Permutation entropy and Lyapunov exponent: Detecting and monitoring the chaotic edge of a closed planar under-actuated system

Abstract

Abstract Generally, under-actuated mechanism possesses a chaotic and quasi-periodic behavior. The edge of chaos is the transitory region between deterministic and chaotic motion, and the main concern of the design engineers is to acquire the region by changing the parameters of the dynamical system at the edge of chaos. To be different with many existed researches focused on the dynamic analysis of clearance joints, the closed under-actuated systems is analyzed in this paper while very limited study has been done on this subject before. A typical under-actuated sieve is used as a demonstration case in which the driving speed and the length of the link can be changed for the purpose of keeping chaotic motion, as it is good for the work efficiency of sieve machine. The Lagrange equation of the first kind is used to build the numerical model for the sieve system, permutation entropy is employed to detect dynamic change in this complex system, and Lyapunov exponent is applied to judge deterministic and chaotic motion. The equations of the closed under-actuated planar sieve are obtained in this work and the experimental results about the sieve motion have then confirmed that the permutation entropy and Lyapunov exponent provide an effective measure for monitoring and detecting the edge of chaotic motion, which can improve the work efficiency of a planar sieve.