What is a crescent flexure (kinematic flexure in precision engineering)?

[kbad]

I'm reading 'Precision Mechanics Notes' by David Kittell and on page number 14, the author talks about 'crescent flexure'. From the given description and the drawing, I'm not able to understand the construction and working of the described kinematics flexure. Can you describe the construction and working of this kinematic arrangement or share more resources (links/ books/ videos) especially for single DoF motion?

 

[desertfox]

Hi
It might help if you can post a pdf of the drawing you are referring to.

“Do not worry about your problems with mathematics, I assure you mine are far greater.” Albert Einstein

 

[IRstuff]

Not sure what the issue is; there are two annular/round pieces with tabs that attach to the 3 crescents that are between them.

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[rb1957]

so "crescent flexure" is flexure of crescents ?

not sure what they mean by "grounded at the outside ends" as a way to react the two out-of-plane moments.

so this cunning design is essentially a single degree of freedom spring ?

another day in paradise, or is paradise one day closer ?

 

[IRstuff]

inside halve rigidly connected, and outside halves rigidly connected eliminates the ability to tilt, so only left with z-axis

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[IRstuff]

These aren't necessarily intended to be cunning, the book is about precision positioning

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[kbad]

@IRstuff Thanks for posting the source picture.
"inside halve rigidly connected, and outside halves rigidly connected eliminates the ability to tilt, so only left with z-axis"
I still don't understand what it means, the construction and how it works.

 

[3DDave]

Using 2 of the planar control flexures - that is, each one constrains 2 degrees of freedom, at each end of a tube; they also control twist around the z-axis, but since they both control the same motion, that adds up to 2 + 2 + 1 degrees of freedom, or 5. That leaves only translation in Z as the major degree of freedom, though they recognize that because it forms a helical deformation that Z translation produces a slight twist around the Z axis, which with axi-symmetric lenses is not noticeable