Planar vertical jumping simulation - A pilot study

Vertical jumping is one of the fundamental motions among other jumping types in sport biomechanics. Two important criteria in sport biomechanics are critical to all athletes: Injury and performance. In literature two major approaches have been investigated: experiment-based methods and optimization-based methods. Experiment-based methods are time consuming and tedious. Optimization-based methods for musculoskeletal models are computationally expensive because their models include all muscles and explicit integration of equation of motion. In this pilot study, a direct optimization-based method for a skeletal model was proposed in sagittal plane, where this formulation was based on joint space that was only considered the resultant results of muscles (joint torques) instead of individual muscles to reduce computational time. The cost function included increasing the center of mass velocity at take-off and increasing the center of mass position at take-off. Constraints included joint limits, torque limits, initial posture, ground contact, initial angular velocity and acceleration, zero-ground reaction forces, and moment at take-off. This optimization problem was solved by a commercial optimization solver SNOPT and the CPU time was 227 seconds on a regular PC (Intel® Core® 2 duo CPU, 3.16 GHZ and 3.25 GB RAM). Preliminary results highly correlated results from the literature. This simple planar simulation is the first step to understand the cause and effect for vertical jumping with or without arm swing.