Abstract
The objective of this paper is to develop a modified strain gradient
beam constraint model (MSGBCM) to improve modeling accuracy of
small-scale compliant mechanisms. First, a simple nano/micro flexure
beam under the effect of end loads is considered. The virtual work
principle is employed to formulate the load-displacement behavior of the
system based on the modified strain gradient theory. It is observed that
as the size of the structure becomes smaller, the elements of the
elastic stiffness and load stiffening matrices severely deviate from
their corresponded values in the beam constraint model (BCM). Then, a
closed-form expression is proposed for the nonlinear strain energy of
the nano/micro flexure beams in terms of their tip displacements. This
energy expression is then utilized to model load-displacement
relationship of micron/submicron size parallelogram (P) flexures.
Moreover, analytical formulas are derived for the axial, transverse and
rotational stiffnesses of P-flexures. The most important observation is
that the axial stiffness loss of small-scale P-flexures resulted from
the movement of the stage in the transverse direction, may be seriously
overestimated by the BCM. The MSGBCM developed in this paper can be
easily extended for investigating static and dynamic behavior of more
complex micron and submicron size flexure units.