The basic idea of the method is to alter the link or links to bring the generated path or function close to the desired one. Planar mechanisms are modelled very easily by means of constraint equations. This approach minimizes the error between the actual path and the desired one when a large number of precision points are required. Large in this context means that only approximate synthesis is possible because the number of equations is much larger than the number of unknowns. The method proposes an objective function as a measurement of the synthesis error. The differentiated expression of the objective function is approximated by means of the Taylor’s series expansion in every increment of the input links. That means that a successive linearization of the differentiated function is used. As consequence, increments considered in the motion must be small enough to avoid errors during the optimization process. Constraints are formulated to obtain the exact gradient elements, avoiding typical problems occurring when approximate methods are used. In this way, a low computational time is necessary because the search direction is always accurate.

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