  Tensegrity mechanisms are composed of rigid and tensile parts that are in
equilibrium. They are interesting alternative designs for some applications,
such as modelling musculo-skeleton systems. Tensegrity mechanisms are more
difficult to analyze than classical mechanisms as the static equilibrium
conditions that must be satisfied generally result in complex equations. A
class of planar one-degree-of-freedom tensegrity mechanisms with three linear
springs is analyzed in detail for the sake of systematic solution
classifications. The kinetostatic equations are derived and solved under
several loading and geometric conditions. It is shown that these mechanisms
exhibit up to six equilibrium configurations, of which one or two are stable,
depending on the geometric and loading conditions. Discriminant varieties and
cylindrical algebraic decomposition combined with Groebner base elimination are
used to classify solutions as a function of the geometric, loading and actuator
input parameters.
