Suggest a way to cause a continuous jogging motion to my bed to help me sleep like I do when travelling by car?

Screw two planks of wood to the feet of the bed at the top and base of the bed and make a 2" curve on them similar to a baby's cradle.

Then you just need a power source to provide the lifting motion. Something like a geared motor producing 40rpm would be suitable with a crank on it.

Another way would be to support the bed on 4 chains from the ceiling which would have a natural sway to it- but just moving one end would cause a rotation rather than a sway.

If the bed had a headboard and footboard, you could place a 2" x 4" vertically, centred at each end, and fasten them just slightly higher than the centre of gravity of the bed (when fully occupied) so that it doesn't flip when entering or exiting. The 2x4 would need a cross brace, so the end result looks like an upside down capital letter "T" at head and foot of bed.

The other option is to put runners, like under a rocking chair, on either end. Probably the easier solution, but would give a different (higher) rocking motion.

Then, a solenoid or other actuator could be placed under one corner or edge of the bed, and push up that corner or edge on demand. This could then be hooked to a computer using a control board, so that the computer could send a pulse to raise one side of the bed at a programmable rate, speed and height.

You could even program it to "tip the occupant" out of bed in the morning. :P

labview + phidgets.com

Perhaps a local mechanical engineering student would like this as a project?

Please.. just one comment?

Oh well, no fun.

If you have space you could bolt an electric motor to the base of the bed (fairly powerful one but slow moving - or use gears). At the end have a disc with a heavy weight on and attach this off centre to the motor. This should rock the bed in a regular fashion if you get it right. (think of a washing machine on a spin cycle...)

Good choice since you can put it on a timer switch to turn off after say an hour