Research Papers: Design of Mechanisms and Robotic Systems

Determinate Synthesis of Symmetrical, Monolithic Tip–Tilt–Piston Flexure Stages

[+] Author and Article Information
Guangbo Hao

School of Engineering-Electrical
and Electronic Engineering,
University College Cork,
Cork, Ireland
e-mail: G.Hao@ucc.ie

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received October 27, 2016; final manuscript received January 27, 2017; published online February 24, 2017. Assoc. Editor: Oscar Altuzarra.

J. Mech. Des 139(4), 042303 (Feb 24, 2017) (9 pages) Paper No: MD-16-1720; doi: 10.1115/1.4035965 History: Received October 27, 2016; Revised January 27, 2017

This paper mainly deals with the determinate design/synthesis of a class of symmetrical and monolithic flexure mechanisms. Each is composed of six identical in-plane wire beams with uniform square cross sections. These flexure stages can provide three out-of-plane tip–tilt–piston motions for applications in high-precision or miniaturization environments. A generic symmetrical structure is proposed at first with a group of defined parameters considering constraint and noninterference conditions. Normalized static analytical compliance entries for the diagonal compliance matrix of a generic structure are derived and symbolically represented by the parameters. Comprehensive compliance analysis is then followed using the analytical results, and quick insights into the effects of parameters on compliances in different directions are gained. Case studies without and with actuation consideration are finally discussed. As a second contribution, a physical prototype with three actuation legs is monolithically fabricated (using computer numerical control milling machining), kinematically modeled, and experimentally tested, which shows that the desired out-of-plane motion can be generated from the in-plane actuation.

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Fig. 2

Several specific structures of the symmetric six-beam mechanism: (a) α = 7π/6, (b) α = 4π/3, (c) α = 3π/2, (d) α = 5π/3, and (e) α = 11π/6

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Fig. 1

Generic structure of the symmetric six-beam mechanism

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Fig. 3

Change of c44 for different conditions of parameters

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Fig. 4

Change of c44/c66 for different conditions of parameters

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Fig. 5

Change of ri for different conditions of parameters

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Fig. 6

CAD model of the 3-DOF six-beam mechanism: (a) top view before deformation, (b) 3D view before deformation, (c) translation along the Z-axis in FEA, and (d) rotation about the X-axis in FEA

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Fig. 8

The fabricated prototype and initial experimental testing: (a) no actuation exerted, (b) three equal actuation forces/displacements exerted, (c) one actuation force exerted, and (d) center testing using micrometers and dial gauge

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Fig. 9

Comparisons of kinematics: (a) output translation for single-axis actuation, (b) output rotation for single-axis actuation, and (c) output translation for three equal actuations

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Fig. 7

The monolithic manipulator with three symmetric actuation legs: (a) top view before deformation, (b) 3D view before deformation, (c) three equal actuation forces resulting in translation along the Z-axis only, using FEA, and (d) one actuation force resulting in coupling rotation and translation for the center, using FEA



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