A flexure guiding with 2 leaf springs or flexures in parallel are often use as a (quasi-) linear guidance were play must be eliminated. This sheet allows you to design such a construction, how to reinforce it and how to eliminate the parasitic motion.
Well predictable stiffness (Cx)
Parasitic displacements (uz )
(small) Stiffness in direction of movement
Through a double parallel leaf spring (in series) the parasitic displacement can be eliminated, like:
The drive stiffness (Cx) halves; however the guiding stiffness (Cz) halves as well.
For machinability, often reinforced leaf springs or 2 elastic hinges in series are used as an alternative per leaf spring. If so use the following guide-lines:
Each flexure with then:
(elastic hinge guide line)
dynamic movements: fatigue stress limit
quasi-static movements: yield stress limit ()
Essentially, 2 parallel leaf springs are over constrained. This could be overcome if internal elasticity is introduced like low torsion stiffness of the moving body or notching 1 out of 2 leaf springs. Practically, the best way is to machine the fixed world, the leaf spring and the moving body monolithically.
To ensure identical normal force on each leaf spring and thus; a pure linear guidance, the force Fx should be applied at as depicted below.
Enter your data and get this sheet in PDF format for free, including a handy Mathcad calculator (xmcd file)!