In this article, we propose a new method for providing assistance during cyclical movements. This method is trajectory-free, in the sense that it provides user assistance irrespective of the performed movement, and requires no other sensing than the assisting robot's own encoders. The approach is based on adaptive oscillators, i.e., mathematical tools that are capable of learning the high level features (frequency, envelope, etc.) of a periodic input signal. Here we present two experiments that we recently conducted to validate our approach: a simple sinusoidal movement of the elbow, that we designed as a proof-of-concept, and a walking experiment. In both cases, we collected evidence illustrating that our approach indeed assisted healthy subjects during movement execution. Owing to the intrinsic periodicity of daily life movements involving the lower-limbs, we postulate that our approach holds promise for the design of innovative rehabilitation and assistance protocols for the lower-limb, requiring little to no user-specific calibration.