Gerhard Dohrn-van Rossum places the date of the invention of the mechanical clock between 1270 and 1330.
Gerhard Dohrn-van Rossum, History of the Hour: Clocks and Modern Temporal Orders (trans. Thomas Dunlap; Chicago: University of Chicago Press, 1996), 94
From the end of the thirteenth century there is a noticeable increase in the number of sources on clocks and clock-use, and this holds true even if we adjust for the spread of written accounting. All over Europe new clocks were being built or bought. During this transitional period — that is to say, between the presumed termini post and ante quos, framed by the dates ca. 1270-ca. 1330 —it is hardly possible to determine in any given instance whether we are still dealing with a hydraulic clock, already with a mechanical clock, or with a bell that was part of a clock.