Capture Video of Android's Screen

Android 4.4 (KitKat) and higher devices have a shell utility for recording the Android device screen. Connect a device in developer/debug mode running KitKat with the adb utility over USB and then type the following:

adb shell screenrecord /sdcard/movie.mp4
(Press Ctrl-C to stop)
adb pull /sdcard/movie.mp4

Screen recording is limited to a maximum of 3 minutes.

Reference: https://developer.android.com/studio/command-line/adb.html#screenrecord

I know this is an old question but since it appears to be unanswered to the OPs liking. There is an app that accopmlishes this in the Android Market Screencast link

Yes, use a phone with a video out, and use a video recorder to capture the stream

See this article http://graphics-geek.blogspot.com/2011/02/recording-animations-via-hdmi.html