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I have recently discovered flexure springs (see image below), and I am interested in using one in an amateur project I am building.

However, I would prefer if I am able to adjust the "stiffness" of the flexure spring, to allow the spring to bear different loads.

Despite extensive searching online, I have not found a flexure spring design that provides flexible or adaptable stiffness.

Is it possible to have a flexure spring, the stiffness of which, can be adjusted?

enter image description here

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In your case the adjustable stiffens can be archived by modifying the shape from the spring. If you use different stiffens and allow some blocking this can be achieved. See screenshot. enter image description here