  Combining experiments and numerical simulations with a mechanical/statistical
model of twisted yarns, we discuss the spinning transition between a
cohesion-less assembly of fibers into a yarn. We show that this transition is
continuous but very sharp due to a giant amplification of frictional forces
which scales as $\exp \theta ^2$, where $\theta$ is the twist angle. We
demonstrate that this transition is controlled solely by a non-dimensional
number ${\mathcal{H}}$ involving twist, friction coefficient, and geometric
lengths. A critical value of this number ${\mathcal{H}} \simeq 30$ can be
linked to a locking of the fibers together as the tensile strength is reached.
This critical value imposes that yarns must be very slender structures with a
given pitch. It also induces the existence of an optimal yarn radius.
Predictions of our theory are successfully compared to yarns made from natural
cotton fibers.
