Multibody System Dynamics

, Volume 46, Issue 1, pp 63–76 | Cite as

Subject-specific strength percentile determination for two-dimensional symmetric lifting considering dynamic joint strength

  • Yujiang XiangEmail author
  • Rahid Zaman
  • Ritwik Rakshit
  • James Yang


This paper describes an efficient optimization method for determining the subject-specific strength percentile and predicting the maximum weight lifting motion by considering dynamic joint strength in symmetric box lifting. Dynamic strength is modeled as a three-dimensional function of joint angle and joint angular velocity based on experimentally obtained joint strength data from the literature. The function is further formulated as the joint torque limit constraint in an inverse dynamics optimization formulation to predict the maximum weight lifting motion. The initial, mid-time, and final postures are obtained from experiments and imposed as tracking constraints in the optimization formulation. In addition, the box weight and time duration are given as inputs for the lifting optimization problem. The normalized joint torque squared is used as the objective function. Subject-specific strength percentile (\(z\_\mathrm{score}\)) is enumerated until the optimal solution is achieved. The determined strength percentile is a global score considering interactions of all joints for the two-dimensional symmetric lifting task. Results show that incorporating dynamic strength is critical in predicting lifting motion in extreme lifting conditions. The proposed algorithm can determine the subject-specific strength percentile based on experimental box lifting data. The accurate strength percentile is critical to predict strength related tasks to protect workers from injury.


Lifting Dynamic joint strength Strength percentile Maximum weight Inverse dynamics optimization Motion prediction Manual material handling 



This research is supported by projects from NSF (Award #1700865, 1849279, and 1703093).


  1. 1.
    Stockdale, A.A.: Modeling three-dimensional hip and trunk peak torque as a function of joint angle and velocity. Ph.D. thesis, Department of Biomedical Engineering, The University of Iowa, Iowa City, IA (2011) Google Scholar
  2. 2.
    Frey-Law, L.A., Laake, A., Avin, K.G., Heitsman, J., Marler, T., Abdel-Malek, K.: Knee and elbow 3D strength surfaces: peak torque-angle–velocity relationships. J. Appl. Biomech. 28(6), 726–737 (2012) CrossRefGoogle Scholar
  3. 3.
    Looft, J.M.: Adaptation and validation of an analytical localized muscle fatigue model for workplace tasks. Ph.D. thesis, Department of Biomedical Engineering, The University of Iowa, Iowa City, IA (2014) Google Scholar
  4. 4.
    Hussain, S.J., Frey-Law, L.A.: 3D strength surfaces for ankle plantar- and dorsi-flexion in healthy adults: an isometric and isokinetic dynamometry study. J. Foot Ankle Res. 9(43), 1–10 (2016) Google Scholar
  5. 5.
    Freivalds, A., Chaffin, D.B., Garg, A., Lee, K.S.: A dynamic biomechanical evaluation of lifting maximum acceptable loads. J. Biomech. 17(4), 251–262 (1984) CrossRefGoogle Scholar
  6. 6.
    Zhang, X., Nussbaum, M.A., Chaffin, D.B.: Back lift versus leg lift: an index and visualization of dynamic lifting strategies. J. Biomech. 33(6), 777–782 (2000) CrossRefGoogle Scholar
  7. 7.
    Ayoub, M.M.: Problems and solutions in manual materials handling—the state-of-the-art. Ergonomics 35(7–8), 713–728 (1992) CrossRefGoogle Scholar
  8. 8.
    Huang, C., Sheth, P.N., Granata, K.P.: Multibody dynamics integrated with muscle models and space–time constraints for optimization of lifting movements. In: ASME IDETC/CIE Conference, September 24–28, 2005, Long Beach, California (2005) Google Scholar
  9. 9.
    Arisumi, H., Chardonnet, J.R., Kheddar, A., Yokoi, K.: Dynamic lifting motion of humanoid robots. In: IEEE International Conference on Robotics and Automation, Roma, Italy, pp. 2661–2667 (2007) Google Scholar
  10. 10.
    Xiang, Y., Arora, J.S., Rahmatalla, S., Marler, T., Bhatt, R., Abdel-Malek, K.: Human lifting simulation using a multi-objective optimization approach. Multibody Syst. Dyn. 23(4), 431–451 (2010) MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Xiang, Y., Arora, J.S., Abdel-Malek, K.: 3D human lifting motion prediction with different performance measures. Int. J. Humanoid Robot. 9(02), 1250012 (2012) CrossRefGoogle Scholar
  12. 12.
    Song, J., Qu, X., Chen, C.H.: Simulation of lifting motions using a novel multi-objective optimization approach. Int. J. Ind. Ergon. 53, 37–47 (2016) CrossRefGoogle Scholar
  13. 13.
    Xiang, Y., Arora, J.S., Abdel-Malek, K.: Physics-based modeling and simulation of human walking: a review of optimization-based and other approaches. Struct. Multidiscip. Optim. 42(1), 1–23 (2010) MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    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) CrossRefGoogle Scholar
  15. 15.
    Shourijeh, M.S., McPhee, J.: Forward dynamic optimization of human gait simulations: a global parameterization approach. J. Comput. Nonlinear Dyn. 9, 031018 (2014) CrossRefGoogle Scholar
  16. 16.
    Fregly, B.J., Reinbolt, J.A., Rooney, K.L., Mitchell, K.H., Chmielewski, T.L.: Design of patient-specific gait modifications for knee osteoarthritis rehabilitation. IEEE Trans. Biomed. Eng. 54(9), 1687–1695 (2007) CrossRefGoogle Scholar
  17. 17.
    Ren, L., Jones, R.K., Howard, D.: Predictive modelling of human walking over a complete gait cycle. J. Biomech. 40(7), 1567–1574 (2007) CrossRefGoogle Scholar
  18. 18.
    Xiang, Y., Arora, J.S., Rahmatalla, S., Abdel-Malek, K.: Optimization-based dynamic human walking prediction: one step formulation. Int. J. Numer. Methods Eng. 79(6), 667–695 (2009) CrossRefzbMATHGoogle Scholar
  19. 19.
    Farahani, S.D., Andersen, M.S., de Zee, M., Rasmussen, J.: Optimization-based dynamic prediction of kinematic and kinetic patterns for a human vertical jump from a squatting position. Multibody Syst. Dyn. 36(1), 37–65 (2016) MathSciNetCrossRefGoogle Scholar
  20. 20.
    Arora, J.S., Wang, Q.: Review of formulations for structural and mechanical system optimization. Struct. Multidiscip. Optim. 30(4), 251–272 (2005) MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Ackermann, M., van den Bogert, A.J.: Optimality principles for model-based prediction of human gait. J. Biomech. 43(6), 1055–1060 (2010) CrossRefGoogle Scholar
  22. 22.
    Cahalan, T.D., Johnson, M.E., Liu, S., Chao, E.Y.: Quantitative measurements of hip strength in different age-groups. Clin. Orthop. Relat. Res. 246, 136–145 (1989) Google Scholar
  23. 23.
    Kumar, S.: Isolated planar trunk strengths measurement in normal: Part III—results and database. Int. J. Ind. Ergon. 17(2), 103–111 (1996) MathSciNetCrossRefGoogle Scholar
  24. 24.
    Farizeh, T., Sadigh, M.J.: A mathematical framework to study fast walking of human. Multibody Syst. Dyn. 40(2), 99–122 (2017) MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Denavit, J., Hartenberg, R.S.: A kinematic notation for lower-pair mechanisms based on matrices. ASME J. Appl. Mech. 22, 215–221 (1955) MathSciNetzbMATHGoogle Scholar
  26. 26.
    Xiang, Y., Arora, J.S., Abdel-Malek, K.: Optimization-based motion prediction of mechanical systems: sensitivity analysis. Struct. Multidiscip. Optim. 37(6), 595–608 (2009) MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Toogood, R.W.: Efficient robot inverse and direct dynamics algorithms using micro-computer based symbolic generation. IEEE Int. Conf. Robot. Autom. 3, 1827–1832 (1989) Google Scholar
  28. 28.
    Cloutier, A., Boothby, R., Yang, J.: Motion capture experiments for validating optimization-based human models. In: HCI International, 3rd International Conference on Digital Human Modelling, July 9–14, 2011, Florida, USA (2011) Google Scholar
  29. 29.
    Mital, A., Kromodihardjo, S.: Kinetic analysis of manual lifting activities: Part I—Development of a three-dimensional computer model. Int. J. Ind. Ergon. 1, 77–101 (1986) CrossRefGoogle Scholar
  30. 30.
    Schultz, A., Andersson, G., Ortengren, R., Haderspeck, K., Nachemson, A.: Loads on the lumbar spine. Validation of a biomechanical analysis by measurements of intradiscal pressures and myoelectric signals. J. Bone Jt. Surg. 64(5), 713–720 (1982) CrossRefGoogle Scholar
  31. 31.
    Kim, J.H., Xiang, Y., Yang, J., Arora, J.S., Abdel-Malek, K.: Dynamic motion planning of overarm throw for a biped human multibody system. Multibody Syst. Dyn. 24(1), 1–24 (2010) MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Gill, P.E., Murray, W., Saunders, M.A.: SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J. Optim. 12(4), 979–1006 (2002) MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Xiang, Y., Arora, J.S., Abdel-Malek, K.: Hybrid predictive dynamics: a new approach to simulate human motion. Multibody Syst. Dyn. 28(3), 199–224 (2012) MathSciNetCrossRefGoogle Scholar
  34. 34.
    Anderson, D.E., Madigan, M.L., Nussbaum, M.A.: Maximum voluntary joint torque as a function of joint angle and angular velocity: model development and application to the lower limb. J. Biomech. 40(14), 3105–3113 (2007) CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mechanical and Aerospace EngineeringOklahoma State UniversityStillwaterUSA
  2. 2.Department of Mechanical EngineeringTexas Tech UniversityLubbockUSA

Personalised recommendations