A virtual holonomic constraint (VHC) is a relation among the generalized coordinates of a mechanical system that can be made invariant via feedback control. The autonomous dynamics of the system resulting on the enforcement of the VHC are called the constraint dynamics. This work presents a method for the synthesis of VHCs that guarantees the existence of an asymptotically stable limit cycle on the constraint dynamics. (C) 2018 Elsevier Ltd. All rights reserved.