Linear Spring Compliant Mechanisms — Designing/Calculating Force and Deflection

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Curious if anyone has advice on how to design “Spring” dimensions for intended deflection force and distance? Wondering if there’s a simple formula or online calculator for this scenario, or if I should learn to use something like CalculiX, Elmer FEM, FEniCS finite element analysis software ( FEM - Finite Element Method )?

Am trying to mount a Stepper motor onto a plate with built in linear spring compliant mechanism to give it some limited motion (max 5mm left), want initial resistive force ~30N at 0mm deflection, then increase resistive force from there (non linear increase is good). PETG 2.1GPa. Here’s a basic example to help visualize what I’m doing, it’s incomplete and missing rotation constraints…

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Am NOT trying to design a Constant-Force Mechanism like this cool contraption https://www.printables.com/model/583491-constant-force-mechanism…

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Rather, I’m trying to make “regular linear springs which yield an increased force with greater displacements”.

Think I’m trying to do something basic, despite all the cool things that can be done with compliant mechanisms, e.g. see BYU CMR’s research, or BYU CMR’s Compliant Mechanism models on Printables.

Guessing there’s an online calculator for “Linear spring compliant mechanism” that I’ll stumble onto it as soon as I send this out… Cheers!

EDIT: fwiw - am kicking off test print(s) in parallel while I try to learn enough Freedom and constraint topologies (FACT), FEM theory on things like /software to get this done. Using FEM is probably overkill for this scenario, but would be nice to learn and use before making more time/material costly Alu iteration(s) later on.

EDIT: meh, this is good enough…

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That looks really cool and I like your intuition. I did not study mechanical engineering in school, so FEM is a mystery to me. I think it would be hard to calculate with 3D printing because of the way it is manufactured. And I doubt there would be a reference design for this kind of thing the best you could get is to simulate molded plastic part and get the force to displacement graph.

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Mech E is also not my discipline- and its been decades since I was in school.

Amongst the students and practicing professionals I work with, the Mech Es have FEM approaches for modelling an array of additive manufacturing processes and they seem to yield good results and be fairly well correlated for common technologies.

Really interesting stuff.