To share a video link that will begin playback at a specific point, all you need to do is add a bit of code to the end of the URL. Just add:
#t= followed by the timecode of where you'd like playback to begin.
Here is an example where playback begins one minute and two seconds into the video: https://vimeo.com/81400335#t=1m2s
You can also use this parameter for embedded videos. To do this, simply add
#t=(timestamp here) to the end of the player URL in your iframe embed code. For example:
<iframe src="https://player.vimeo.com/video/81400335#t=1m2s?byline=0" width="640" height="360" frameborder="0" webkitallowfullscreen mozallowfullscreen allowfullscreen></iframe>
Note: With this parameter, your video will autoplay at the specified timecode by default. If you're using a mobile device, you'll need to press play for the player to link to the appropriate spot in the video, as autoplay is not supported on mobile devices.