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Research Papers

An Analytical Model for Calculating the Workspace of a Flexure Hexapod Nanopositioner

[+] Author and Article Information
Hongliang Shi

e-mail: shi.347@osu.edu

Hai-Jun Su

e-mail: su.298@osu.edu
Department of Mechanical and
Aerospace Engineering,
The Ohio State University,
Columbus, OH 43210

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received September 14, 2012; final manuscript received June 19, 2013; published online September 11, 2013. Assoc. Editor: Anupam Saxena.

J. Mechanisms Robotics 5(4), 041009 (Sep 11, 2013) (8 pages) Paper No: JMR-12-1143; doi: 10.1115/1.4025041 History: Received September 14, 2012; Revised June 19, 2013

This paper presents an analytical model for calculating the workspace of a flexure-based hexapod nanopositioner previously built by the National Institute of Standards and Technology (NIST). This nanopositioner is capable of producing high-resolution motions in six degrees of freedom by actuating linear actuators on a planar tri-stage. However, the workspace of this positioner is still unknown, which limits its uses in practical applications. In this work, we seek to derive a kinematic model for predicting the workspace of such kinds of flexure based platforms by assuming that their workspace is mainly constrained by the deformation of flexure joints. We first study the maximum deformation including bending and torsion angles of an individual flexure joint. We then derive the inverse kinematics and calculation of bending and torsion angles of each wire flexure in the overall mechanism with given position of the top platform center of the hexapod nanopositioner. At last, we compare results with finite element models of the entire platform. This model is beneficial for workspace analysis and optimization for design of compliant parallel mechanisms.

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Figures

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Fig. 1

The NIST hexapod nanopositioner

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Fig. 2

The workspace of a planar rigid body RR open chain

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Fig. 3

A flexure wires subject to a torque T about its centerline

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Fig. 4

Calculation of bending and torsion angles

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Fig. 5

The short wire is subject to a bending moment τ. The cross section of both ends is constrained in plane.

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Fig. 6

The von Mises and bending angle ψ versus the bending moment τ

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Fig. 7

The kinematic model of the positioner

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Fig. 8

Geometrical description of the top platform and the bottom stages

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Fig. 9

Calculation of bending and torsion angles

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Fig. 10

Flow chart of searching for the maximum θz with specified translation δx,δy,δz and θx,θy

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Fig. 11

The orientation workspace of the positioner at the home position by analytical model

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Fig. 12

The orientation workspace of the positioner at the home position by analytical model, δx = δy = δz = 0

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Fig. 13

Deformation of flexure joints when platform moves along the z axis

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Fig. 14

Assembly of the joint 6 to the stage and strut

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Fig. 15

Rotation of platform along the z axis

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