  Movement within eukaryotic cells largely originates from localized forces
exerted by myosin motors on scaffolds of actin filaments. Although individual
motors locally exert both contractile and extensile forces, large actomyosin
structures at the cellular scale are overwhelmingly contractile, suggesting
that the scaffold serves to favor contraction over extension. While this
mechanism is well understood in highly organized striated muscle, its origin in
disordered networks such as the cell cortex is unknown. Here we develop a
mathematical model of the actin scaffold's local two- or three-dimensional
mechanics and identify four competing contraction mechanisms. We predict that
one mechanism dominates, whereby local deformations of the actin break the
balance between contraction and extension. In this mechanism, contractile
forces result mostly from motors plucking the filaments transversely rather
than buckling them longitudinally. These findings sheds light on recent
$\textit{in vitro}$ experiments, and provides a new geometrical understanding
of contractility in the myriad of disordered actomyosin systems found
$\textit{in vivo}$.
