Jim Tegart wrote to share some info on a walking robot he has made. He writes:
Chebysev, a Russian mathematician invented a walking mechanism circa 1870. A Russian website claims it as the first. Various websites have animations (see the May 30,2016 entry on The Automata Blog) and some attempts to make a functioning model. Here is my contribution to the technology. A single motor drives four linked Chebyshev linkages tromping across my kitchen table.
It's not an easy thing to make a four-legged walker with one motor.
Here is the Wikipedia entry for the Chebyshev linkage.