Synthesis method for the spherical 4R mechanism with minimum center of mass acceleration

• Use of dual numbers to calculate the acceleration of the center of mass (ACoM).
• Use of DE for the optimal dimensional synthesis.
• Experimental comparison between the ACoM balanced and unbalanced mechanisms.

In the mechanisms area, minimization of the magnitude of the acceleration of the center of mass (ACoM) implies shaking force balancing. This article shows an efficient optimum synthesis method for minimum acceleration of the center of mass of a spherical 4R mechanism by using dual functions as well as the counterweights balancing method. Once the dual function for ACoM has been formulated, 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. Our results show that the magnitude of the ACoM can be reduced by about 20 times, which for the presented synthesis, is traduced to a reduction of about 89% for the shaking forces.