In this paper we investigate the application of funnel control to unconstrained path-following problems. While funnel control is a high-gain based time-varying feedback strategy applicable to minimum-phase systems with known relative degree, path following refers to the problem of tracking a reference path in an output space. A particular feature of path following is that the timing along the reference path is not determined a priori. The timing is adjusted online by the controller and may be exploited to improve the tracking performance. We show that the combination of funnel control and path following is applicable to fully-actuated rigid-link revolute-joint robots.