Department of Biomechanical Engineering, Faculty of Mechanical, Maritime and Materials Engineering, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands
Copyright © 2009 N. Tolou and J. L. Herder. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The deflection of compliant mechanism (CM) which involves geometrical nonlinearity due to large
deflection of members continues to be an interesting problem in mechanical systems. This paper deals
with an analytical investigation of large deflections in compliant mechanisms. The main objective is to
propose a convenient method of solution for the large deflection problem in CMs in order to overcome
the difficulty and inaccuracy of conventional methods, as well as for the purpose of mathematical
modeling and optimization. For simplicity, an element is considered which is a cantilever beam out of
linear elastic material under vertical end point load. This can further be used as a building block in
more complex compliant mechanisms. First, the governing equation has been obtained for the
cantilever beam; subsequently, the Adomian decomposition method (ADM) has been utilized to obtain
a semianalytical solution. The vertical and horizontal displacements of a cantilever beam can
conveniently be obtained in an explicit analytical form. In addition, variations of the parameters that
affect the characteristics of the deflection have been examined. The results reveal that the proposed
procedure is very accurate, efficient, and convenient for cantilever beams, and can probably be applied
to a large class of practical problems for the purpose of analysis and optimization.