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Synthesis Method for the Spherical 4R Mechanism with Minimum Center of Mass Acceleration

In the mechanisms area, minimization of the magnitude of the acceleration of the center of mass (ACoM) implies shaking force balancing. For a mechanism operating in cycles, the case when the ACoM is zero implies that the gravitational potential energy (GPE) is constant. This article shows an efficient and effective optimum synthesis method for minimum acceleration of the center of mass of a spherical 4R mechanism by using dual functions and the counterweights balancing method. Once the dual function for ACoM has been written, one can minimize the shaking forces from a kinematic point of view. We present the synthesis of a spherical 4R mechanism for the case of a path generation task. The synthesis process involves the optimization of two objective functions, this multiobjective problem is solved by using the weighted sum method implemented in the evolutionary algorithm known as Differential Evolution.