During REM sleep the body does not move (only rapid eye movement -hence the term) -in fact the body is paralyzed and prevented from moving (this stops you acting out your vivid dreams which occur during this phase of sleep). It is during non-REM sleep that the body can move (and does so roughly every 20 mins or so for postural adjustment so you don't get bed sores). This is the deepest phase of sleep. The only reliable way to tell REM and non-REM sleep is to have scalp electrodes that pick up the very different patterns of brain waves associated with these two states of sleep. So monitoring movement will not give you a REM-aware alarm clock I'm sorry to say. If you used a bluetooth link to a device that could measure your brain waves, then you would get somewhere...