The use of the matrix method for the study of human motion: theory and applications

Kinematics has been successfully used to describe body motion without reference to the kinetics (or forces causing the motion). In this article, both the theory and applications of the matrix method are provided to describe complex human motion. After the definition of a Cartesian coordinate frame is introduced, the description of transformations between multiple coordinate frames is given; the decomposition of a transformation matrix into anatomical joint motion parameters (e.g. Euler angles) is then explained. The advantages of the matrix method are illustrated by three examples related to biomechanical studies. The first describes a reaching and grasping task in which matrix transformations are applied to position the hand with respect to an object during grasping. The second example demonstrates the utility of the matrix method in revealing the coupling motion of the wrist between flexion-extension and radial-ulnar deviation. The last example highlights the indispensable use of the matrix method for the study of knee biomechanics, including the description of knee joint kinematics during functional activities and determination of in-situ ligament forces using robotic technology, which has advanced our understanding of the functions of the cruciate ligaments to knee joint kinematics. It is hoped that the theoretical development and biomechanical application examples will help the readers apply the matrix method to research problems related to human motion.