Session: MR-03-01

Paper Number: 143611

143611 - Nonlinear Static Modeling of a Large Range XY-Nanopositioning System 

High-precision and high-speed requirements in flexure-based positioning systems are achieved through the implementation of feedback controllers. The design of such controllers requires knowledge of the dynamic equations of motion, which, despite being nonlinear due to the large deflection of the constitutive flexure beams, can be linearized around the static operating point with sufficient accuracy, provided that deviations from the operating point are small. On the other hand, the dynamic model, centered on the nominal operating points, is influenced by the flexure's equilibrium state. Therefore, the objective of this paper is to propose a nonlinear static model for a specific XY-flexure capable of decoupling motion along horizontal and vertical axes. Initially, the degrees of freedom (DoF) of the flexure are selected and used to develop nonlinear constraint equations that implicitly relate DoFs to other displacement coordinates. Using the principle of virtual work and considering the constraint equations, the nonlinear equilibrium equations governing the static behavior of the highly constrained flexure are derived. The developed approach for proposing a static model for the constraint XY-flexure is then generalized to present a universal algorithm capable of deriving a nonlinear static model for a diverse class of parallel kinematic flexures. Leveraging a physical understanding of the system, the exact operating point under uniaxial load is derived and applied in subsequent analyses using perturbation expansions to find closed-form, highly accurate solutions for the XY-flexure under biaxial loading conditions. The results are validated through numerical simulations and Finite Element Analysis (FEA) conducted in Abaqus. The approach and results presented in this paper are beneficial for the static and dynamic modeling of various parallel kinematic flexure mechanisms.

Presenting Author: Shorya Awtar University of Michigan

Presenting Author Biography: Shorya Awtar received the B.Tech. degree from the Indian Institute of Technology Kanpur, Kanpur, India, the M.S. degree from Rensselaer Polytechnic Institute, Troy, NY, and the Sc.D. degree from the Massachusetts Institute of Technology, Cambridge, in 1998, 2000, and 2003, respectively, all in mechanical engineering. He is an Assistant Professor of Mechanical Engineering and the Director of the Precision Systems Design Laboratory, University of Michigan, Ann Arbor. Prior to joining the University of Michigan, he was with the General Electric Co. Global Research Center until 2006. His engineering and research interests include machine design, flexure mechanisms, precision engineering, and mechatronic systems. The current focus of his research group is on precision motion systems for nanometrology and nanomanufacturing, minimally invasive surgical tools, and MEMS actuators and sensors. Prof. Awtar received the National Science Foundation’s CAREER Award in 2009 and the ASME Leonardo da Vinci Award in 2011, among others, for his research and innovations in machine and mechanism design. He is also a member of the American Society of Mechanical Engineers.

Authors:

Hamid Moeenfard Ferdowsi University of Mashhad
Siddharth Rath University of Michigan
Shorya Awtar University of Michigan