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In the mechanisms area, minimization of the magnitude of the acceleration ofthe center of mass (ACoM) implies shaking force balancing. For a mechanismoperating in cycles, the case when the ACoM is zero implies that thegravitational potential energy (GPE) is constant. This article shows anefficient and effective optimum synthesis method for minimum acceleration ofthe center of mass of a spherical 4R mechanism by using dual functions and thecounterweights balancing method. Once the dual function for ACoM has beenwritten, one can minimize the shaking forces from a kinematic point of view. Wepresent the synthesis of a spherical 4R mechanism for the case of a pathgeneration task. The synthesis process involves the optimization of twoobjective functions, this multiobjective problem is solved by using theweighted sum method implemented in the evolutionary algorithm known asDifferential Evolution.

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