Modelling the biomechanics of diving using the symbolic dynamics approach - Preston, S. B.; Subic, A. J.; Glover, B. (1996)
Representation of human motion through new and innovative dynamic modeling techniques is a rapidly developing area of human biotechnical analysis. The inverse dynamics approach is well suited to computer modeling of human motion, due to the fact that applied mechanics techniques can be used effectively to develop the model's governing equations of motion. The most common techniques utilised for developing the equations of motion of a human skeletal system are: the Newton-Euler method, Lagrange's method and Kane's method. When applied to complex multibody systems, such as human skeletal systems, both the Newton-Euler and Lagrange methods are computationally slow numeric techniques. Kane's vector based method, however, generates a minimal set of equations of motion as it uses a linearisation approximation to the system generalised velocities, (Kane and Levinson, 1985). The result of the linearisation is a system of linear differential equations, which can be solved effectively using computer technology. Because of this Kane's method forms the basis for the formulation of dynamical equations of motion, in dynamic analysis software, Autolev and MECHANICA. Investigation and analysis of human motion has been the focus of research in several areas. Some researchers, approached the problem from a predominantly biomechanical aspect, (Happee, 1994), whereas others used an engineering or applied mechanics approach, (Amirouche, 1990). Previous research in the areas of take-off such as jumping and diving, has concentrated on either experimental analysis, (Bobbert, 1988; Pandy, 1991; Anderson, 1993), or the development of mathematical models for the human musculoskeletal system, (Pandy, 1990), or computer aided simulation of human motion, (Yeadon, 1990; Angulo, 1991). Rarely has the inverse dynamics approach been used as the basis of detailed computer aided dynamic modeling and optimisation, as proposed in this research. The inverse dynamics approach utilises the experimentally determined joint, angular and linear, kinematic data, which enables the joint forces and moments to be computed using dynamic principles. Experimentation was conducted using a Kistler force plate synchronised with Ariel Motion Analysis equipment, such that complete kinematic representation of the human skeletal system's motion could be recorded. Interactive symbolic dynamics software, Autolev, based on Kane's method, is used to develop the equations of motion for the specified skeletal system motion, when the experimentally determined kinematic parameters are used as input. The results obtained from the dynamic models, developed using an inverse dynamics approach, are tested. Comparison of physical entities, for both experimental and mathematical results, such as kinetic energy and joint trajectories, (Figure 1), determines the accuracy of the procedure used in producing the dynamic model which replicates human motion. Dynamic modeling of human motion has many important applications, including development of active prosthetics, optimisation of human performance and in the robotics industry. MECHANICA Motion provides the options for sensitivity studies for the human skeletal model, which is used to identify the biomechanical parameters which have the greatest effect on the performance of the human body for a specific motor task. The main benefit of dynamic modeling of an articulated human linkage, is that the procedures developed can be applied to provide full description and prediction of human performance for a wide range of different motor tasks.