Flexure based fibre positioners: design optimisation to follow arbitrary focal plane curvature

TL;DR

This paper presents two complementary methods, analytical and FEA-based, for optimizing flexure geometries to accurately follow arbitrary focal plane curvatures and orientations in fibre positioners.

Contribution

It introduces a combined analytical and FEA approach for flexure design optimization, applicable to various fibre positioner configurations.

Findings

Effective optimization of flexure geometries demonstrated.

Sensitivity analysis links design parameter changes to fibre tip motion.

Applicable to UKATC's WST fibre positioner design.

Abstract

The use of flexures to achieve fibre positioner motion is being actively investigated by several institutes, for example at the UK Astronomy Technology Centre (UKATC) and Leibniz-Institute for Astrophysics Potsdam. One challenge when designing with flexures is the large number of degrees of freedom available which makes it difficult or impossible to optimise their motion by hand. In this paper we demonstrate two approaches for optimising flexure geometry to follow arbitrary focal surface curvature and to orient the optical fibre with arbitrary tilt. These approaches are: analytical using MATLAB models and FEA based using Ansys. The approaches are complementary allowing the designer to efficiently explore the parameter space and then do precise optimisation of the flexure geometry. We demonstrate the applicability both to the UKATCs preferred design for WST, and to flexure-based fibre positioner designs generally. We also present a sensitivity analysis relating small changes in design parameters to changes in fibre tip motion. Finally we briefly present the UKATCs preferred geometry for the WST fibre positioner.