Prediction of ground reaction forces and moments during sports-related movements


When performing inverse dynamic analysis (IDA) of musculoskeletal models to study human motion, inaccuracies in experimental input data and a mismatch between the model and subject lead to dynamic inconsistency. By predicting the ground reaction forces and moments (GRF&Ms) this inconsistency can be reduced and force plate measurements become unnecessary. In this study, a method for predicting GRF&Ms was validated for an array of sports-related movements. The method was applied to ten healthy subjects performing, for example, running, a side-cut manoeuvre, and vertical jump. Pearson’s correlation coefficient (\(r\)) and root-mean-square deviation were used to compare the predicted GRF&Ms and associated joint kinetics to the traditional IDA approach, where the GRF&Ms were measured using force plates. The main findings were that the method provided estimates comparable to traditional IDA across all movements for vertical GRFs (\(r\) ranging from 0.97 to 0.99, median 0.99), joint flexion moments (\(r\) ranging from 0.79 to 0.98, median 0.93), and resultant joint reaction forces (\(r\) ranging from 0.78 to 0.99, median 0.97). Considering these results, this method can be used instead of force plate measurements, hereby, facilitating IDA in sports science research and enabling complete IDA using motion analysis systems that do not incorporate force plate data.

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Inverse dynamic analysis


Ground reaction forces and moments


Acceleration from a standing position


AnyBody Modeling System




Ground reaction force


Ground reaction moment


Ankle flexion moment


Ankle subtalar eversion moment


Knee flexion moment


Hip flexion moment


Hip abduction moment


Hip external rotation moment


Joint reaction force

\(r\) :

Pearson’s correlation coefficient


Root-mean-square deviation


Right leg


Left leg


  1. 1.

    Zajac, F.E., Neptune, R.R., Kautz, S.A.: Biomechanics and muscle coordination of human walking: Part I: Introduction to concepts, power transfer, dynamics and simulations. Gait Posture 16(3), 215–232 (2002)

    Article  Google Scholar 

  2. 2.

    Rasmussen, J., Damsgaard, M., Surma, E., Christensen, S.T., de Zee, M., Vondrak, V.: Anybody-a software system for ergonomic optimization. In: Abstracts of the Fifth World Congress on Structural and Multidisciplinary Optimization, Lido di Jesolo, Venice, Italy, 19–23 May 2003

  3. 3.

    Mellon, S.J., Grammatopoulos, G., Andersen, M.S., Pandit, H.G., Gill, H.S., Murray, D.W.: Optimal acetabular component orientation estimated using edge-loading and impingement risk in patients with metal-on-metal hip resurfacing arthroplasty. J. Biomech. 48(2), 318–323 (2015)

    Article  Google Scholar 

  4. 4.

    Payton, C., Bartlett, R.: Biomechanical Evaluation of Movement in Sport and Exercise: The British Association of Sport and Exercise Sciences Guide. Routledge, Abingdon (2007)

    Google Scholar 

  5. 5.

    Thelen, D.G., Anderson, F.C.: Using computed muscle control to generate forward dynamic simulations of human walking from experimental data. J. Biomech. 39(6), 1107–1115 (2006)

    Article  Google Scholar 

  6. 6.

    Barrett, R.S., Besier, T.F., Lloyd, D.G.: Individual muscle contributions to the swing phase of gait: an EMG-based forward dynamics modelling approach. Simul. Model. Pract. Theory 15(9), 1146–1155 (2007)

    Article  Google Scholar 

  7. 7.

    Anderson, F.C., Pandy, M.G.: Dynamic optimization of human walking. J. Biomech. Eng. 123(5), 381–390 (2001)

    Article  Google Scholar 

  8. 8.

    Damsgaard, M., Rasmussen, J., Christensen, S.T., Surma, E., de Zee, M.: Analysis of musculoskeletal systems in the AnyBody Modeling System. Simul. Model. Pract. Theory 14(8), 1100–1111 (2006)

    Article  Google Scholar 

  9. 9.

    Rasmussen, J., Damsgaard, M., Voigt, M.: Muscle recruitment by the min/max criterion—a comparative numerical study. J. Biomech. 34(3), 409–415 (2001)

    Article  Google Scholar 

  10. 10.

    Andersen, M.S., Damsgaard, M., Rasmussen, J.: Kinematic analysis of over-determinate biomechanical systems. Comput. Methods Biomech. Biomed. Eng. 12(4), 371–384 (2009)

    Article  Google Scholar 

  11. 11.

    Psycharakis, S.G., Miller, S.: Estimation of errors in force platform data. Res. Q. Exerc. Sport 77(4), 514–518 (2006)

    Article  Google Scholar 

  12. 12.

    Klein Horsman, M.D., Koopman, H.F.J.M., Van der Helm, F.C.T., Prosé, L.P., Veeger, H.E.J.: Morphological muscle and joint parameters for musculoskeletal modelling of the lower extremity. Clin. Biomech. 22(2), 239–247 (2007)

    Article  Google Scholar 

  13. 13.

    Lund, M.E., Andersen, M.S., de Zee, M., Rasmussen, J.: Scaling of musculoskeletal models from static and dynamic trials. Int. J. Sport Biomech. 2(1), 1–11 (2015)

    Article  Google Scholar 

  14. 14.

    Pàmies-Vila, R., Font-Llagunes, J.M., Cuadrado, J., Javier Alonso, F.: Analysis of different uncertainties in the inverse dynamic analysis of human gait. Mech. Mach. Theory 58, 153–164 (2012)

    Article  Google Scholar 

  15. 15.

    Riemer, R., Hsiao-Wecksler, E.T., Zhang, X.: Uncertainties in inverse dynamics solutions: a comprehensive analysis and an application to gait. Gait Posture 27(4), 578–588 (2008)

    Article  Google Scholar 

  16. 16.

    Hatze, H.: The fundamental problem of myoskeletal inverse dynamics and its implications. J. Biomech. 35(1), 109–115 (2002)

    Article  Google Scholar 

  17. 17.

    Cahouët, V., Luc, M., David, A.: Static optimal estimation of joint accelerations for inverse dynamics problem solution. J. Biomech. 35(11), 1507–1513 (2002)

    Article  Google Scholar 

  18. 18.

    Kuo, A.D.: A least-squares estimation approach to improving the precision of inverse dynamics computations. J. Biomech. Eng. 120(1), 148–159 (1998)

    Article  Google Scholar 

  19. 19.

    Fluit, R., Andersen, M.S., Kolk, S., Verdonschot, N., Koopman, H.: Prediction of ground reaction forces and moments during various activities of daily living. J. Biomech. 47(10), 2321–2329 (2014)

    Article  Google Scholar 

  20. 20.

    Riemer, R., Hsiao-Wecksler, E.T.: Improving joint torque calculations: optimization-based inverse dynamics to reduce the effect of motion errors. J. Biomech. 41(7), 1503–1509 (2008)

    Article  Google Scholar 

  21. 21.

    Audu, M.L., Kirsch, R.F., Triolo, R.J.: Experimental verification of a computational technique for determining ground reactions in human bipedal stance. J. Biomech. 40(5), 1115–1124 (2007)

    Article  Google Scholar 

  22. 22.

    Choi, A., Lee, J.-M., Mun, J.H.: Ground reaction forces predicted by using artificial neural network during asymmetric movements. Int. J. Precis. Eng. Manuf. 14(3), 475–483 (2013)

    Article  Google Scholar 

  23. 23.

    Robert, T., Causse, J., Monnier, G.: Estimation of external contact loads using an inverse dynamics and optimization approach: general method and application to sit-to-stand maneuvers. J. Biomech. 46(13), 2220–2227 (2013)

    Article  Google Scholar 

  24. 24.

    Ren, L., Jones, R.K., Howard, D.: Whole body inverse dynamics over a complete gait cycle based only on measured kinematics. J. Biomech. 41(12), 2750–2759 (2008)

    Article  Google Scholar 

  25. 25.

    Lugrís, U., Carlín, J., Pàmies-Vilà, R., Font-Llagunes, M., Cuadrado, J.: Solution methods for the double-support indeterminacy in human gait. Multibody Syst. Dyn. 30(3), 247–263 (2013)

    MathSciNet  Article  Google Scholar 

  26. 26.

    Jackson, J.N., Hass, C.J., Fregly, B.J.: Development of a subject-specific foot-ground contact model for walking. J. Biomech. Eng. 138(9), 091002 (2016)

    Article  Google Scholar 

  27. 27.

    Challis, J.H.: The variability in running gait caused by force plate targeting. J. Appl. Biomech. 17(1), 77–83 (2001)

    Article  Google Scholar 

  28. 28.

    De Zee, M., Hansen, L., Wong, C., Rasmussen, J., Simonsen, E.B.: A generic detailed rigid-body lumbar spine model. J. Biomech. 40(6), 1219–1227 (2007)

    Article  Google Scholar 

  29. 29.

    Veeger, H.E.J., Van der Helm, F.C.T., Van der Woude, L.H.V., Pronk, G.M., Rozendal, R.H.: Inertia and muscle contraction parameters for musculoskeletal modelling of the shoulder mechanism. J. Biomech. 24(7), 615–629 (1991)

    Article  Google Scholar 

  30. 30.

    Veeger, H.E.J., Yu, B., An, K.-N., Rozendal, R.H.: Parameters for modeling the upper extremity. J. Biomech. 30(6), 647–652 (1997)

    Article  Google Scholar 

  31. 31.

    Van der Helm, F.C., Veeger, H., Pronk, G., Van der Woude, L., Rozendal, R.: Geometry parameters for musculoskeletal modelling of the shoulder system. J. Biomech. 25(2), 129–144 (1992)

    Article  Google Scholar 

  32. 32.

    Rasmussen, J., de Zee, M., Damsgaard, M., Christensen, S.T., Marek, C., Siebertz, K.: A general method for scaling musculo-skeletal models. Paper presented at the 10th International Symposium on Computer Simulation in Biomechanics, Case Western Reserve University, Cleveland, USA, 28–30 July 2005

  33. 33.

    Winter, D.A.: Biomechanics and Motor Control of Human Movement, 4th edn. John Wiley & Sons, Hoboken (2009)

    Google Scholar 

  34. 34.

    Frankenfield, D.C., Rowe, W.A., Cooney, R.N., Smith, J.S., Becker, D.: Limits of body mass index to detect obesity and predict body composition. Nutrition 17(1), 26–30 (2001)

    Article  Google Scholar 

  35. 35.

    Andersen, M.S., Damsgaard, M., MacWilliams, B., Rasmussen, J.: A computationally efficient optimisation-based method for parameter identification of kinematically determinate and over-determinate biomechanical systems. Comput. Methods Biomech. Biomed. Eng. 13(2), 171–183 (2010)

    Article  Google Scholar 

  36. 36.

    Taylor, R.: Interpretation of the correlation coefficient: a basic review. J. Diagn. Med. Sonog. 6(1), 35–39 (1990)

    Article  Google Scholar 

  37. 37.

    Marra, M.A., Vanheule, V., Fluit, R., Koopman, B.H., Rasmussen, J., Verdonschot, N., Andersen, M.S.: A subject-specific musculoskeletal modeling framework to predict in vivo mechanics of total knee arthroplasty. J. Biomech. Eng. 137(2), 020904 (2015)

    Article  Google Scholar 

  38. 38.

    Leardini, A., Chiari, L., Della Croce, U., Cappozzo, A.: Human movement analysis using stereophotogrammetry: Part 3. Soft tissue artifact assessment and compensation. Gait Posture 21(2), 212–225 (2005)

    Article  Google Scholar 

  39. 39.

    Benoit, D.L., Damsgaard, M., Andersen, M.S.: Surface marker cluster translation, rotation, scaling and deformation: their contribution to soft tissue artefact and impact on knee joint kinematics. J. Biomech. 48(10), 2124–2129 (2015)

    Article  Google Scholar 

  40. 40.

    Roetenberg, D., Luinge, H., Slycke, P.: Xsens MVN: full 6DOF human motion tracking using miniature inertial sensors. Xsens Motion Technologies BV. Tech. Rep. (2009)

  41. 41.

    Sandau, M., Koblauch, H., Moeslund, T.B., Aanæs, H., Alkjær, T., Simonsen, E.B.: Markerless motion capture can provide reliable 3D gait kinematics in the sagittal and frontal plane. Med. Eng. Phys. 36(9), 1168–1175 (2014)

    Article  Google Scholar 

  42. 42.

    Skals, S., Rasmussen, K., Bendtsen, K., Andersen, M.S.: Validation of musculoskeletal models driven by dual Microsoft Kinect Sensor data. In: Abstracts of the 13th International Symposium on 3D Analysis of Human Movement, Lausanne, Switzerland, 14–17 July 2014

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This work received funding from the Danish Council for Independent Research under grant number DFF-4184-00018 to M.S. Andersen and from the European Union’s Seventh Framework Programme (FP7/2007–2013) under the LifeLongJoints Project, Grant Agreement no. GA-310477 to M. Jung and M. Damsgaard.

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Correspondence to Michael S. Andersen.

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M. Damsgaard is the head of development, minority shareholder, and member of the board of directors of AnyBody Technology A/S that owns and sells the AnyBody Modeling System.

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Skals, S., Jung, M.K., Damsgaard, M. et al. Prediction of ground reaction forces and moments during sports-related movements. Multibody Syst Dyn 39, 175–195 (2017).

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  • Musculoskeletal model
  • Inverse dynamics
  • Sports science
  • AnyBody Modeling System
  • Force plates