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σ / MPa 700 600 500 400

σ / MPa 700 600 500 400 300 200 100 0 4 – FUNDAMENTALS 10 4 10 5 10 6 10 7 Number of Cycles Figure 4.2: Ti-6Al-4V fatigue tests [4]. Figure 4.3 (left) shows the main principle of the stage with two parallel blades. The formulas for calculating the deflection, the rigidity and the buckling load for this FH structure are deduced in [4] using the approximated Euler-Bernoulli beam theory. The formula for the deflection f thereby follows to f = P l3 . (4.2) 2Ebh3 It is obvious that the length l and the thickness h have the highest significance for the blade dimensioning, because they raise to the power of three. P characterizes the force applied on the FH and is reasonably equal to the force generated by the VCA, which will be introduced in chapter 4.3. The rigidity, which is represented by the spring constant c, can be calculated with and the buckling load Nc with c = 24EI l 3 , (4.3) Nc = 8π2 EI l 2 . (4.4) 16

P d Parallel Spring Stage Parabolic Translation (1 Degree-of-Freedom (DOF)) l/2 Mobile Block A B l e h b f λ S. Henein, Slide 3.8 4 – FUNDAMENTALS Linear stage with necked down flexu Mobile Bloc mobile block d P l/2 A B l e f b Fixed Bloc de base Figure 4.3: Stage with two parallel blades (left) and linear stage with necked down flexures (right) [4]. 2lc ξ = 0 < ξ ≤ 1 l l c h l ξ = 1 ξ → 0 λ P f C M N For a given stroke f and given outer dimension what is the optimal hinge length l c ? Figure 4.4: Occuring blade deflections during the wire-cut EDM process limit the maximum aspect ratio aF H = l/h [4]. 17

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