Optimal synthesis of mechanical systems using natural coordinates

This paper presents a comprehensive optimal design procedure for constrained dynamic systems formulated with natural coordinates. Natural coordinates formulation has linear (or quadratic) kinematic constraints in terms of generalized coordinates, sparse and simple generalized mass matrix, as well as explicit form of design variables in the coordinate transformations. It is particularly suitable for optimization related problems of multibody systems. The direct differentiation method is used to calculate the first order design sensitivity of the objective function during the optimization process. The motion equations and the sensitivity equations of the constrained systems share with the same Jacobian matrix, therefore they can be integrated simultaneously using the general-α algorithm. A slider-crank mechanism is provided to illustrate effectiveness of this method for obtaining the optimal synthesis of a multibody system.