Multi-Objective Scale Independent Optimization of 3-RPR Parallel Mechanisms

This paper deals with the optimization of 3- RPR planar parallel mechanisms based on different per- formance indices including kinematic sensitivity, stiffness, workspace and singularity. The optimization is imple- mented in sequence using first a single objective tech- nique, differential evolution, and then resorting to a multi- objective optimization concept, the so-called nondomi- nated sorting genetic algorithm-II. The results revealed that the optimality of the mechanism under study is scale- independent for the considered optimization objectives. Moreover, based on the scale invariance property of the main objectives, it follows that different kinetoestatic ob- jective functions must be scale invariant. The relations for the kinetoestatic objective expressions as functions of mech- anism scale are derived and to circumvent the problem of unit inconsistency the rotational and translational parts of these objectives are considered separately. To overcome the problem of inconsistent objectives in optimization al- gorithm, a Pareto-based multi-objective approach is used which preserves the scale invariance property.

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