Subject: ScienceDirect - Journal of Biomechanics : Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps

 doi:10.1016/j.jbiomech.2004.08.023      

Copyright © 2004 Elsevier Ltd All rights reserved.

Optimal compliant-surface jumping:  a multi-segment model of springboard standing jumps

Kuangyou B. Cheng and Mont Hubbard

Sports Biomechanics Laboratory, Department of Mechanical and Aeronautical Engineering, University of California, Davis, CA 95616, USA

Accepted 22 August 2004.  Available online 13 November 2004. 

Abstract

A multi-segment model is used to investigate optimal compliant-surface  jumping  strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk–head–arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle,  knee,  and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard  jumping  simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface  jumping  where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface  jumping.  The fulcrum–height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models’ prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.

Keywords: Optimization;  Jumping ; Surface compliance; Muscular activation; Diving

Article Outline

1. Introduction

2. Materials and methods

3. Results

4. Discussion

5. Conclusions

Appendix

References