  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.
