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302                                                         Chapter 5
















              Figure 5.37  Input and output displacements for a sagittal displacement amplification
                           microdevice: (a) quarter model; (b) full model

         Example 5.17
             Express the  input and output  stiffnesses, as  well  as the displacement
         amplification of the microdevice with four curved flexure hinges sketched in
         Fig. 5.27.  The  quarter-model of this  sagittal microdevice, together  with the
          defining geometry, are shown in Fig. 5.38.






















           Figure 5.38 Quarter-model of displacement-amplification microdevice with four curved
                                       flexure hinges

          Solution:
             The curvature radius  of the  flexure  is  R and the  corresponding  center
          angle (not indicated in Fig. 5.38) is   The lengths of the two adjoining rigid
          links are   and    respectively. The  input  stiffness, output stiffness  and
          displacement amplification are calculated in a manner similar to the one used
          for the straight-flexure quarter-model analyzed previously.
              The reaction  moment    which is set when the force F acts at point 1,
          can be found by  considering that the rotation at point 2  is zero  (the circular
          flexure remains  rigidly  connected to  the  link 1-2  at  that  point). It  is
          considered that the local frame indicated in Fig.  1.20 of Chapter  1,  it is also
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