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The function of the distance of the curve from its centroid in optimal synthesis of a planar five-bar linkage

A functional description of a closed curve, applied in computer image processing and pattern recognition, is adapted to optimal synthesis of 2-DOF planar five-bar mechanism. The function is the distance of a curve from its centroid (DCC). In the applicable form the DCC is represented by normalized coefficients of its expansion into Fourier series. On the basis of the DCC a new function is defined, which itself is invariant under affine transformations. A distance norm in the sense of the affinity of two curves is introduced. The norm is applied as an objective function in the problem of mechanism synthesis carried out by the genetic algorithm.
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