Estimation of joint forces and moments for the in-run and take-off in ski jumping based on measurements with wearable inertial sensors

Abstract

This study uses inertial sensors to measure ski jumper kinematics and joint dynamics, which was until now only a part of simulation studies. For subsequent calculation of dynamics in the joints, a link-segment model was developed. The model relies on the recursive Newton-Euler inverse dynamics. This approach allowed the calculation of the ground reaction force at take-off. For the model validation, four ski jumpers from the National Nordic center performed a simulated jump in a laboratory environment on a force platform; 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-square errors. The error is under 12% of the reference value. For field tests, six jumpers participated in the study; in total, 28 jumps were recorded. All of the measured forces and moments were within the range of prior simulated studies. The proposed system was able to indirectly provide 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 to the force platform installed on the table. Kinematics assessment and estimation of dynamics parameters can be applied to jumps from any ski jumping hill.

Keywords: Newton–Euler inverse dynamics; force; moments; ski-jumping; wearable inertial sensors.

Figure 1

Wearable measurement system composed of 10 inertial measurement units and the setup for positioning the units on the jumper.

Figure 2

Data flow for measurement data processing. (A1) The acceleration and angular velocity of each IMU are obtained; (A2) The ski jumpers anthropometric data and equipment are measured; (A3) Measuring ground reaction force (GRF) from a force platform; (B1) Kinematic and (B2) anthropometric parameter calculation; (C1) The ski jumper link-segment model calculation.

Figure 3

Recursive Newton–Euler inverse dynamics model of a ski jumper. The basic idea of the recursive approach is to first calculate variables for segment i, then calculate the unknown joint variables i + 1 and, in the next step, proceed with the calculation.

Figure 4

A comparison of the mean with the standard deviation of the calculated forces (a–c) and moments (d–f) in the joints according to the bottom-up, top-down and top-down-up methods during the laboratory experiment.

Figure 5

A comparison of the mean with the standard deviation of the calculated ground reaction force by the top-down-up method and the measured force with a force platform during the laboratory experiment.

Figure 6

RMSE and calculated deviation for joint forces, GRF and joint moments for top-down-up and top-down inverse dynamics based on the reference value. Measurements were performed in the laboratory on a force platform. The middle line, the bottom and the top of the box present the median, 25th and 75th percentiles, respectively. The whiskers present the furthermost value in the 1.5 interquartile ranges.

Figure 7

A comparison of the calculated forces and moments in the joints according to the top-down-up method during a ski jumping training session. The values represent one jump.

Figure 8

Comparison of the mean with the standard deviation of the calculated GRF and measured force with the built-in force platform according to the top-down-up method during the outdoor experiment.

Figure 9

RMSE and calculated deviation of GRF for the top-down-up inverse dynamics based on the reference value. Measurements were performed during the outdoor experiment on the ski hill. The middle line, the bottom and the top of the box present the median, 25th and 75th percentiles, respectively. The whiskers present the furthermost value in the 1.5 interquartile ranges.