Page 189 - Mechanics of Microelectromechanical Systems
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176 Chapter 3
Example 3.17
Consider that point 1 in Fig. 3.43 is confined to move about the x-
direction. Find the stiffness of a thin spiral spring with small number of turns
knowing and
Solution:
The stiffness about the x-direction in this case can be found after
determining the reactions and When taking into account that the y-
displacement and z-rotation at point 1 are zero, the unknown reactions can be
written in terms of in the form:
where and are functions of and After finding the x-
displacement at point 1 as a function of and the geometry/material
properties defining the spiral, the corresponding stiffness about the x-direction
(according to the definition) can be expressed as:
The function is too complex to be presented here, but Fig. 3.44
shows the variation of the stiffness about the x-direction as a function of the
