A simple method for measuring force, velocity and power output during squat jump

Our aim was to clarify the relationship between power output and the different mechanical parameters influencing it during squat jumps, and to further use this relationship in a new computation method to evaluate power output in field conditions. Based on fundamental laws of mechanics, computations were developed to express force, velocity and power generated during one squat jump. This computation method was validated on eleven physically active men performing two maximal squat jumps. During each trial, mean force, velocity and power were calculated during push-off from both force plate measurements and the proposed computations. Differences between the two methods were not significant and lower than 3% for force, velocity and power. The validity of the computation method was also highlighted by Bland and Altman analyses and linear regressions close to the identity line (P<0.001). The low coefficients of variation between two trials demonstrated the acceptable reliability of the proposed method. The proposed computations confirmed, from a biomechanical analysis, the positive relationship between power output, body mass and jump height, hitherto only shown by means of regression-based equations. Further, these computations pointed out that power also depends on push-off vertical distance. The accuracy and reliability of the proposed theoretical computations were in line with those observed when using laboratory ergometers such as force plates. Consequently, the proposed method, solely based on three simple parameters (body mass, jump height and push-off distance), allows to accurately evaluate force, velocity and power developed by lower limbs extensor muscles during squat jumps in field conditions.     

Reliability and factorial validity of squat and countermovement jump tests

The primary aim of this study was to determine reliability and factorial validity of squat (SJ) and countermovement jump (CMJ) tests. The secondary aim was to compare 3 popular methods for the estimation of vertical jumping height. Physical education students (n = 93) performed 7 explosive power tests: 5 different vertical jumps (Sargent jump, Abalakow's jump with arm swing and without arm swing, SJ, and CMJ) and 2 horizontal jumps (standing long jump and standing triple jump). The greatest reliability among all jumping tests (Cronbach's alpha = 0.97 and 0.98) had SJ and CMJ. The reliability alpha coefficients for other jumps were also high and varied between 0.93 and 0.96. Within-subject variation (CV) in jumping tests ranged between 2.4 and 4.6%, the values being lowest in both horizontal jumps and CMJ. Factor analysis resulted in the extraction of only 1 significant principal component, which explained 66.43% of the variance of all 7 jumping tests. Since all jumping tests had high correlation coefficients with the principal component (r = 0.76-0.87), it was interpreted as the explosive power factor. The CMJ test showed the highest relationship with the explosive power factor (r = 0.87), that is, the greatest factorial validity. Other jumping tests had lower but relatively homogeneous correlation with the explosive power factor extracted. Based on the results of this study, it can be concluded that CMJ and SJ, measured by means of contact mat and digital timer, are the most reliable and valid field tests for the estimation of explosive power of the lower limbs in physically active men.     

Effect of arm motion on standing lateral jumps

The role of arm swing in jumping has been examined in numerous studies of standing jumps for height and forward distance, but no prior studies have explored its effect on lateral jumping. The purpose of the present study was to investigate the effect of arm motion on standing lateral jump performance and to examine the biomechanical mechanisms that may explain differences in jump distance. Six participants executed a series of jumps for maximum lateral distance from two in-ground force platforms for two jump cases (free and restricted arms) while an eight-camera, passive-reflector, motion capture system collected 3D position data throughout the movements. Inverse kinematics and dynamics analyses were performed for all jumps using three-dimensional (3D) link models to calculate segment angular velocities, joint moments, joint powers, and joint work. Free arm motion improved standing lateral jump performance by 29% on average. This improvement was due to increased takeoff velocity and improved lateral and vertical positions of the center of gravity (CG) at takeoff and touchdown. Improved velocity and position of the CG at takeoff resulted from a 33% increase in the work done by the body. This increase in work in free arm jumps compared to restricted arm jumps was found in both upper and lower body joints with the largest improvements (>30 J) occurring at the lower back, right hip, and right shoulder.     

A preliminary investigation into the relationship between functional movement screen scores and athletic physical performance in female team sport athletes

There is little research investigating relationships between the Functional Movement Screen (FMS) and athletic performance in female athletes. This study analyzed the relationships between FMS (deep squat; hurdle step [HS]; in-line lunge [ILL]; shoulder mobility; active straight-leg raise [ASLR]; trunk stability push-up; rotary stability) scores, and performance tests (bilateral and unilateral sit-and-reach [flexibility]; 20-m sprint [linear speed]; 505 with turns from each leg; modified T-test with movement to left and right [change-of-direction speed]; bilateral and unilateral vertical and standing broad jumps; lateral jumps [leg power]). Nine healthy female recreational team sport athletes (age = 22.67 ± 5.12 years; height = 1.66 ± 0.05 m; body mass = 64.22 ± 4.44 kilograms) were screened in the FMS and completed the afore-mentioned tests. Percentage between-leg differences in unilateral sit-and-reach, 505 turns and the jumps, and difference between the T-test conditions, were also calculated. Spearman''s correlations (p ≤ 0.05) examined relationships between the FMS and performance tests. Stepwise multiple regressions (p ≤ 0.05) were conducted for the performance tests to determine FMS predictors. Unilateral sit-and-reach positive correlated with the left-leg ASLR (r = 0.704-0.725). However, higher-scoring HS, ILL, and ASLR related to poorer 505 and T-test performance (r = 0.722-0.829). A higher-scored left-leg ASLR related to a poorer unilateral vertical and standing broad jump, which were the only significant relationships for jump performance. Predictive data tended to confirm the correlations. The results suggest limitations in using the FMS to identify movement deficiencies that could negatively impact athletic performance in female team sport athletes.     

Lower-body power,linear speed,and change-of-direction speed in Division I collegiate women’s volleyball players

Volleyball players need to sprint and change direction during a match. Lower-body power, often measured by jump tests, could contribute to faster movements. How different jumps relate to linear and change-of-direction (COD) speed has not been analyzed in Division I (DI) collegiate women’s volleyball players. Fifteen female volleyball players completed the vertical jump (VJ), two-step approach jump (AppJ), and standing broad jump (SBJ). Peak power and power-to-body mass ratio (P:BM) were derived from VJ and AppJ height; relative SBJ was derived from SBJ distance. Linear speed was measured via a 20-m sprint (0–10 and 0–20 m intervals); COD speed was measured using the pro-agility shuttle. Pearson’s correlations (p < 0.05) calculated relationships between the power variables, and speed tests. There were no significant relationships between the power variables and the 0–10 m sprint interval. Greater VJ height (r = -0.534) and P:BM (r = -0.557) related to a faster 0–20 m sprint interval. This be due to a greater emphasis on the stretch-shortening cycle to generate speed over 20 m. However, although a 20-m sprint may provide a measure of general athleticism, the distance may not be specific to volleyball. This was also indicated as the AppJ did not relate to any of the speed tests. Nonetheless, VJ height and P:BM, and SBJ distance and relative SBJ, all negatively correlated with the proagility shuttle (r = -0.548 to -0.729). DI women’s collegiate volleyball players could develop absolute and relative power in the vertical and horizontal planes to enhance COD speed.     

Effect of forward trunk inclination on joint power output in vertical jumping

It is commonly accepted that vertical jump performance is a good indicator of maximal joint power. Some studies, however, have indicated that knee joint power output in the vertical jump is limited due to forward trunk inclination early in the push-off. The aim of this experimental study was to investigate the effect of forward trunk inclination on joint power output in vertical jumping. A group of 20 male subjects performed maximal vertical countermovement jumps from stance while minimizing the contribution of arm swing by holding their hands on their hips (arms akimbo). They also performed maximal jumps while holding the trunk as upright as possible throughout the jump, still holding the arms akimbo. Jump height, joint kinematics (angles), and joint kinetics (torque, power) were calculated. Jump height of vertical jumps while holding the trunk upright was 10% less than in normal jumps. Hip joint power was decreased by 37% while knee joint power was increased by 13%. Ankle joint power did not change. These results demonstrated that maximal jump performance does not necessarily represent maximal power of each individual joint. The implication is that jump performance may well be a good representation of overall joint power; it is, however, not an accurate measure to evaluate maximal individual joint power as part of contemporary training and rehabilitation methods.     

Dependence of jumping performance on muscle properties when humans use only calf muscles for propulsion

Using optimal control techniques, maximum height jumps were simulated for humans who held their body rigid except for the ankle. Three dynamic models of ankle torque generation based on known calf muscle properties were used. Force and kinematics obtained from the simulations using nominal and perturbed parameters were compared with data obtained from humans who had performed this type of jump. One torque model incorporated the series elastic, force-length and force-velocity properties of muscle. Our results suggest that higher jumps would be achieved by those who have the most compliant and fastest contracting muscles. It was also found that height attained depended much more on the ability of muscles to generate isometric force at long lengths than at short lengths. Studies of forward and strictly vertical jumps using similar computer methods suggest that for any maximal jump the optimal strategy is first to achieve a unique state (position, velocity and acceleration) with the feet flat on the ground, and then to maximally activate one's calf muscles until lift-off.     

ASSESSMENT OF EXTERNAL AND INTERNAL LOADS IN THE TRIPLE JUMP VIA INVERSE DYNAMICS SIMULATION

The triple jump is a demanding athletics event that, after an approach run, consists of three consecutive phases: the hop, the bound, and the jump. During the involved three take-off actions a jumper is exposed to increased risk of injury due to the high impact forces from the ground and powerful muscle/tendon efforts, which are further reflected in the internal loads of the lower limb joints. While external ground reactions can possibly be measured using force platforms, in vivo measurements of the internal loads are practically not feasible. The purpose of the paper is to present the development of an effective formulation for the inverse dynamics simulation of the triple jump, based on the jumper dynamical model and non-invasive kinematic recordings of the movement. The developed simulation model serves for the analysis of all the triple jump phases, irrespective of whether the jumper is in flight or in contact with the ground with one of his feet, and is focused on effective assessment of the external reactions on the supporting leg as well as the muscle forces and joint reaction forces in the leg. Some numerical results of inverse dynamics simulation of the triple jump are reported.     

基于相关系数的水文序列跳跃变异分级原理与方法

跳跃变异是环境变化影响下水文过程发生急剧变化的一种重要表现形式,体现了水文非线性系统对外界干扰的响应.目前研究主要是对序列跳跃变异发生的时间、次数等进行识别和检验,但缺乏对其变异程度进行定量描述和分级,给开展流域环境变化研究及其影响评价带来很大困难.本文选取相关系数作为基础指标,提出了一种理论严密且便于应用的水文序列跳跃变异分级方法,并利用统计试验验证了文中方法对变异点显著性的检验精度,以及跳跃变异分级原理的合理性和分级方法的可靠性.经推导相关系数与跳跃变异相对幅度的关系,选取不同显著水平下的若干典型相关系数值作为分级阈值,将跳跃变异程度划分为无变异、弱变异、中变异、强变异、巨变异5个等级.通过应用于分析我国不同气候区的5个实测水文序列,结合物理成因分析验证了该方法的实用性.     

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.     

Understanding how an arm swing enhances performance in the vertical jump

This investigation was conducted to examine the various theories that have been proposed to explain the enhancement of jumping performance when using an arm swing compared to when no arm swing is used. Twenty adult males were asked to perform a series of maximal vertical jumps while using an arm swing and again while holding their arms by their sides. Force, motion and electromyographical data were recorded during each performance. Participants jumped higher (0.086 m) in the arm swing compared to the no-arm swing condition and was due to increased height (28%) and velocity (72%) of the center of mass at take-off. The increased height at take-off was due to the elevation of the arm segments. The increased velocity of take-off stemmed from a complex series of events which allowed the arms to build up energy early in the jump and transfer it to the rest of the body during the later stages of the jump. This energy came from the shoulder and elbow joints as well as from extra work done at the hip. This energy was used to (i) increase the kinetic and potential energy of the arms at take-off, (ii) store and release energy from the muscles and tendons around the ankle, knee and hip joint, and (iii) ‘pull’ on the body through an upward force acting on the trunk at the shoulder. It was concluded that none of the prevailing theories exclusively explains the enhanced performance in the arm swing jump, but rather the enhanced performance is based on several mechanisms operating together.     

The jump as a fast mode of locomotion in arboreal and terrestrial biotopes

The jump is always used for locomotion. For its execution in arboreal and terrestrial biotopes the requirements are of somewhat different nature. In an arboreal biotope the jump is characterized by a rapid progression through discontinuous substrates and the ability to take off from a small area and a secure landing on a spot. This requires well coordinated movements in all phases of the jump. On the ground, the jump is less frequent and often used for crossing obstacles or gaps. In primates both variants can be observed. In order to relate the details of locomotor behaviour to a certain environment, the biomechanics of jumping are analyzed in five primate species: The three mainly arboreal prosimian species Galago moholi, the smallest and most specialized leaper of all, Galago garnettii, a medium-sized bushbaby with some capacities for jumping, and Lemur catta also with some abilities to jump. The two simian species, Macaca fuscata and Homo sapiens, are usually terrestrial and have good jumping capacities, although not in terms of quantity. The investigation is based on high-speed motion analyses (100-500 frames/second) and the synchronized records of a force-plate from which all subjects had to jump off. On the basis of the results two kinds of jumping can be distinguished: standing and running jumps. The three prosimian species perform standing jumps. Dorsiflexion of their tails compensates ventrally oriented rotational moments of the trunk during body extension at take-off. The upward arm swing yields an overall increase in take-off velocity without additional muscular force exerted by the legs. The main difference among the species are the high relative forces in the small Galago moholi (up to 13 times body weight) as compared to the larger G. garnettii (8.5 times body weight) and the even larger Lemur catta (4.5 times body weight). In Homo sapiens the standing jump is characterized by an extensive arm swing backward, which is then followed by a forward and upward movement. The velocity at take-off is much smaller if compared to the prosimians. The running jump in Macaca fuscata is always preceded by at least one gallop cycle. The body assumes a ball shape at the beginning of the actual take-off. This is advantageous for rotating the body into a position in which the trunk axis is in line with the direction of movement. The tail of the Japanese macaque is too short to compensate the trunk's lift exerted on the hip region by the extending hindlimbs.(ABSTRACT TRUNCATED AT 400 WORDS)     

Optimal harvesting of a logistic population in an environment with stochastic jumps

Dynamic programming is employed to examine the effects of large, sudden changes in population size on the optimal harvest strategy of an exploited resource population. These changes are either adverse or favorable and are assumed to occur at times of events of a Poisson process. The amplitude of these jumps is assumed to be density independent. In between the jumps the population is assumed to grow logistically. The Bellman equation for the optimal discounted present value is solved numerically and the optimal feedback control computed for the random jump model. The results are compared to the corresponding results for the quasi-deterministic approximation. In addition, the sensitivity of the results to the discount rate, the total jump rate and the quadratic cost factor is investigated. The optimal results are most strongly sensitive to the rate of stochastic jumps and to the quadratic cost factor to a lesser extent when the deterministic bioeconomic parameters are taken from aggregate antarctic pelagic whaling data.Research supported in part by the National Science Foundation under grants MCS 81-01698 and MCS 83-00562.     

A deterministic model of the vertical jump: implications for training

Increasing vertical jump height is a critical component for performance enhancement in many sports. It takes on a number of different forms and conditions, including double and single legged jumps and stationary and run-up jumps. In an attempt to understand the factors that influence vertical jump performance, an extensive analysis was undertaken using the deterministic model. Once identified, practical training strategies enabling improvement in these factors were elucidated. Our analysis showed that a successful vertical jump performance was the result of a complex interplay of run-up speed, reactive strength, concentric action power of the take-off leg(s), hip flexors, shoulders, body position, body mass, and take-off time. Of special interest, our analysis showed that the concentric action power of the legs was the critical factor affecting stationary double leg vertical jumps, whereas reactive strength was the critical component for a single leg jump from a run-up.     

Optimal control simulations reveal mechanisms by which arm movement improves standing long jump performance

Optimal control simulations of the standing long jump were developed to gain insight into the mechanisms of enhanced performance due to arm motion. The activations that maximize standing long jump distance of a joint torque actuated model were determined for jumps with free and restricted arm movement. The simulated jump distance was 40 cm greater when arm movement was free (2.00 m) than when it was restricted (1.60 m). The majority of the performance improvement in the free arm jump was due to the 15% increase (3.30 vs. 2.86 m/s) in the take-off velocity of the center of gravity. Some of the performance improvement in the free arm jump was attributable to the ability of the jumper to swing the arms backwards during the flight phase to alleviate excessive forward rotation and position the body segments properly for landing. In restricted arm jumps, the excessive forward rotation was avoided by "holding back" during the propulsive phase and reducing the activation levels of the ankle, knee, and hip joint torque actuators. In addition, swinging the arm segments allowed the lower body joint torque actuators to perform 26 J more work in the free arm jump. However, the most significant contribution to developing greater take-off velocity came from the additional 80 J work done by the shoulder actuator in the jump with free arm movement.     

Biological Jumping Mechanism Analysis and Modeling for Frog Robot

This paper presents a mechanical model of jumping robot based on the biological mechanism analysis of frog. By biological observation and kinematic analysis the frog jump is divided into take-offphase, aerial phase and landing phase. We find the similar trajectories of hindlimb joints during jump, the important effect of foot during take-off and the role of forelimb in supporting the body. Based on the observation, the frog jump is simplified and a mechanical model is put forward. The robot leg is represented by a 4-bar spring/linkage mechanism model, which has three Degrees of Freedom （DOF） at hip joint and one DOF （passive） at tarsometatarsal joint on the foot. The shoulder and elbow joints each has one DOF for the balancing function of arm. The ground reaction force of the model is analyzed and compared with that of frog during take-off. The results show that the model has the same advantages of low likelihood of premature lift-off and high efficiency as the frog. Analysis results and the model can be employed to develop and control a robot capable of mimicking the jumping behavior of frog.     

Effects of sprint and plyometric training on muscle function and athletic performance

The purpose of this study was to evaluate the effects of sprint training on muscle function and dynamic athletic performance and to compare them with the training effects induced by standard plyometric training. Male physical education students were assigned randomly to 1 of 3 groups: sprint group (SG; n = 30), plyometric group (PG; n = 30), or control group (CG; n = 33). Maximal isometric squat strength, squat- and countermovement jump (SJ and CMJ) height and power, drop jump performance from 30-cm height, and 3 athletic performance tests (standing long jump, 20-m sprint, and 20-yard shuttle run) were measured prior to and after 10 weeks of training. Both experimental groups trained 3 days a week; SG performed maximal sprints over distances of 10-50 m, whereas PG performed bounce-type hurdle jumps and drop jumps. Participants in the CG group maintained their daily physical activities for the duration of the study. Both SG and PG significantly improved drop jump performance (15.6 and 14.2%), SJ and CMJ height ( approximately 10 and 6%), and standing long jump distance (3.2 and 2.8%), whereas the respective effect sizes (ES) were moderate to high and ranged between 0.4 and 1.1. In addition, SG also improved isometric squat strength (10%; ES = 0.4) and SJ and CMJ power (4%; ES = 0.4, and 7%; ES = 0.4), as well as sprint (3.1%; ES = 0.9) and agility (4.3%; ES = 1.1) performance. We conclude that short-term sprint training produces similar or even greater training effects in muscle function and athletic performance than does conventional plyometric training. This study provides support for the use of sprint training as an applicable training method of improving explosive performance of athletes in general.