One of the main problems to improve the convergence rate in deterministic optimization of mechanisms is to obtain the Hessian matrix. The required second-order derivatives are difficult to obtain or they are not available. Levenberg-Marquardt optimization method is a pseudo-second order method which means that uses the jacobian information to estimate the Hessian matrix. In this paper, the formulation to obtain the exact form of the jacobian matrix is presented and how can be implemented in the Levenberg-Marquardt method. This formulation gives a very effective method to optimize mechanism geometry considering a large number of prescribed positions and design variables. At the same time it is possible to have control over singularities and permits to compare the desired and generated path avoiding translation and rotation effects.

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