A universal modelling approach and a response index to the vibration analysis for space parallel robots by means of screw theory

Abstract

Vibration analysis is very important for evaluating the vibration performance of some space parallel robots (SPRs), but most of the matrix analysis methods are case-by-case treatment and the vibration response is difficult to estimate accurately in the design phase. In order to enrich this field, a universal vibration modelling approach and a vibration response index are proposed in this paper. Utilizing the strong universality of the screw theory, a universal dynamic modelling method is proposed, in which the complicated Lie algebra terms are appear explicitly and the Coriolis acceleration term is intentionally independent of each other. Based on the Rayleigh quotient and considering the effects of gravity and joint clearances, a vibration response index is presented to reflect the vibration amplitude of SPRs under the unit initial conditions. Based on the built experimental prototype and some applications, numerical examples are presented and some performances of the vibration index have been fully discussed, and the results show that the mean error between the mathematical models and experimental results is about 5.4%. When researchers are engaged in vibration research on different SPRs, we expect that the proposed mathematical model and the proposed index will provide a convenient way for vibration modelling and optimization.