Design and Experiment of a Multi-DOF Shaker Based on Rotationally Symmetric Stewart Platforms with an Insensitive Condition Number

Abstract

This study proposes a method for designing a class of rotationally symmetric Stewart platforms (RSSPs) with an insensitive condition number (ICN), which is used to minimize the condition number to achieve a high accuracy for a multi-degree-of-freedom (multi-DOF) shaker. Considering the rotational symmetry of RSSPs, an analytical relationship between the architecture parameters and transfer coefficients is first established. Then, the decoupling conditions of the RSSPs are derived, and the transfer coefficient formulas are simplified by the given decoupling conditions and iso-length assumption. Following further analyses and discussions, the ICN condition and analytical form of the condition number are provided. The area of the ICN (AICN) is, subsequently, derived to evaluate the insensitivity of the condition number. To validate the effectiveness of the method, a design example (ICN-RSSP), along with a numerical analysis, is implemented, and, finally, a multi-DOF shaker is developed. The results of the numerical analysis show a smaller condition number and a larger AICN than those of the RSSP, for comparison. And the experiment results of the multi-DOF shaker show a high accuracy of vibration waveform reproduction. The method can reduce the condition number of RSSPs, improve the insensitivity, and further improve the accuracy of the multi-DOF shaker.