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After substitution in (2.13), the second equation of equilibrium becomes d2

dr D

With the hypothesis (2.1) of paraboloid flexure generating a curvature 1/R = 2A20 when external forces are applied, and since dD/D = 3dt/t, the substitutions in (2.28) and (2.31) lead to the system (Ferrari [17, 18])

d2u /1 dt 1\ du iv dt 1\ u /1 dt 3 - v\ r2 dr2 I t dr r j dr \ t dr r ) r \ t dr r ) 2R2 '

du u t dt r , R Qr d-r +v ;- 3(1+v) rdr + 2r2 +12(1 - v2) rEt = °,

requiring a numerical integration. This was carried out for the design of some VCM with large zoom range.

For each of three VTD types studied in Sect. 2.1.2, the associated shearing force Qr is expressed by (2.15), (2.18), or (2.20). The boundary conditions are defined by a null thickness at the edge and a finite radial elongation e0 at the center t) = 0, (ddU) = £o . (2.33)

Given a VTD type, the integration is carried out by use of dimensionless variables r rr u T t q o

0 0

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