Dynamics modeling and verification of a large-displacement precision preloaded-flexure stage

Qinan Zhou, Nicholas Toombs, Placid Ferreira

Research output: Contribution to journalArticlepeer-review


Precision stages, specifically flexure stages, are critical elements in micro- and nano-fabrication and metrology because of their ability to produce motion with nanoscale resolution as they are not limited by the effects of friction at sliding surfaces. In addition, they have the advantages of lower wear, longer life, no maintenance, and more repeatable and robust behaviors. However, these advantages come at the expense of the travel range. Displacements of flexure stages are typically very small and attempts to extend the range of motion by using less stiff flexures also increase the stage's susceptibility to parasitic motions. Thus, in situations where accuracy, resolution, range, and stiffness are simultaneously needed, one is forced to deal with nonlinear (stiffening) behaviors that are inherent in any flexure stages. This paper addresses the problem of modeling the dynamics of a typical flexure stage used for producing oscillating linear motions for a micro-machining system. The nonlinear behavior of the flexure stage due to stretching of the flexures is modeled from first principles. Practical considerations associated with flexure stages such as preloading of the flexures, the distribution of its mass at different locations, and coupling to an actuator that itself has dynamics are also included in the model. Experimental verification of the model is used to assess its accuracy. Simulations are used to predict behavior in regimes not accessible by experiments.

Original languageEnglish (US)
Pages (from-to)36-45
Number of pages10
JournalJournal of Manufacturing Processes
StatePublished - Jul 2019


  • Dynamics modeling
  • Flexure mechanism
  • Nanomanufacturing
  • Precision engineering
  • Precision stage

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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