skip to main content

SciTech ConnectSciTech Connect

This content will become publicly available on June 23, 2017

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

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
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
OSTI Identifier:
Report Number(s):
Journal ID: ISSN 0141-6359
Grant/Contract Number:
Accepted Manuscript
Journal Name:
Precision Engineering
Additional Journal Information:
Journal Volume: 46; Journal Issue: C; Journal ID: ISSN 0141-6359
Research Org:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org:
Country of Publication:
United States
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