1. Flexure Mounts For High Resolution Optical Elements
Mir Salek
Optomechanics
Fall 2008
Review of: Vukobratovich D, Richard R M, Proc of SPIE Vol. 0959, Jan 1988

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

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

4. Plunging to the Idea
Lens
Mount

5. Plunging to the Idea (idea from Yoder’s book)CR
Inward CT
The Lens
120º CT
120º CR CT CR

6. 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

7. 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)

8. 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

9. Flexure Material
Should provide required compliance within length limitation
Should have high dimensional stability for repeated use in time

10. Flexure Material Should have high fracture toughness
Thermal properties to maintain operation with temperature change

11. Compliance For a given length: Higher RTS ->maximum compliance
Reduced tensile strength is the ratio of yield strength to modulus of elasticity.

12. 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

13. Flexure Design

14. Basic Flexures: Single Strip Flexure
It can be used to guide both translation and rotation
The strain is a function of axial preload

16. 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; .

17. Strain versus Axial Stress constant force

18. 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

19. Cross-Strip Rotational Hinge: rotation-torque relations

20. 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

21. Parallel Spring Guide Flexure: Force-Displacement Relations
If the force is not applied at the midpoint, the flexure would tilt as it translates

22. Basic Flexures: Cruciform Flexure
Provides limited rotation in very confined spaces

23. Basic Flexures: and Tapered Uniform-Stress Cantilever Flexure
It is used to provide a small range of translation motion in very confined space

24. Flexure Mount Example 1

25. Flexure Mount Example 2

26. Flexure Mount Example 3

27. Bipod Flexure Mount

28. Happy Finals