Volume 10 Issue 7 - September 18, 2009 PDF
The mechanisms that enable arm motion to enhance vertical jump performance—A simulation study
Kuangyou B. Cheng*, Chih-Hung Wang, Hui-Chuan Chen, Chin-Dai Wu, and Hung-Ta Chiu

Institute of Physical Education, Health & Leisure Studies, College of Management, National Cheng Kung University
* kybcheng@mail.ncku.edu.tw

Journal of Biomechanics 2008, 41 (9), 1847-1854

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Although numerous studies have reported increased height with arm swing in standing vertical jumps, contradictory results have also been reported. Knee joint torque/work was found to decrease [1][2] or increase [3] in arm swing jumps. Increase in ankle joint torque/work was substantial in most studies but insignificant in some other researches [3][4]. This inconsistency may be due to different training or proficiency levels of the subjects, but these proficiency-related factors are difficult to control in experimental studies. Moreover, errors in data recording and smoothing are inevitable. The purpose of this study is to investigate the mechanisms which enhance vertical jumping performance by arm motion. Forward simulation without the disadvantages (e.g. errors in data recording or subject skill/psychological factors) in actual experiments is employed for the present study.

Two planar human body models with 4 and 5 segments (4S and 5S, respectively) are used to simulate the standing vertical jumping from a static initial posture to takeoff. Body segments are connected by frictionless hinge joints. Segments represent the feet, shanks, thighs, and head-arms-trunk (HAT) in model 4S. In model 5S the HAT is partitioned into head-trunk (HT) and arms with fixed elbow joint [1]. Torque T generated at each joint is assumed to be the product of three functions: T = Tmax(θ)h(ω)A(t). Here Tmax(θ) depending on joint angle is the maximum isometric torque for both extremities. Joint angular velocity the dependence is modeled by h(ω). Hence the model preserves features of muscle force production depending on maximum isometric force, muscle length, and shortening velocity. The coordination strategy is characterized by activation level A(t) which corresponds to the effective activation of muscles across the joint.

The objective is to optimize A(t) such that jump height J0 = (yf + vf2/2g) is maximized. Here yf and vf are center of mass (CM) vertical position and velocity at the takeoff instant because jump height is purely determined by the 2 variables. The optimization is subject to constraints such as the takeoff condition which requires zero ground reaction force (GRF) calculated with simulated CM acceleration. To prevent joint hyperextension, joint ranges of motion are also constrained. In addition, a rotational spring-damper system generating exponentially increasing passive torque is applied at the toe joint to prevent the heel from penetrating the ground [5].

Simulated jumps with arms (5S) and without arms (4S) are compared (Table 1 and Fig. 1). With arm motion height is increased by 0.091 m. About 62% of the height increase is due to increased vertical velocity at takeoff, and 38% is from higher CM position (due to raised arms). Although movements start from squat postures, minor joint flexion (countermovement) still occurs prior to upward extension. Arm motion results in longer contact duration and greater total work done (Table 1). The duration in which hip angular velocity starts to increase is about 0.11s longer in 5S.
Table 1  Features of simulated jumps with (5S) and without (4S) arm motion
Fig. 1  Simulated stick diagrams vs. time. Takeoff time is set at 0.

The expected pattern of relaxation followed by maximal extension (A(t) = 1) is observed in all joints in both jumps (Fig. 2). In the 4S jump the knee starts to relax first and also activates first, followed by hip and ankle activation. In the 5S jump the shoulder relaxes first but the actual activation starts in the sequence of hip, shoulder, knee, and ankle. Except the shoulder, joint torques decrease to about zero at takeoff.
Fig. 2  Joint torque/activation in 4S (left) and 5S (right) jumps. Each torque is normalized by dividing by its maximum isometric value.

Different vertical GRF profiles are observed in jumps with and without arm motion (Fig. 3). In 5S jumps a small pulse (slight increase and decrease of force) exists before the GRF reaches its maximum. Two kinds of GRF patterns are obtained in searching for optimal 5S jumps. One involves shorter or nearly identical upward thrust duration compared to 4S jumps but with larger GRF before takeoff (5S, Fig. 3). The other pattern (5Sa) with slightly less jump height contains longer upward thrust duration but about the same maximum GRF compared to the 4S jump. The vertical component of the force applied to the arms at shoulder is mostly positive throughout ground contact, implying that the arms are pushed upward by the trunk for most of the time.

Fig. 3  Vertical GRF patterns in 4S and 5S jumps.
Substantial negative power (implying eccentric muscle contraction) prior to maximum power production is observed in almost all joints in 5S jumps. But in 4S jumps this is noticeable mainly in the knee and slightly in the hip. With arm swing joint work is 7% less in the ankle, 18% less in the knee, but 47% more in the hip compared to the no-arm jump (Table 1). Together with the additional shoulder joint work, total work production is 28% more in the 5S jump.

From the simulation results theories explaining the mechanisms enhancing jump performance by arms can be examined. The force transmission theory is doubtful because the change in vertical GRF does not exactly correspond to shoulder joint force caused by arm motion. The joint torque/work augmentation theory is acceptable only at the hip rather than the knee/ankle because only hip joint work is considerably increased. The pull/impart energy theory is also acceptable because shoulder joint work is responsible for about half of the additional energy created by arm swing.


  1. Ashby, B.M., Delp, S.L., 2006. Optimal control simulations reveal mechanisms by which arm movement improves standing long jump performance. Journal of Biomechanics 39, 1726-1734.
  2. Hara, M., Shibayama, A., Takeshita, D., Fukashiro, S., 2006. The effect of arm swing on lower extremities in vertical jumping. Journal of Biomechanics 39, 2503-2511.
  3. Feltner, M.E., Fraschetti, D.J., Crisp, R.J., 1999. Upper extremity augmentation of lower extremity kinetics during countermovement vertical jumps. Journal of Sports Sciences 17, 449-466.
  4. Lees, A., Vanrenterghem, J., Clercq, D.D., 2004. Understanding how an arm swing enhances performance in the vertical jump. Journal of Biomechanics 37, 1929–1940.
  5. Anderson, F.C., Pandy, M.G., 1999. A dynamic optimization solution for vertical jumping in three dimensions. Computer Methods in Biomechanics and Biomedical Engineering 2, 201-231.
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