Linear displacement by flexure, spring or ?

  1. Linear displacement by flexure, spring or ???

    I'm doing a little project of mine and I have encountered a problem..

    The project is basically a motion platform that moves in three directions at very low forces (few mN). I got the first two direction done (X,Y), but the third is giving me trouble due to the gravitational force.

    Basically I use some very thin metal sheets (flexures) that allow deflection in one direction and none in all others. In X and Y I have no issues with gravity, but in the Z direction the beams own weight and as the force is not applied directly at the centre of the flexures, my whole thing starts to rotate which I don't want. In this image you can see how X and Y sort of look like; you can imagine Z has a problem with it's own weight.

    So I was thinking of maybe using a linear spring that is very stiff in the other directions, or maybe a different method. Do such springs exist at such a stiffness (20 N/m)? Maybe other options? It is at milimeter/few centimeter scale. I can elaborate on the design if necessary!
  2. jcsd
  3. Baluncore

    Baluncore 3,305
    Science Advisor

    You should model the narrow metal straps as thin wires. Then you will see that your first stage is stable, like a pendulum, and hangs from it's 4 corners. But the next stage is an inverted pendulum that will want to fall sideways slightly. That unstable sideways movement may result in some rotation. This becomes a column stability problem.

    To control rotation you need a wide strap at the centre of the hinge rather than one narrow strap at each end. Think of the stage as a circle rather than a rectangle and you will see why the middle is important.
    I would consider using continuous metal shim sheet rather than two narrow strips since it will reduce rotation. Very thin cold rolled brass shim stock is widely available.
    An alternative would be to use two diagonal fibres, (Kevlar or carbon?), in addition to the corner straps, (or fibres where in tension), to prevent rotation.

    When a heavy object is suspended with the intention that it be able to rotate slightly with minimal force, it is not hung from a circular section wire but from a thin band having the same cross sectional area as the wire.

    To counter gravity you will need to present an opposite force. You have not specified how you will set the 3D position of the stage. That missing information will be critical to solving the gravitational bias problem.
  4. AlephZero

    AlephZero 7,248
    Science Advisor
    Homework Helper

    You could design something where the weight of the device is supported by a large airbag. The pressure in the bag will support the weight, and the larger the volume of the bag, the smaller the "spring stiffness" of the air when you deform it by moving your the device vertically.

    You could adjust the vertical "zero position" with a separate device to deform the shape of the bag slightly.
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