An Explicit Method for Analysis of Three-Dimensional Linear and Angular Velocity of a Joint, with Specific Application to the Knee Joint
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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.
KeywordsKinematics 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.
- 3.Beveridge, J. E., Heard, B. J., Shrive, N. G., & Frank, C. B. (2013). Tibiofemoral centroid velocity correlates more consistently with cartilage damage than does contact path length in two ovine models of stifle injury. Journal of Orthopaedic Research, 31(11), 1745–1756. doi: 10.1002/jor.22429.Google Scholar
- 10.Wang, T. M., Yen, H. C., Lu, T. W., Chen, H. L., Chang, C. F., Liu, Y. H., et al. (2009). Bilateral knee osteoarthritis does not affect inter-joint coordination in older adults with gait deviations during obstacle-crossing. Journal of Biomechanics, 42(14), 2349–2356. doi: 10.1016/j.jbiomech.2009.06.029.CrossRefGoogle Scholar
- 18.Li, G., Park, S. E., DeFrate, L. E., Schutzer, M. E., Ji, L., Gill, T. J., et al. (2005). The cartilage thickness distribution in the tibiofemoral joint and its correlation with cartilage-to-cartilage contact. Clinical Biomechanics, 20(7), 736–744. doi: 10.1016/j.clinbiomech.2005.04.001.CrossRefGoogle Scholar
- 22.Defrate, L. E., Papannagari, R., Gill, T. J., Moses, J. M., Pathare, N. P., & Li, G. (2006). The 6 degrees of freedom kinematics of the knee after anterior cruciate ligament deficiency: An in vivo imaging analysis. The American Journal of Sports Medicine, 34(8), 1240–1246. doi: 10.1177/0363546506287299.CrossRefGoogle Scholar
- 24.Gatti, G., Mundo, D., & Danieli, G. (2010). Kinematic analysis and performance evaluation of 6R instrumented spatial linkages. Transactions of the Canadian Society for Mechanical Engineering, 34(1), 57–73.Google Scholar
- 25.Gatti, G. (2012). On the estimate of the two dominant axes of the knee using an instrumented spatial linkage. Journal of Applied Biomechanics, 28(2), 200–209. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/21904008.
- 26.Bonny, D. P., Hull, M. L., & Howell, S. M. (2013). Optimized design of an instrumented spatial linkage that minimizes errors in locating the rotational axes of the tibiofemoral joint: A computational analysis. Journal of Biomechanical Engineering, 135(3), 31003. doi: 10.1115/1.4023135.CrossRefGoogle Scholar
- 27.Sholukha, V., Salvia, P., Hilal, I., Feipel, V., Rooze, M., & Jan, S. V. S. (2004). Calibration and validation of 6 DOFs instrumented spatial linkage for biomechanical applications. A practical approach. Medical Engineering & Physics, 26(3), 251–260. doi: 10.1016/j.medengphy.2003.10.002.CrossRefGoogle Scholar
- 28.Atarod, M., Rosvold, J. M., Frank, C. B., & Shrive, N. G. (2014). A novel testing platform for assessing knee joint mechanics: A parallel robotic system combined with an instrumented spatial linkage. Annals of Biomedical Engineering, 42(5), 1121–1132. doi: 10.1007/s10439-014-0985-9.CrossRefGoogle Scholar
- 33.Lu, T. W., & O’Connor, J. J. (1999). Bone position estimation from skin marker co-ordinates using global optimisation with joint constraints. Journal of Biomechanics, 32(2), 129–134. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/10052917.
- 34.Andersen, M. S., Benoit, D. L., Damsgaard, M., Ramsey, D. K., & Rasmussen, J. (2010). Do kinematic models reduce the effects of soft tissue artefacts in skin marker-based motion analysis? An in vivo study of knee kinematics. Journal of Biomechanics, 43(2), 268–273. doi: 10.1016/j.jbiomech.2009.08.034.CrossRefGoogle Scholar
- 36.Preuschl, E., Hassmann, M., & Baca, A. (2016). A Kinematic Analysis of the Jumping Front-Leg Axe-Kick in Taekwondo. Journal of Sports Science & Medicine, 15(1), 92–101. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/26957931.
- 39.Levangie, P. K., & Cynthia, C. N. (2011). Joint structure and function: A comprehensive analysis (5th ed.). Philadelphia: F.A Davis Co.Google Scholar
- 47.Kessler, M. A., Behrend, H., Henz, S., Stutz, G., Rukavina, A., & Kuster, M. S. (2008). Function, osteoarthritis and activity after ACL-rupture: 11 years follow-up results of conservative versus reconstructive treatment. Knee Surgery, Sports Traumatology, Arthroscopy: Official Journal of the ESSKA, 16(5), 442–448. doi: 10.1007/s00167-008-0498-x.CrossRefGoogle Scholar