the pivot point of an inverted pendulum around the curve without making the pendulum fall over. On the other hand, the seemingly different problem of maneuvering Hauser’s PVTOL aircraft [@HauSasMey92] along a closed curve in the vertical plane can be viewed as the problem of moving the pivot of an inverted pendulum around the curve without making the pendulum fall over. The two problems are, therefore, closely related, the main difference being the fact that in the former case the pendulum lies on a plane which is orthogonal to the plane of the curve, while in the latter case it lies on the same plane. In [@ConMagNieTos10], the path following problem for the PVTOL was solved by enforcing a virtual holonomic constraint (VHC) which specifies the roll angle of the PVTOL as a function of its position on the curve. In this paper we follow a similar approach for the bicycle model, and impose a VHC relating the bicycle’s roll angle to its position along the curve. However, rather than finding one VHC, as we did in [@ConMagNieTos10], we show how to automatically generate VHCs as periodic solutions of a scalar periodic differential equation which we call the [*virtual constraint 