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Research Papers: Mechanisms and Robotics

Analysis of Rotational Precision for an Isosceles-Trapezoidal Flexural Pivot

[+] Author and Article Information
Pei Xu

Robotics Institute, Beihang University, Beijing, 100083, P.R.C.peixu@me.buaa.edu.cn

Yu Jingjun

Robotics Institute, Beihang University, Beijing, 100083, P.R.C.jjyu@buaa.edu.cn

Zong Guanghua

Robotics Institute, Beihang University, Beijing, 100083, P.R.C.ghzong@buaa.edu.cn

Bi Shusheng

Robotics Institute, Beihang University, Beijing, 100083, P.R.C.ssbi@buaa.edu.cn

Yu Zhiwei

Robotics Institute, Beihang University, Beijing, 100083, P.R.C.

J. Mech. Des 130(5), 052302 (Mar 25, 2008) (9 pages) doi:10.1115/1.2885507 History: Received February 01, 2007; Revised July 25, 2007; Published March 25, 2008

An isosceles-trapezoidal flexural pivot can be of great use for practical designs, especially in the cases that a pure rotation about a virtual pivot is required. The analysis of rotational precision for such a structure is important for the mechanical design in precise-required applications. For this purpose, a rigid isosceles-trapezoidal linkage model is first proposed to provide an accurate analytical result for its notch-type flexural counterpart. The influence of dimensional parameters on the center shift is discussed. In order to disclose the equivalence between leaf-type flexure structure and its pseudo-rigid-body model, a transitional model is introduced, from which an equivalent pseudo-rigid-body model for leaf-type isosceles-trapezoidal flexure structure is then derived. The results of both simulation and experiment verify that the equivalent rigid model is also accurate enough in the case of a larger deflection.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

An isosceles trapezoidal structure: (a) four bar linkage, (b) notch type, and (c) leaf type

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Figure 2

Two large-deflection flexural pivots: (a) a cartwheel hinge and (b) a butterfly flexural pivot

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Figure 3

Four kinds of criterions to evaluate the rotational precision: (a) offset of the center point, (b) offset of the intersection of the tangent to the free end of the cantilever with the unloaded beam axis, (c) distance between the pseudo-rigid-body and the actual deflected flexure body, and (d) offset of the fixed center point

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Figure 4

Model of the isosceles-trapezoidal four-bar mechanism: (a) parameterized model, and (b) center-shift

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Figure 5

The influence on δ and γ by different parameters of the rigid-body model: (a) δ versus θ, (b) γ versus θ, (c) δ versus φ, (d) γ versus φ, (e) δ versus h, (f) γ versus h, (g) δ versus H, (h) γ versus H, (i) δ versus φ, and (j) γ versus φ and h

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Figure 14

Comparisons of results of experiment, simulation, and pseudo-rigid-body model for the trapezoid structure: (a) Structure I and (b) Structure II

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Figure 15

Comparisons of the simulated results and the equivalent rigid model: (a) φ varies and (b) h varies

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Figure 16

The errors caused by the pseudo-rigid-body model: (a) the case of applied force and (b) the case of applied moment

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Figure 17

The position of center: (a) the case of applied force and (b) the case of applied moment

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Figure 13

Experimental setup: (a) overview and (b) specimen of Structure I

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Figure 12

Position of rotational center versus m and P

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Figure 11

Equivalence relation between flexure model (left) and rigid model (right)

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Figure 10

Position of rotational center versus R and P

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Figure 9

Leaf-type isosceles-trapezoidal flexure model: (a) isosceles-trapezoidal flexure, (b) analytic model, and (c) single leaf spring

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Figure 8

Comparisons of the rigid model and the transitional model

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Figure 7

Equivalence relationship between the transitional model (left) and the rigid model (right)

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Figure 6

A transitional model of leaf-type isosceles-trapezoidal flexural pivot: (a) transitional isosceles-trapezoidal flexure, (b) analytic model, and (c) single leaf spring

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