Session: 07-02-02: Nonlinear Dynamics, Control, and Stochastic Mechanics

Paper Number: 144431

144431 - Measurement of Chaotic Complexity in a Planar Mechanism Due to the Motion of the Follower With Clearance Using Lyapunov Exponent, Phase Plane Diagram, Poincare’ Map, and Entropy Representations 

A planar mechanism with three moving links is connected to a cam. A planar system with clearance in the presence of crank arm and connecting rod is used in the investigation of nonlinear dynamics. The crank arm with the connecting rod can be used to convert the circular motion into reciprocating motion and vice versa. The proposed work can be seen in electrical toothbrushes, sewing machines, and car engines. The Global false nearest neighbor’s algorithm is used to determine the value of embedding dimensions while the algorithm of average mutual information is used to evaluate the value of time delay. Spectral, sample, and an approximate entropy are used to detect and measure the level of chaotic complexity. The higher value of entropy, the more chaos motion. Moreover the level of chaos is also detected using the conception of largest Lyapunov exponent at different cam speeds. Positive value of Lyapunov exponent represents the chaos motion while the negative value reflects for the periodic motion of the planar mechanism. The crank arm and connecting rod are oscillating like a double pendulum motion which provides chaotic motion to the stem of flat-faced follower which makes the follower moves with three degrees of freedom inside its guides. There is a clearance between the follower and its guides. The crank arm and cam are spinning about a fixes pivot while the connecting rod is moving with three degrees of freedom. The two guides are fixed. Also, Poincare’ map and phase-plane diagram are used to detect the chaotic motion. The Matlab software is used to run the algorithms of the dynamic tool.

Presenting Author: Louay Yousuf San Diego State University

Presenting Author Biography: Dr. Louay S. Yousuf is a lecturer professor in the Department of Mechanical Engineering, San Diego State University, USA. He received his Ph.D. from the University of Baghdad, Iraq, and was a postdoctoral fellow at the Mechanical Engineering Department, University of Auburn, USA, before joining San Diego State University. His research interests include nonlinear dynamics, composite materials, finite element methods, mechanical vibrations, mechanisms, and robotics.

Authors:

Louay Yousuf San Diego State University