Optimization of desired multiple resonant modes of compliant parallel mechanism using specific frequency range and targeted ratios

Abstract

In this paper, a dynamic optimization method capable of optimizing the dynamic responses of a compliant parallel mechanism (CPM), in terms of its multiple primary resonant modes, is presented. A novel two-term objective function is formulated based on the specific frequency range and targeted ratios. The first term of the function is used to optimize the first resonant mode of the CPM, within a specific frequency range. The obtained frequency value of the first mode is used in the second term to define the remaining resonant modes to be optimized in terms of targeted ratios. Using the proposed objective function, the resonant modes of a CPM can be customized for a specific purpose, overcoming the limitations of existing methods. A 6-degree-of-freedom (DoF) CPM with decoupled motion is synthesized, monolithically prototyped, and investigated experimentally to demonstrate the effectiveness of the proposed function. The experimental results showed that the objective function is capable of optimizing the six resonant modes within the desired frequency range and the targeted ratios. The highest deviation between the experimental results and the predictions among the six resonant modes is found to be 9.42%, while the highest deviation in the compliances is 10.77%. The ranges of motions are found to be 10.0 mm in the translations, and 10.8° in the rotations.