Estimation of Joint Forces and Moments for the In-Run and Take-Off in Ski Jumping Based on Measurements with Wearable

Grega Logar * and Marko MunihFaculty of Electrical Engineering, University of Ljubljana, Tržaska cesta 25, 1000 Ljubljana, Slovenia;E-Mail: marko@robo.fe.uni-lj.si* Author to whom correspondence should be addressed; E-Mail: grega.logar@robo.fe.uni-lj.si;Tel.: +386-147-68-227; Fax: +386-147-68-239.Academic Editor: Oliver AmftReceived: 24 March 2015 / Accepted: 8 May 2015 / Published: 13 May 2015Abstract: This study uses inertial sensors to measure ski jumper kinematics and jointdynamics, which was until now only a part of simulation studies. For subsequent calculationof dynamics in the joints, a link-segment model was developed. The model relies on therecursive Newton–Euler inverse dynamics. This approach allowed the calculation of theground reaction force at take-off. For the model validation, four ski jumpers from theNational Nordic center performed a simulated jump in a laboratory environment on a forceplatform; in total, 20 jumps were recorded. The results fit well to the reference system,presenting small errors in the mean and standard deviation and small root-mean-squareerrors. The error is under 12% of the reference value. For field tests, six jumpers participatedin the study; in total, 28 jumps were recorded. All of the measured forces and moments werewithin the range of prior simulated studies. The proposed system was able to indirectlyprovide the values of forces and moments in the joints of the ski-jumpers’ body segments,as well as the ground reaction force during the in-run and take-off phases in comparison tothe force platform installed on the table. Kinematics assessment and estimation of dynamicsparameters can be applied to jumps from any ski jumping hill.Keywords: ski-jumping; force; moments; wearable inertial sensors; Newton–Eulerinverse dynamics