  Unlike conventional mechanisms, compliant mechanisms produce the desired
deformations by exploiting elastic strain and do not need, therefore, moving
parts. The number of degrees of freedom of a conventional mechanism, also
called mobility, is the number of independent coordinates needed to define a
configuration of the mechanism. Due to the different operating principle, such
definition of degree of freedom or mobility cannot be directly applied to
compliant mechanisms. While those terms are not able to denote a property of a
given compliant mechanism, they are meaningful when applied to the design of a
compliant mechanism. Compliant mechanisms are, however, mostly seen as elastic
structures, for which the term degree of freedom is used in a different
meaning. In order to avoid ambiguities, the term pseudo-mobility (already
introduced in previous published work) will be used to denote the number of
scalar parameters needed to identify one single desired deformation, i.e. one
single deformation for which the compliant mechanism is designed. Many
synthesis approaches exist for compliant mechanisms with single pseudo-mobility
(commonly referred to as "single degree of freedom mechanisms"). In the case of
compliant mechanisms with multiple pseudo-mobility (multiple-degree of freedom
mechanisms), only synthesis approaches for relatively simple mechanisms exist
so far, while systems for more complex tasks like shape adaptation are not
covered. In addition, only certain cases of transverse loads are included in
the synthesis with these approaches. In this paper, a novel optimization
algorithm is presented that addresses these two shortcomings. The algorithm is
tested on a simple mechanism with one translation and one rotation kinematic
degree of freedom, a compliant parallel mechanism for pure translation and a
shape-adaptive structure.
