Well not exactly a "picture frame", but... Icons march around the frame calling attention to the picture of your choice.
Video of the prototype is here: http://www.youtube.com/watch?v=aXC7k8weS-M&list=UUv_zm49u-RjnCJVwhUO-ecA.
When it comes to the icons, you can design and print your own, or use light weight material such as heavy construction paper, balsa wood, stickers on cardboard, etc., and glue them to the pins. For the prototype, my wife wanted "Lora & Greg & Lora", so I printed the letters in PLA and glued each to the pins using thick cyanoacrylate and accelerator (hot glue should also work, just not too hot).
Designed using Sketchup 8 and printed in PLA on a Makerbot Replicator 2 using Makerware 22.214.171.124.
I used "6VDC 45 RPM Pinky Finger Sized Gear Motor 1" Long x 15/32" x 3/8"" from either amazon.com or directly from http://sciplus.com/p/MICROMOTOR_47952 to move the track. Other sources are available, I've not tested them though.
I also used a coaxial power jack (Radio Shack part number 274-1583) and a 1.5vdc power supply (Radio Shack part number 273-315). You can skip the coaxial power jack and solder the power supply directly to the motor if desired.
Print "TopInside.stl". Using a glue stick, double sided tape, etc., attach your photo onto the smooth surface side of "TopInside.stl". Then using a very sharp razor knife or blade, trim the photo to follow exactly the outside edge of "TopInside.stl" making sure no part of the photo extends beyond the surface of "TopInside.stl".
Print "Chain.stl". Snap chains end to end making sure the pin holding cups are on the same side. Carefully work the chain to loosen all links. This may take awhile. All links must move freely.
Print "MotorMount.stl". Install motor into motor mount, solder your power supply or coaxial power jack to the motor, then press the assembly onto "Track.stl". Note the orientation as it will only fit one way.
Place "Gear.stl" inside "Chain.stl", carefully lowering the two into "Track.stl", then press "Gear.stl" onto the motor shaft making sure the flats align. Also make sure the pin cups on "Chain.stl" are facing up.
Print as many of "Pin.stl" that you will require. Carefully sand the base of each pin until if fits snuggly inside the pin cup in "Chain.stl". Repeat with the remaining pins as required in the location you choose. You can glue the pins in the pin cup, but I don't recommend it for two reasons; first, grandkids, if they pick up the frame in the wrong manner the pins will release from the pin cups with little or no damage, and second, after the icons are glued onto the pins, it is difficult if not impossible to remove "FrontOutside.stl" since the icons are in the way (depending on the size of the icons).
Press "TopInside.stl" onto "Track.stl", noting the orientation of the gear guide.
Print "TopOutside.stl", then press it onto "Track.stl".
Print "Back.stl", then press it onto "Track.stl".
Glue icons onto the pins. I positioned my pins on the chain first. Then to glue a letter to a pin, I placed a small (and I mean small) dot of thick cyanoacrylate (thick cyanoacrylate is available at most model hobby shops) on the pin tip, sprayed the back side of the letter with accelerator, then positioned the letter on the pin. The cyanoacrylate sets within 5 seconds.
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