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

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.