Kinematic analysis of over-determinate biomechanical systems

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Andersen, M. S.¹; Damsgaard, M.²; Rasmussen, J.¹

Kinematic analysis of over-determinate biomechanical systems

Comput Methods Biomech Biomed Eng. August 2009;12(4):371-384

©2009 Taylor & Francis

Affiliations

¹Department of Mechanical Engineering, Aalborg University, Aalborg, Denmark

²AnyBody Technology A/S, Aalborg, Denmark
Abstract and keywords

In this paper, we introduce a new general method for kinematic analysis of rigid multi body systems subject to holonomic constraints. The method extends the standard analysis of kinematically determinate rigid multi body systems to the over-determinate case. This is accomplished by introducing a constrained optimisation problem with the objective function given as a function of the set of system equations that are allowed to be violated while the remaining equations define the feasible set.

We show that exact velocity and acceleration analysis can also be performed by solving linear sets of equations, originating from differentiation of the Karush-Kuhn-Tucker optimality conditions.

The method is applied to the analysis of an 18 degrees-of-freedom gait model where the kinematical drivers are prescribed with data from a motion capture experiment.

The results show that significant differences are obtained between applying standard kinematic analysis or minimising the least-square errors on the two fully equivalent 3D gait models with only the way the experimental data is processed being different.

Keywords: kinematic analysis; over-determinate; motion capture
Links

DOI: 10.1080/10255840802459412

PubMed: 18949590

WoS: 000268912000001

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Year	Entry
2011	Madeleine P, Samani A, de Zee M, Kersting U. Biomechanical assessments in sports and ergonomics. In: Klika V, ed. Theoretical Biomechanics. InTech; 2011:335-360.
2010	Andersen MS, Benoit DL, Damsgaard M, Ramsey DK, Rasmussen J. Do kinematic models reduce the effects of soft tissue artefacts in skin marker-based motion analysis? an in vivo study of knee kinematics. J Biomech. January 19, 2010;43(2):268-273.
2010	Saraswat P, Andersen MS, MacWilliams BA. A musculoskeletal foot model for clinical gait analysis. J Biomech. 2010;43(9):1645-1652.
2010	Duprey S, Cheze L, Dumas R. Influence of joint constraints on lower limb kinematics estimation from skin markers using global optimization. J Biomech. 2010;43(14):2858-2862.
2023	Bahramian M, Arjmand N, El-Rich M, Parnianpour M. Effect of obesity on spinal loads during load-reaching activities: a subject- and kinematics-specific musculoskeletal modeling approach. J Biomech. December 2023;161:111770.
2015	Marra MA, Vanheule V, Fluit R, Koopman BHFJM, Rasmussen J, Verdonschot N, Andersen MS. A subject-specific musculoskeletal modeling framework to predict in vivo mechanics of total knee arthroplasty. J Biomech Eng. February 2015;137(2):020904.
2013	Sanford BA. An Assessment of Tibiofemoral Kinematics Amd Kinetics Following Anterior Cruciate Ligament Reconstruction [PhD thesis]. University of Memphis; May 2013.
2014	Yoder A. Low Back Biomechanics During Walking of Individuals With a Lower-Limb Amputation [Master's thesis]. Colorado School of Mines; 2014.