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. 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%.

Kinematic analysis of parallel transfer mechanism

“…Parallel displacement is obtained for several lifting mechanisms using a double parallelogram linkage [2] or single parallelogram [3] linkage. The application of the pantograph mechanism, which contains a parallelogram [4] allows to easily control the manipulator in 3D space. Slider movement accuracy in parallel displacement is one of the most important indicators for evaluating the operation of press mechanisms.…”