Journal of Medical and Biological Engineering

, Volume 38, Issue 2, pp 273–283 | Cite as

An Explicit Method for Analysis of Three-Dimensional Linear and Angular Velocity of a Joint, with Specific Application to the Knee Joint

  • Mehdi Shekarforoush
  • Kristen I. Barton
  • Mohammad Atarod
  • Bryan J. Heard
  • John L. Sevick
  • Ryan Martin
  • David A. Hart
  • Cyril B. Frank
  • Nigel G. Shrive
Original Article


Velocity analysis in a joint is a major area of interest in research involving the dynamics of joints and in diagnosing and monitoring the progression of some diseases such as osteoarthritis. In this study, we provide a general analytical method to determine three-dimensional linear and angular velocity of a joint. The formulations presented are explicit, having neither the limitations of numerical methods nor the necessity of simplifying the joint to a hinge or spherical (ball and socket) joint. In addition to conventional analysis of joint kinematics where only the position and orientation of the joint is considered, velocity analysis provides more information regarding the dynamics of the joint. The methodology presented is a systematic approach and can be used for various joints. As an example, a formulation to measure the velocity of the tibiofemoral component of a knee joint is presented, in terms of clinical rotations by using a joint coordinate system. The method is used to examine the in vivo velocity formulations in five ovine stifle (knee) joints by using joint kinematic data measured with an instrumented spatial linkage. The results demonstrate that the classical hinge model of the knee joint cannot predict the exact three-dimensional velocity of the knee joint through the gait cycle for all subjects.


Kinematics Velocity analysis Linear velocity Angular velocity Knee joint 



The authors gratefully acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada, the Canadian Institutes of Health Research, The Arthritis Society, the Osteoarthritis Team of Alberta Innovates Health Solutions, and the University of Calgary. The technical support of Leslie Jacques and Yamini Achari was much appreciated.

Compliance with Ethical Standards

Conflicts of interest

The authors have no conflicts of interest to disclose regarding the present study.


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Copyright information

© Taiwanese Society of Biomedical Engineering 2017

Authors and Affiliations

  • Mehdi Shekarforoush
    • 1
    • 2
  • Kristen I. Barton
    • 1
  • Mohammad Atarod
    • 1
    • 2
  • Bryan J. Heard
    • 1
  • John L. Sevick
    • 1
    • 2
  • Ryan Martin
    • 1
    • 3
  • David A. Hart
    • 1
  • Cyril B. Frank
    • 1
  • Nigel G. Shrive
    • 1
    • 2
  1. 1.McCaig Institute for Bone & Joint Health, Cumming School of MedicineUniversity of CalgaryCalgaryCanada
  2. 2.Schulich School of EngineeringUniversity of CalgaryCalgaryCanada
  3. 3.Section of OrthopaedicsUniversity of Calgary, Foothills HospitalCalgaryCanada

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