  The synthesis of compliant mechanisms (CMs) is frequently achieved through
topology optimization. Many synthesis approaches simplify implementation by
assuming small distortions, but this limits their practical application since
CMs typically undergo large deformations that include geometric and material
nonlinearities. CMs designed to generate a desired deformation path at the
output points under specific loads are known as path-generating CMs. However,
these CMs face significant challenges in topology optimization, resulting in
the development of only a few optimization methods. Existing approaches often
include only certain load cases in the optimization process. Consequently, if a
CM designed this way encounters different load cases in practice, its
path-generating behavior cannot be guaranteed.
  The authors have previously contributed to the development of an approach
suitable for synthesizing load case insensitive CMs. This paper extends that
approach to account for nonlinearities, enabling the synthesis of
path-generating CMs. The effectiveness of this extended approach is
demonstrated through appropriate design examples. Additionally, the paper
presents, for the first time, a shape-adaptive path-generating CM.
