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Development of a planar multibody model of the human knee joint

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Abstract

The aim of this work is to develop a dynamic model for the biological human knee joint. The model is formulated in the framework of multibody systems methodologies, as a system of two bodies, the femur and the tibia. For the purpose of describing the formulation, the relative motion of the tibia with respect to the femur is considered. Due to their higher stiffness compared to that of the articular cartilages, the femur and tibia are considered as rigid bodies. The femur and tibia cartilages are considered to be deformable structures with specific material characteristics. The rotation and gliding motions of the tibia relative to the femur cannot be modeled with any conventional kinematic joint, but rather in terms of the action of the knee ligaments and potential contact between the bones. Based on medical imaging techniques, the femur and tibia profiles in the sagittal plane are extracted and used to define the interface geometric conditions for contact. When a contact is detected, a continuous nonlinear contact force law is applied which calculates the contact forces developed at the interface as a function of the relative indentation between the two bodies. The four basic cruciate and collateral ligaments present in the knee are also taken into account in the proposed knee joint model, which are modeled as nonlinear elastic springs. The forces produced in the ligaments, together with the contact forces, are introduced into the system’s equations of motion as external forces. In addition, an external force is applied on the center of mass of the tibia, in order to actuate the system mimicking a normal gait motion. Finally, numerical results obtained from computational simulations are used to address the assumptions and procedures adopted in this study.

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Authors and Affiliations

  1. Departamento de Engenharia Mecânica, Universidade do Minho, Campus de Azurém, 4800-058, Guimarães, Portugal

    Margarida Machado, Paulo Flores & J. C. Pimenta Claro

  2. Departamento de Engenharia Mecânica, Instituto Superior Técnico, IST/IDMEC, Av. Rovisco Pais, 1, 1049-001, Lisboa, Portugal

    Jorge Ambrósio & Miguel Silva

  3. Departamento de Engenharia Mecânica, Universidade de Aveiro, Campus Universitário de Santiago, 3810-193, Aveiro, Portugal

    António Completo

  4. Department of Mechanical Engineering, Wichita State University, Wichita, KS, 67260-133, USA

    Hamid M. Lankarani

Authors
  1. Margarida Machado
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  2. Paulo Flores
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  3. J. C. Pimenta Claro
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  4. Jorge Ambrósio
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  5. Miguel Silva
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  6. António Completo
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  7. Hamid M. Lankarani
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Correspondence to Paulo Flores.

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Machado, M., Flores, P., Claro, J.C.P. et al. Development of a planar multibody model of the human knee joint. Nonlinear Dyn 60, 459–478 (2010). https://doi.org/10.1007/s11071-009-9608-7

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  • DOI: https://doi.org/10.1007/s11071-009-9608-7

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