Método dimensional óptimo de sistemas multicuerpo con restricciones dinámicasaplicación al diseño de mecanismos planos

Résumé

The thesis presents a method for the optimal dimensional synthesis of multibody systems with topological, geometric, position, kinematic and dynamic constraints. The method is based on the minimization of an elastic potential energy objective function whose design variables are natural coordinates and bar lengths of the system with a system modelling similar to that used in the finite elements method. The optimisation is performed by means of a sequential quadratic programming algorithm implemented through routine E04UCF of the mathematical library NAG. The resulting method can be applied to multibody systems composed of rigid bodies, irrespective of the dimension of their movement, geometric configuration and kinematic pairs of the kinematic chain, and allows for the mobility of fixed points. Using previous developments to resolve velocity and acceleration kinematic problems, the equations systems of the multibody system dynamic equilibrium and their partial derivatives with respect to the designing variables are analytically solved. The resolution of these equations systems provides analytical expressions of the dynamic problem parameters that can be imposed as restrictions in the designing phase, and well as their Jacobians. The Hessians, which are also required by the sequential quadratic programming algorithm, are calculated from the analytical expressions of the dynamic parameters and Jacobians following the numerical method of finite differences. The expressions for the dynamic constraints of input and output forces, constraint forces, support reactions, mass of bodies, as well as the main merit indexes -ratio of angular velocities, mechanical advantage and transmission angle- are developed. These expressions are subsequently used to optimise the dynamic behaviour of planar mechanisms. The described method enables the simultaneous optimisation of the kinematic and dynamic behaviour of the system from the very earliest phases of design, thus making design tasks easier and shortening the design cycle of the system.