Natural frequency analysis and experiment for 3SPS+1PS parallel hip joint manipulator based on rigid-flexible coupling theory

Abstract

For analyzing natural frequency of a 3SPS+1PS parallel hip joint manipulator, a rigid-flexible coupling theory is proposed. 3SPS denotes that the PHJM has three legs and each leg type is SPS. 1PS denotes that the PHJM has one constrained leg and the constrained leg type is PS. The rigid finite element method and flexible finite element method are the base of the rigid-flexible coupling theory. Firstly, the basic element models of the PHJM are established based on the rigid-flexible coupling analysis. Secondly, the elastic dynamic models of the flexible legs are established based on the Lagrange equation and flexible finite method. Finally, the rigid-flexible coupling model of the PHJM is assembled by building the relationship between the rigid and flexible elements. Based on the rigid-flexible model, the natural frequency of the PHJM is analyzed. In addition, the effect parameters of the natural frequency are analyzed. The analysis results of the natural frequency show that the natural frequency is symmetric distribution in the working space, and the minimum value of the 1st order natural frequency is 2.3 Hz. The operating frequency (1 Hz) is much lower than the 1st order natural frequency, so the PHJM will not generate resonance and can operate stably. The analysis results of the parameter show that the PHJM has the minimal sensitivity with the effect parameter E and has the maximal sensitivity with the effect parameter H, so the length of the middle leg has the biggest impact on the natural frequency. Natural frequency analysis results have been checked by the hammer test, which verifies the feasibility of the rigid-flexible coupling theory. At the same time, the regression analysis is carried out based on the hammer test results. Using the rigid-flexible coupling theory to solve the natural frequency of the parallel manipulator, the physical meaning is explicit and the modeling process is clear, so the rigid-flexible coupling theory is a universal method.