As you get old, it gets harder to slip on socks since the skin presents a resistance to sliding material over it and it frequently becomes hard to get the sock over the heel for people who do not bend at the waist easily. Instead of a tube sealed at one end, a sock can be a strip of material slightly wider than the width of a foot with velcro strips on the side. To put the sock on, you merely place the toes in the middle of the strip and then fold the rest of the strip back over the top of the foot. The velcro side strips on the bottom of the strip are then folded over the front to fasten on the material with no strain. This could also be a kind of house slipper with a footprint shaped sheet of rubber or plastic fastened to the portion of the cloth that is in contact with the floor.
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i know an engineering professor who, with his students, developed a solution to the difficult-to-put-on-socks problem, though i don't know what that solution is. i do know, though, that it was inexpensive to make and did not involve re-inventing the sock. his name is richard culver and is (maybe was, he may have retired) a professor at State University of New York, Binghamton (SUNY Binghamton), U.S.A. you can probably get to the school via "suny.edu" and find your way from there, he may well have posted the solution, as the intent was to solve a problem for the public good, not to make money. cheers!