Flexure Mounts For High Resolution Optical Elements

Mir SalekOptomechanics

Fall 2008Review of: Vukobratovich D, Richard R

M, Proc of SPIE Vol. 0959, Jan 1988

Summary What is a flexure? Compare to other mounts Basic types of Flexure Some examples

What is a Flexure By definition, flexure is an elastic element which provides controlled motion

Plunging to the Idea

Lens

Mount

Plunging to the Idea (idea from Yoder’s book)

120º

The Lens

120º

Inward

CT

CR

CT

CT

CR

CR

Points Equal Compliances -> Keeps the lens

centered when temperature changes The spring forces allow the lens to

decenter during shocks and return afterwards

Minimize stress in optics during shocks Typically stiff tangentionally and axially

and compliant radially Uses Kinematic principles to find the

location of flexures

High Performance Lens Assembly Tight tolerance alignment Maintain alignment under

operational level shock, vibration, pressure, temperature change

Retain its alignment upon exposure to survival level of environmental effects

Low stress on optics (particularly mirrors)

Advantages of Flexure Mounts

Free of slick-slip and friction effects of semi-kinematic design

Less hysteresis than rolling or sliding contacts

More robust to adverse environment effects such as extreme temperatures, vacuum, and abrasive dust

Needs very little maintenance if any

* Ideal for space applications

Flexure Material Should provide required

compliance within length limitation Should have high dimensional

stability for repeated use in time

Flexure Material Should have high fracture

toughness Thermal properties to maintain

operation with temperature change

Compliance For a given length:

Higher RTS ->maximum compliance Reduced tensile strength is the ratio

of yield strength to modulus of elasticity.

Dimensional Stability Material instability or room temperature

creep can happen at stresses less than micro-yield strength

Andrea’s Beta Law predicts instability with time:

ε = βtm

m ≈ 0.33

Flexure Design

Basic Flexures: Single Strip Flexure It can be used to guide both

translation and rotation The strain is a function of axial

preload

In the table L is the flexure length; E is the elastic modulus; I is the moment of inertia; P is the applied axial load; θ is the end slope of the flexure; M is the applied torque; δ is the end displacement of the flexure; F is the applied force; .

Strain versus Axial Stressconstant force

Basic Flexures: Cross-Strip Rotational Hinge Two single stripped flexures at right

angles provide a rotational hinge center of rotation shifts as a function of

angle of rotation

Cross-Strip Rotational Hinge: rotation-torque relations

Basic Flexures: Parallel Spring Guide Flexure A pair of parallel single strip guides

provides linear translation The range of motion is limited to 1-2mm also the motion is not purely linear and

there is a height shift as well

Parallel Spring Guide Flexure: Force-Displacement Relations

If the force is not applied at the midpoint, the flexure would tilt as it translates

Basic Flexures: Cruciform Flexure Provides limited rotation in very

confined spaces

Basic Flexures: and Tapered Uniform-Stress Cantilever Flexure It is used to provide a small range of

translation motion in very confined space

Flexure Mount Example 1

Flexure Mount Example 2

Flexure Mount Example 3

Bipod Flexure Mount

Happy Finals