Dynamic modeling of musculoskeletal motion. A vectorized approach for biomechanical analysis in three dimensions (Q2762774)

This book is devoted to dynamic musculoskeletal models. Vector methods in kinematics are emphasized over the standard trigonometric approaches. Kane's method of formulating the dynamical equations of motion is emphasized over the more traditional Newton-Euler and Lagrangian formulations, in part because it is better suited to three-dimensional systems. The book is aimed at both the biomechanist seeking to expand his or her analytical skills and at graduate students.NEWLINENEWLINENEWLINEA thorough review of the biomechanics and physiology of skeletal muscles is provided. The reader is introduced to direction cosines, which provide the key to analyzing models with multiple degrees of freedom. Vector based kinematics is used to find the positions and velocities of points at which forces act, angular velocities of bodies on which torques act, and accelerations of centers of mass. Joint models are presented showing how moments are created by muscles and ligaments. A case study describing a simple model of the knee is presented.NEWLINENEWLINENEWLINEThe central theme of the book is the use of Kane's method for the development of the dynamic equations of motion of musculoskeletal systems. Kane's method differs from classical treatments in several ways: (1) Since it is vector-based, it is well suited to three-dimensional analysis. (2) Vector cross and dot products, rather than calculus, are used to determine velocities and accelerations. (3) Dynamical system equations are formed from generalized forces, which are simplified forms of conventional forces, moments and torques. (4) Inertial forces and inertial torques are also incorporated in simplified form as generalized inertial forces in the fashion of d'Alembert. Kane's concepts of generalized speed, partial velocity, partial angular velocity, generalized active force, and generalized inertia force provide key simplifications enabling forces and torques having no influence on the dynamic equations to be eliminated early in the analysis. For example, in biomechanical models, joint reaction forces can usually be ignored when using Kane's method. NEWLINENEWLINENEWLINEFinally, optimal control techniques are applied to the ``redundant problem'' in biomechanics. Methods are given for finding which set of muscle forces, among the many that are possible, is used by the central nervous system to drive the musculoskeletal system along a specified motion trajectory.