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research-article

Modeling Complex Non-Minimum Phase Zeros in Flexure Mechanisms

[+] Author and Article Information
Leqing Cui

Precision Systems Design Lab, Mechanical Engineering University of Michigan, Ann Arbor, MI 48103
leqing@umich.edu

Chinedum Okwudire

Precision Systems Design Lab, Mechanical Engineering University of Michigan, Ann Arbor, MI 48103
okwudire@umich.edu

Shorya Awtar

Precision Systems Design Lab, Mechanical Engineering University of Michigan, Ann Arbor, MI 48103
awtar@umich.edu

1Corresponding author.

ASME doi:10.1115/1.4036032 History: Received July 10, 2016; Revised February 02, 2017

Abstract

This paper presents a model to explain complex non-minimum phase (CNMP) zeros seen in the non-collocated frequency response of a large displacement XY flexure mechanism, which employs multiple double parallelogram flexure modules (DPFM) as building-blocks. Geometric non-linearities associated with large displacement along with the kinematic under-constraint in the DPFM, lead to a coupling between the X and Y direction displacements. Via a lumped-parameter model that captures the most relevant geometric non-linearity, it is shown that specific combinations of the operating point (i.e. flexure displacement) and mass asymmetry (due to manufacturing tolerances) give rise to CNMP zeros. This model demonstrates the merit of an intentionally asymmetric design over an intuitively symmetric design in avoiding CNMP zeros. Furthermore, a study of how the eigenvalues and eigenvectors of the flexure mechanism vary with the operating point and mass asymmetry indicates the presence of curve veering when the system transitions from minimum phase to CNMP. Based on this, the hypothesis of an inherent correlation between CNMP zeros and curve veering is proposed.

Copyright (c) 2017 by ASME
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