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Title: Large displacement behavior of double parallelogram flexure mechanisms with underconstraint eliminators

Abstract

This paper presents a new analytical method for predicting the large displacement behavior of flexural double parallelogram (DP) bearings with underconstraint eliminator (UE) linkages. This closed-form perturbative Euler analysis method is able to – for the first time – directly incorporate the elastomechanics of a discrete UE linkage, which is a hybrid flexure element that is linked to ground as well as both stages on the bearing. The models are used to understand a nested linkage UE design, however the method is extensible to other UE linkages. Design rules and figures-of-merit are extracted from the analysis models, which provide powerful tools for accelerating the design process. The models, rules and figures-of-merit enable the rapid design of a UE for a desired large displacement behavior, as well as providing a means for determining the limits of UE and DP structures. This will aid in the adoption of UE linkages into DP bearings for precision mechanisms. Models are generated for a nested linkage UE design, and the performance of this DP with UE structure is compared to a DP-only bearing. As a result, the perturbative Euler analysis is shown to match existing theories for DP-only bearings with distributed compliance within ≈2%, andmore » Finite Element Analysis for the DP with UE bearings within an average 10%.« less

Authors:
ORCiD logo [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1313550
Report Number(s):
LLNL-JRNL-657740
Journal ID: ISSN 0141-6359
Grant/Contract Number:
AC52-07NA27344; 31006/12.1.1.A.4; LLNL-JRNL-657740
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Precision Engineering
Additional Journal Information:
Journal Volume: 46; Journal Issue: C; Journal ID: ISSN 0141-6359
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; underconstraint elimination; four-bar flexure; folded flexure; double parallelogram flexure; nested linkage; nonlinear beam analysis; elastokinematic effect; large displacement axial stiffness; large stroke; flexure mechanism

Citation Formats

Panas, Robert M. Large displacement behavior of double parallelogram flexure mechanisms with underconstraint eliminators. United States: N. p., 2016. Web. doi:10.1016/j.precisioneng.2016.06.010.
Panas, Robert M. Large displacement behavior of double parallelogram flexure mechanisms with underconstraint eliminators. United States. doi:10.1016/j.precisioneng.2016.06.010.
Panas, Robert M. 2016. "Large displacement behavior of double parallelogram flexure mechanisms with underconstraint eliminators". United States. doi:10.1016/j.precisioneng.2016.06.010. https://www.osti.gov/servlets/purl/1313550.
@article{osti_1313550,
title = {Large displacement behavior of double parallelogram flexure mechanisms with underconstraint eliminators},
author = {Panas, Robert M.},
abstractNote = {This paper presents a new analytical method for predicting the large displacement behavior of flexural double parallelogram (DP) bearings with underconstraint eliminator (UE) linkages. This closed-form perturbative Euler analysis method is able to – for the first time – directly incorporate the elastomechanics of a discrete UE linkage, which is a hybrid flexure element that is linked to ground as well as both stages on the bearing. The models are used to understand a nested linkage UE design, however the method is extensible to other UE linkages. Design rules and figures-of-merit are extracted from the analysis models, which provide powerful tools for accelerating the design process. The models, rules and figures-of-merit enable the rapid design of a UE for a desired large displacement behavior, as well as providing a means for determining the limits of UE and DP structures. This will aid in the adoption of UE linkages into DP bearings for precision mechanisms. Models are generated for a nested linkage UE design, and the performance of this DP with UE structure is compared to a DP-only bearing. As a result, the perturbative Euler analysis is shown to match existing theories for DP-only bearings with distributed compliance within ≈2%, and Finite Element Analysis for the DP with UE bearings within an average 10%.},
doi = {10.1016/j.precisioneng.2016.06.010},
journal = {Precision Engineering},
number = C,
volume = 46,
place = {United States},
year = 2016,
month = 6
}

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