When simulating human movements it is frequently desirable to optimise multiple phase movements where the phases represent, e.g., different contact conditions. The different constraints are usually acting in parts of the movements and their time durations are in most cases unknown. Therefore a multiple phase free-time optimisation method is formulated in this work, with phase times included as variables. Through a temporal finite element approach, a discrete representation is derived and a nonlinear optimisation algorithm solves for the rather high number of variables (similar to 6000) and constraints (similar to 15000) in the presented numerical problem. A four degrees of freedom test problem, representing a standing high jump, is solved in order to test some basic aspects. A more realistic problem shows its performance in its intended applications, biomechanical simulations. This is a sagittal eight degrees of freedom model for a human backward somersault, including preparing movement, flight phase and landing. The numerical performance as well as some application specific results are discussed. The method description is general and applicable to other movements in its presented format.
When simulating human movements it is frequently desirable to optimize multiple phase movements where the phases represent, e.g., different contact conditions. The different constraints are usually acting in parts of the movements and their time durations are in most cases unknown. Therefore a multiple phase free-time optimization method is formulated in this work, with phase times included as variables. Through a temporal finite element approach, a discrete representation is derived and a nonlinear optimization algorithm solves for the rather high number of variables (∼ 6000) and constraints (∼ 15000) in the presented numerical problem. The method is applied to a test problem and a more realistic problem in order to test some basic aspects as well as to see its performance in its intended applications, biomechanical simulations. First a four degrees of freedom test problem, representing a standing high jump, is solved. Then a sagittal eight degrees of freedom model is used with application to a human backward somersault, including preparing movement, flight phase and landing. The numerical performance as well as some application specific results are discussed. The method description is general and applicable to other movements in its presented format.
Competitive rowing requires efforts close to the physiological limits, where oxygen consumption is one main aspect. The rowing event also incorporates interactions between the rower, the boat and oars, and water. When the intention is to improve the performance, all these properties make the sport interesting from a scientific point of view, as the many variables influencing the performance form a complex optimization problem. Our aim was to formulate the rowing event as an optimization problem where the movement and forces are completely determined by the optimization, giving at least qualitative indications on good performance. A mechanical model of rigid links was used to represent rower, boat and oars. A multiple phase cyclic movement was simulated where catch slip, driving phase, release slip and recovery were modeled. For this simplified model, we demonstrate the influence of the stated mathematical cost function as well as a parameter study where the optimal performance is related to the planned average boat velocity. The results show qualitatively good resemblance to expected movements for the rowing event. An energy loss model in combination with case specific properties of rower capacities, boat properties, and rigging was required to draw qualitative practical conclusions about the rowing technique.
The inherent dynamics of bipedal, passive mechanisms are studied to investigate the relation between motions constrained to two-dimensional (2D) planes and those free to move in a three-dimensional (3D) environment. In particular, we develop numerical and analytical techniques using dynamical-systems methodology to address the persistence and stability changes of periodic, gait-like motions due to the relaxation of configuration constraints and the breaking of problem symmetries. The results indicate the limitations of a 2D analysis to predict the dynamics in the 3D environment. For example, it is shown how the loss of constraints may introduce characteristically non-2D instability mechanisms, and how small symmetry-breaking terms may result in the termination of solution branches.
Simulation results for two-axle freight wagons were found to be extremely sensitive to minor changes of some input parameters. Therefore the influence of non-linearities in the model - especially friction damping - on the running behaviour of the wagon is investigated. After a description of the vehicle model and the basic running behaviour a brief introduction into differences between linear an non-linear systems is given. A typical bifurcation diagram for railway vehicle dynamics is presented. For different wheel-rail geometries limit cycle diagrams are calculated. Furthermore phase diagrams at different speeds are shown. Attractors with a broad band structure' which indicate chaotic behaviour can be observed. The chaotic content of the oscillations is, however, restricted to small changes of the amplitude of the limit cycles. The conclusion is therefore that the observed behaviour mentioned above is due to co-existing stable attractors rather than to chaotic behaviour.