  We study a three-dimensional articulated rigid-body biped model that
possesses zero cost of transport walking gaits. Energy losses are avoided due
to the complete elimination of the foot-ground collisions by the concerted
oscillatory motion of the model's parts. The model consists of two parts
connected via a universal joint. It does not rely on any geometry altering
mechanisms, massless parts or springs. Despite the model's simplicity, its
collisionless gaits feature walking with finite speed, foot clearance and
ground friction. The collisionless spectrum can be studied analytically in the
small movement limit, revealing infinitely many periodic modes. The modes
differ in the number of sagittal and coronal plane oscillations at different
stages of the walking cycle. We focus on the mode with the minimal number of
such oscillations, presenting its complete analytical solution. We then
numerically evolve it toward a general non-small movement solution. A general
collisionless mode can be tuned by adjusting a single model parameter. Some of
the presented results display a surprising degree of generality and
universality.
