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

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 re-sponse index are proposed in this paper. Utilizing the strong universality of the screw the-ory, a universal dynamic modelling method is proposed, in which the complicated Lie alge-bra terms are appear explicitly and the Coriolis acceleration term is intentionally indepen-dent 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 ampli-tude 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 be-tween 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 mathe-matical model and the proposed index will provide a convenient way for vibration mod-elling and optimization.(c) 2022 Elsevier Inc. All rights reserved.