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Research Papers

Analysis and Design of a Spherical Micromechanism With Flexure Hinges

[+] Author and Article Information
Massimo Callegari

Department of Mechanics, Polytechnic University of Marche, Ancona 60131, Italym.callegari@univpm.it

Alessandro Cammarata

Department of Industrial and Mechanical Engineering, University of Catania, Catania 95125, Italyacamma@diim.unict.it

Andrea Gabrielli

Department of Mechanics, Polytechnic University of Marche, Ancona 60131, Italyandrea.gabrielli@univpm.it

Maurizio Ruggiu

Department of Mechanical Engineering, University of Cagliari, Cagliari 09123, Italyruggiu@dimeca.unica.it

Rosario Sinatra

Department of Industrial and Mechanical Engineering, University of Catania, Catania 95125, Italyrsinatra@diim.unict.it

J. Mech. Des 131(5), 051003 (Apr 03, 2009) (11 pages) doi:10.1115/1.3086796 History: Received April 11, 2008; Revised January 08, 2009; Published April 03, 2009

The article describes the design of a robotic wrist able to perform spherical motions: Its mechanical architecture is based on parallel kinematics and is suitable to be realized at the mini- or microscale by means of flexible joints. In view of the preliminary design, a rigid-body model has been studied first and the direct and inverse kinematic analyses have been performed, allowing for the determination of theoretical workspace and passive joints’ displacements. The rigid-body dynamic behavior and the operative ranges of the machine have been assessed through the development of an inverse dynamics model. Then, the microparts have been designed with the help of finite element method (FEM) and multibody software and the study has been focused on the flexures: Since the analyses showed that the center of the spherical motion moves around several millimeters in the workspace, the original kinematic concept has been modified with the introduction of a ball joint constraining the mobile platform to frame so as to prevent unwanted translations.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 9

Mapping of the inverse of the condition number, kF−1(JO′), inside the restricted workspace

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Figure 1

Scheme of the 3-CRU spherical parallel mechanism

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Figure 2

Kinematic scheme of the ith limb

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Figure 3

Definition of the new frames used to define the operative workspace of the wrist

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Figure 4

Translation singularities’ maps for ψ equal to 0 deg, 40 deg, and 90 deg

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Figure 5

Comparison among the limit spheres (a) and mapping of the inner sphere into the joint space (b)

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Figure 6

Subspace generated by the limited stroke of the actuators for ψ=0

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Figure 7

Ellipsoids of manipulability of force in the Tait–Bryan angle space

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Figure 8

Mapping of the inverse of the condition number, kF−1(JO′), for ψ equal to −30 deg, −15 deg, 0 deg, 15 deg, and 30 deg

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Figure 10

Force of the first actuator for motions with frequencies 0.1 Hz (a), 1 Hz (b), and 10 Hz (c)

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Figure 11

Dynamic ellipsoids of manipulability of the wrist in the Tait–Bryan angle space

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Figure 12

Design of the legs

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Figure 13

Details of the flexure hinges R1, R2, R3, and R4 (the directions of the principal stresses at one sample point are shown with indication of the traction/compression state)

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Figure 14

FEM model of the 3-CRU+S wrist: field of displacements (a) and von Mises equivalent stresses (b)

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Figure 15

The Tait–Bryan angle workspace of the 3-C̱RU+S wrist (by FEM analysis of flexible model)

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