weightlifting jerk to improve awareness of the control strategies and correspondence between these activities, and to facilitate understanding of the likely transfer of training effects. Athletic men completed maximal unloaded vertical jumps (n = 12) and explosive push jerks at 40 kg (n = 9). Kinematic data were collected using optical motion tracking and kinetic data via a force plate, both at 200 Hz. Joint moments were calculated using a previously described biomechanical model of the right lower limb. Peak moment results highlighted that sagittal plane control strategies differed between jumping and jerking (p < 0.05) with jerking being a knee dominant task in terms of peak moments as opposed to a more balanced knee and hip strategy in jumping and landing. Jumping and jerking exhibited proximal to distal joint involvement and landing was typically reversed. High variability was seen in nonsagittal moments at the hip and knee. Significant correlations were seen between jump height and hip and knee moments in jumping (p < 0.05). Although hip and knee moments were correlated between jumping and jerking (p < 0.05), joint moments in the jerk were not significantly correlated to jump height (p > 0.05) possibly indicating a limit to the direct transferability of jerk performance to jumping. Ankle joint moments were poorly related to jump performance (p > 0.05). Peak knee and hip moment generating capacity are important to vertical jump performance. The jerk appears to offer an effective strategy to overload joint moment generation in the knee relative to jumping. However, an absence of hip involvement would appear to make it a general, rather than specific, training modality in relation to jumping.

Movement in a gravitational field: The question of limb interarticular coordination in terrestrial vertebrates

In this paper, we demonstrated that interarticular coordination of terrestrial tetrapods emerges from an environment highly constrained by friction and the gravitational field. We briefly review recent works on the jumping behavior in squamates, lemurs and amphibians. We then explore previously published work as well as some unpublished experimental data on human jumping. Finally, we end by inferring locomotion in some of the first limbed vertebrates using a simulation procedure. All these data show that despite changes in shape, structure, and motor controls of taxa, the same spatio-temporal sequence of joint displacements always occurs when the movement is executed in a terrestrial environment. Comparison with aquatic locomotion argues for the hypothesis that this pattern emerged in early terrestrial tetrapods as a response to the gravitational constraint and the terrestrial frictional environment.

Measurement of pelvic motion is a prerequisite for accurate estimation of hip joint work in maximum height squat jumping

In experiments investigating vertical squat jumping, the HAT segment is typically defined as a line drawn from the hip to some point proximally on the upper body (eg, the neck, the acromion), and the hip joint as the angle between this line and the upper legs (θUL-HAT). In reality, the hip joint is the angle between the pelvis and the upper legs (θUL-pelvis). This study aimed to estimate to what extent hip joint definition affects hip joint work in maximal squat jumping. Moreover, the initial pelvic tilt was manipulated to maximize the difference in hip joint work as a function of hip joint definition. Twenty-two male athletes performed maximum effort squat jumps in three different initial pelvic tilt conditions: backward (pelvisB), neutral (pelvisN), and forward (pelvisF). Hip joint work was calculated by integrating the hip net joint torque with respect to θUL-HAT (WUL-HAT) or with respect to θUL-pelvis (WUL-pelvis). θUL-HAT was greater than θUL-pelvis in all conditions. WUL-HAT overestimated WULpelvis by 33%, 39%, and 49% in conditions pelvisF, pelvisN, and pelvisB, respectively. It was concluded that θUL-pelvis should be measured when the mechanical output of hip extensor muscles is estimated.

A biomechanical study of side steps at different distances

Lateral quickness is a crucial component of many sports. However, biomechanical factors that contribute to quickness in lateral movements have not been understood well. Thus, the purpose of this study was to quantify 3-dimensional kinetics of hip, knee, and ankle joints in side steps to understand the function of lower extremity muscle groups. Side steps at nine different distances were performed by nine male subjects. Kinematic and ground reaction force data were recorded, and net joint torque and work were calculated by a standard inverse- dynamics method. Extension torques and work done at hip, knee, and ankle joints contributed substantially to the changes in side step distances. On the other hand, hip abduction work was not as sensitive to the changes in the side step distances. The main roles of hip abduction torque and work were to accelerate the center of mass laterally in the earlier phase of the movement and to keep the trunk upright, but not to generate large power for propulsion.

Kinetic and Kinematic Compensations in Amputee Vertical Jumping

A unilateral transtibial amputation causes a disruption to the musculoskeletal system, which results in asymmetrical biomechanics. The current study aimed to assess the movement asymmetry and compensations that occur as a consequence of an amputation when performing a countermovement vertical jump. Six unilateral transtibial amputees and 10 able-bodied (AB) participants completed 10 maximal vertical jumps, and the highest jump was analyzed further. Three-dimensional lower limb kinematics and normalized (body mass) kinetic variables were quantified for the intact and prosthetic sides. Symmetry was assessed through the symmetry index (SI) for each individual and statistically using the Mann-WhitneyUtest between the intact and prosthetic sides for the amputee group. A descriptive analysis between the amputee and AB participants was conducted to explore the mechanisms of amputee jumping. The amputee jump height ranged from 0.09 to 0.24 m. In the countermovement, all ankle variables were asymmetrical (SI > 10%) and statistically different (p< .05) for the amputees. At the knee and hip, there was no statistical difference between the intact and prosthetic sides range of motion, although there was evidence of individual asymmetry. The knees remained more extended compared with the AB participants to prevent collapse. In propulsion, the prosthesis did not contribute to the work done and the ankle variables were asymmetrical (p< .05). The knee and hip variables were not statistically different between the intact and prosthetic sides, although there was evidence of functional asymmetry and the contribution tended to be greater on the intact compared with the prosthetic side. The lack of kinetic involvement of the prosthetic ankle and both knees due to the limitation of the prosthesis and the altered musculoskeletal mechanics of the joints were the reason for the reduced height jumped.

Pelvic Kinematic Method for Determining Vertical Jump Height

Sacral marker and pelvis reconstruction methods have been proposed to approximate total body center of mass during relatively low intensity gait and hopping tasks, but not during a maximum effort vertical jumping task. In this study, center of mass displacement was calculated using the pelvic kinematic method and compared with center of mass displacement using the ground-reaction force-impulse method, in experienced athletes (n= 13) performing restricted countermovement vertical jumps. Maximal vertical jumps were performed in a biomechanics laboratory, with data collected using an 8-camera motion analysis system and two force platforms. The pelvis center of mass was reconstructed from retro-reflective markers placed on the pelvis. Jump height was determined from the peak height of the pelvis center of mass minus the standing height. Strong linear relationships were observed between the pelvic kinematic and impulse methods (R2= .86;p< .01). The pelvic kinematic method underestimated jump height versus the impulse method, however, the difference was small (CV = 4.34%). This investigation demonstrates concurrent validity for the pelvic kinematic method to determine vertical jump height.

Hindlimb interarticular coordinations in Microcebus murinus in maximal leaping

The purpose of this study was to investigate the pattern of coordinations of the hindlimb joints in the world's smallest living primate (Microcebus murinus). The sequencing and timing of joint rotations have been analyzed in five adult males performing maximal leaping from a take-off immobile platform to their own wooden nest. Angular kinematics of hip, knee, angle and metatarso-phalangeal (MT) joints were deduced from high-speed X-ray films in the sagittal plane of the animals. The body mass center (BMC) of the lemurs was assimilated to their iliac crest. The maximal airborne performance of the lemurs was 0.33+/-0.04 m, which represented 2.55+/-0.36 times their snout-vent length. Take-off instant occurred 72+/-7 ms after the start of the push-off, with a BMC velocity of 3.23+/-0.48 m s(-1), oriented 55+/-14 deg. with the horizontal plane. The kinematic analysis of the joints and musculo-tendon architecture of the M. murinus plantar flexors pointed out mechanical power amplifier mechanisms (i.e. stretch-shortening cycle of hindlimb muscles and proximo-to-distal sequence).

Is energy expenditure taken into account in human sub-maximal jumping? – A simulation study

This paper presents a simulation study that was conducted to investigate whether the stereotyped motion pattern observed in human sub-maximal jumping can be interpreted from the perspective of energy expenditure. Human sub-maximal vertical countermovement jumps were compared to jumps simulated with a forward dynamic musculo-skeletal model. This model consisted of four interconnected rigid segments, actuated by six Hill-type muscle actuators. The only independent input of the model was the stimulation of muscles as a function of time. This input was optimized using an objective function, in which targeting a specific sub-maximal height value was combined with minimizing the amount of muscle work produced. The characteristic changes in motion pattern observed in humans jumping to different target heights were reproduced by the model. As the target height was lowered, two major changes occurred in the motion pattern. First, the countermovement amplitude was reduced; this helped to save energy because of reduced dissipation and regeneration of energy in the contractile elements. Second, the contribution of rotation of the heavy proximal segments of the lower limbs to the vertical velocity of the centre of gravity at take-off was less; this helped to save energy because of reduced ineffective rotational energies at take-off. The simulations also revealed that, with the observed movement adaptations, muscle work was reduced through improved relative use of the muscle's elastic properties in sub-maximal jumping. According to the results of the simulations, the stereotyped motion pattern observed in sub-maximal jumping is consistent with the idea that in sub-maximal jumping, subjects are trying to achieve the targeted jump height with minimal energy expenditure.