Page 187 - Mechanics of Microelectromechanical Systems
P. 187
174 Chapter 3
An arbitrary point is situated an angle measured from the vertical line
passing through the fixed end.
The radius r corresponding to the generic point P of Fig. 3.43 can be
calculated in the case it varies linearly as:
where is the maximum angle subtended by the spiral. The aim here is to
determine the in-plane compliances that relate the loads which
are shown in Fig. 3. 43, to the corresponding displacements and
The Castigliano’s displacement theorem is applied in order to find the six
compliances of the 3 x 3 symmetric compliance matrix. In the case of a
relatively thick spiral spring (where the maximum radius is less than 10
times the cross-sectional width w), the bending energy is expressed in Eq.
(3.52) and the bending moment is:
The resulting in-plane compliances are:
