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%, and Finite Element Analysis for the DP with UE bearings within an average 10%.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- AC52-07NA27344; 31006/12.1.1
- OSTI ID:
- 1313550
- Alternate ID(s):
- OSTI ID: 1397450
- Report Number(s):
- LLNL-JRNL-657740
- Journal Information:
- Precision Engineering, Vol. 46, Issue C; ISSN 0141-6359
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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