  This paper studies the equilibrium formulation of a three degree of freedom
planar compliant platform mechanism, which is in contact with a solid body in
its environment. The mechanism includes two platforms, which are connected in
parallel by three linear springs. The capability of deformation by manipulating
both platforms exceptionally complicates the problem. The analysis aims to
determine all equilibrium configurations for two different cases: FIRST CASE
all three springs have zero free lengths and SECOND CASE only two of the
springs have zero free lengths. The proposed procedure calculates the pose of
the top platform when it is not in contact with the surface, and then detects
if the top platform is in contact to determine the equilibrium configurations.
To solve the geometric equations of the mechanism, we use Sylvester method of
elimination. The approach obtains 4th and 48th degree polynomial equations for
the first and second cases, respectively. Numerical examples have been applied
to verify the process of analysis. The results, which are numerically
calculated by software Maple, prove the validity of the analysis.
