  Thin viscous fluid threads falling onto a moving belt behave in a way
reminiscent of a sewing machine, generating a rich variety of periodic
stitch-like patterns including meanders, W-patterns, alternating loops, and
translated coiling. These patterns form to accommodate the difference between
the belt speed and the terminal velocity at which the falling thread strikes
the belt. Using direct numerical simulations, we show that inertia is not
required to produce the aforementioned patterns. We introduce a quasi-static
geometrical model which captures the patterns, consisting of three coupled ODEs
for the radial deflection, the orientation and the curvature of the path of the
thread's contact point with the belt. The geometrical model reproduces well the
observed patterns and the order in which they appear as a function of the fall
height.
