A stiffness model for control and analysis of a MEMS hexapod nanopositioner

Abstract This paper presents a stiffness-based kinematic model for analysis and control of a Micro-Electro-Mechanical Systems (MEMS) flexure-based hexapod nanopositioner that was previously built by the National Institute of Standards and Technology (NIST). This nanopositioner is capable of producing high-resolution motions in 6 degrees of freedom (DOF) by actuating three planar X–Y positioning stages. Given a large number of flexure-based nanopositioners, the modeling and controller design has been a challenging task due to their inherent structural complexity and difficulties in measuring 6DOF positioning accuracy. In this paper, we discuss kinematic models for developing an open loop controller and an analytical approach routine for this nanopositioner. These models include a novel model for calculating the nonlinear stiffness of the X–Y positioning stage and a stiffness-based Jacobian matrix of the hexapod mechanism for the controller. Compared with Finite Element (FE) simulations, we conclude that the mean error of the X–Y stage control model is 1.93 % within a 55 μm range of motion. To validate the control model, the top platform is commanded to trace a circle of diameter 20 μm. The result shows a mean error of 3.38 %.

[1]  Nicholas G. Dagalakis,et al.  Microelectromechanical systems based Stewart platform with sub-nano resolution , 2012 .

[2]  Kazuhiro Hane,et al.  Design and fabrication of GaN crystal ultra-small lateral comb-drive actuators , 2012 .

[3]  Larry L. Howell,et al.  Design and characterization of a dual-stage, thermally actuated nanopositioner , 2005 .

[4]  Nicholas G. Dagalakis,et al.  Creating large out-of-plane displacement electrothermal motion stage by incorporating beams with step features , 2013 .

[5]  Johannes Bernardus Charles Engelen.  Optimization of Comb-Drive Actuators [Nanopositioners for probe-based data storage and musical MEMS] , 2011 .

[6]  Stuart T. Smith,et al.  Flexures: Elements of Elastic Mechanisms , 2000 .

[7]  Placid Mathew Ferreira,et al.  Design analysis, fabrication and testing of a parallel-kinematic micropositioning XY stage , 2007 .

[8]  John T. Wen,et al.  Analysis and design of parallel mechanisms with flexure joints , 2005, IEEE Trans. Robotics.

[9]  P. Ferreira,et al.  A SOI-MEMS-based 3-DOF planar parallel-kinematics nanopositioning stage , 2008 .

[10]  Hai-Jun Su,et al.  An Analytical Model for Calculating the Workspace of a Flexure Hexapod Nanopositioner , 2013 .

[11]  S. O. R. Moheimani,et al.  A 2-DOF Electrostatically Actuated MEMS Nanopositioner for On-Chip AFM , 2012, Journal of Microelectromechanical Systems.

[12]  Mehmet Rasit Yuce,et al.  A micromachined 2DOF nanopositioner with integrated capacitive displacement sensor , 2010, 2010 IEEE Sensors.

[13]  Tien-Fu Lu,et al.  Review of circular flexure hinge design equations and derivation of empirical formulations , 2008 .

[14]  Y. K. Yong,et al.  Design of an Inertially Counterbalanced $Z$ -Nanopositioner for High-Speed Atomic Force Microscopy , 2013, IEEE Transactions on Nanotechnology.

[15]  Hai-Jun Su,et al.  Workspace of a Flexure Hexapod Nanopositioner , 2012 .

[16]  K. Leang,et al.  Design and Control of a Three-Axis Serial-Kinematic High-Bandwidth Nanopositioner , 2012, IEEE/ASME Transactions on Mechatronics.

[17]  Jim Euchner.  Design , 2014, Catalysis from A to Z.

[18]  Shorya Awtar,et al.  Characteristics of Beam-Based Flexure Modules , 2007 .

[19]  Nicholas G. Dagalakis,et al.  Design, fabrication and testing of a serial kinematic MEMS XY stage for multifinger manipulation , 2012 .

[20]  Dannis Michel Brouwer,et al.  Design and modeling of a six DOFs MEMS-based precision manipulator , 2010 .

[21]  P. Gao,et al.  A new piezodriven precision micropositioning stage utilizing flexure hinges , 1999 .

[22]  Weibin Rong,et al.  A silicon integrated micro nano-positioning XY-stage for nano-manipulation , 2008 .

[23]  Il Hong Suh,et al.  Design and experiment of a 3-DOF parallel micromechanism utilizing flexure hinges , 2002, IEEE Trans. Robotics Autom..

[24]  Nicholas G. Dagalakis,et al.  AFM characterization of nanopositioner in-plane stiffnesses , 2010 .

[25]  Placid Mathew Ferreira,et al.  A novel parallel-kinematics mechanism for integrated, multi-axis nanopositioning: Part 2: Dynamics, control and performance analysis , 2008 .

[26]  Shuo-Hung Chang,et al.  A six-DOF prismatic-spherical-spherical parallel compliant nanopositioner , 2008, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[27]  Yuen Kuan Yong,et al.  Design, Modeling, and FPAA-Based Control of a High-Speed Atomic Force Microscope Nanopositioner , 2013, IEEE/ASME Transactions on Mechatronics.

[29]  YunJian Ge,et al.  Micromanipulator with integrated force sensor based on compliant parallel mechanism , 2010, 2010 IEEE International Conference on Robotics and Biomimetics.

[30]  Xinbo Huang,et al.  A new generalized model for elliptical arc flexure hinges. , 2008, The Review of scientific instruments.

[31]  Hai-Jun Su,et al.  A Symbolic Formulation for Analytical Compliance Analysis and Synthesis of Flexure Mechanisms. , 2012, Journal of mechanical design.

[32]  S. O. R. Moheimani,et al.  A Low-Flicker-Noise MEMS Electrothermal Displacement Sensing Technique , 2012, Journal of Microelectromechanical Systems.

[33]  Malgorzata Kujawinska,et al.  A two directional electrostatic comb-drive X–Y micro-stage for MOEMS applications , 2010 .

[34]  Nicolae Lobontiu,et al.  Compliant Mechanisms: Design of Flexure Hinges , 2002 .

[35]  Il Hong Suh,et al.  Design and experiment of a 3 DOF parallel micro-mechanism utilizing flexure hinges , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[36]  Nicholas G. Dagalakis,et al.  Kinematic modeling and calibration of a flexure based hexapod nanopositioner , 2013 .

[37]  Herman Soemers,et al.  Design principles for precision mechanisms , 2011 .