Adaptive Kriging elastodynamic modelling and analysis for a redundantly actuated parallel manipulator

Abstract

This paper presents a quantitative analysis comparing the elastodynamic performance of a redundantly actuated parallel manipulator to its non-redundantly actuated counterpart. A unified elastodynamic model is established to encompasses both actuation types, facilitating a comprehensive analysis of their performance characteristics. To assess the impact of redundant actuation, frequency variation indices are defined to measure the influence of the redundantly actuated limbs on the overall system dynamics. Two global sensitivity indices are introduced to quantify how variations in design variables affect elastodynamic performance. An adaptive Kriging-based algorithm is developed to predict elastodynamic behavior, and it is numerically validated for both accuracy and efficiency. Through a detailed elastodynamic comparison and sensitivity analysis, we identify the key effects of redundant actuation and pinpoint the most significant design variables. Our findings reveal that the enhancements in low-order natural frequencies due to redundant actuation are configuration- and order-dependent. The redundantly actuated parallel manipulator demonstrates heightened sensitivity to geometric variables in terms of elastodynamic performance, surpassing that of its non-redundantly actuated variant. The sensitivity analysis provides valuable insights, guiding future improvements in elastodynamic performance. Notably, the thickness of the moving platform emerges as a critical parameter that warrants optimization during the design phase. Therefore, this analysis is particularly pivotal in the initial evaluation stages of parallel manipulators, ensuring that designs are refined for enhanced dynamic responses. With necessary modifications, this work can be applied to other redundantly actuated parallel manipulators to contribute a deeper understanding of how redundancy influences their dynamic characteristics.