1350 is probably a tad late, but only by a generation or so. Popular legend has it that the modern clock was invented by one Canon Gerbert {later Pope Sylvester II} around the turn of the first millenium. However, although Gerbert was undoubtedly a learned mathematician and astronomer, and may even have constructed simple orreries, this date seems far too early, given that public clocks didn’t appear until much later, and there are no written or pictorial traces of what would have been a remarkable device. Indeed, attributing “the invention of the clock” to a single inventor or artisan is probably naive.
Establishing a precise date for the appearance of mechanical clocks is difficult in any case because written references of the period are to horologia, which could mean any type of time-keeping device, from sundials to water clocks. Circumstantial evidence seems to point to the mechanical clock first appearing in Europe in the late 13th century: for example, a sudden explosion of literary references to clocks, such as in Dante’s Paradiso
And like the wheels in clock works, which
Turn, so that the beholder
Seems still, and the last, to fly.
[Canto 24]
which was written between 1316 and 1321 {although such references are technically ambiguous as to what kind of device they’re describing} or such documents as cathedral accounts detailing the various outlays on a tower clock.
The first unmistakeable reports of modern clocks come early in the 14th Century, such as the Norwich Cathedral tower clock constructed by Roger Stoke between 1321 and 1325, and an astronomical clock at St Albans made by Richard of Wallingford around 1330. Bear in mind, though, that these early tower clocks were huge, crudely cut and unreliable: limitations in both design and metal-working techniques meant that room clocks with spring mechanisms instead of huge weights requiring towers to house them would not appear for another 150 years, with truly portable watches probably appearing around the start of the 16th Century.