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Noncircular gears are used in several technological applications in order to enhance the performance of different mechanical instruments (flow meters, bikes, internal combustion engines, etc.)• The mathematical models for manufacturing elliptical and oval gears are included.• The algorithm of the mathematical models is implemented using MatlabTM.• Simulations are carried out, and the method is implemented in a real WEDM machine.• Two pairs of elliptical and oval gears are obtained applying this method.

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