I have hundreds of hobby paint bottles, some over ten years old, that are difficult to mix/shake. A lot of people duct tape or rubber band the bottles to a reciprocating saw and it works great. I wanted a better solution so I made this device that shakes four bottles at a time without the need for rubber bands or tape to hold them in. Works great.
You will need to cut a saw blade to a length of 4 to 5 inches and grind or file the teeth down. There are two holes to bolt the blade in but I found it wasn't necessary. I smeared teh blade with epoxy and drove it into the slot with a hammer til it bottomed out. I've used it about 20 times to date and the blade has not slipped. Video of it in operation here. https://www.youtube.com/watch?v=5qyl9-yxdKk&feature=youtu.be
WARNING Since this does attach to a power tool use precautions.Safety glasses, point it in a bucket or at the ground. Use common sense. It's designed so the bottles won't come out but sh#t happens.
I put 25% above but to be honest I printed mine at 10% to save time thinking it would just be a prototype - but it works great and is holding up well.