What is the purpose of using bearings to build a crank mechanism as in 39? https://507movements.com/mm_039.html
Maybe it's for bearing efficiency? Note that the spur gears are rigidly attached to, respectively, the crank and the shaft. So they don't require bearings at their centres. There is a link arm which pulls the gears together, and that rotates. But the key is that this arm is not transmitting the cranking power; it just holds the parts together. So its bushings/bearings don't have to be so hefty. (Their load is going to be proportional to the transmitted power; obviously the bigger the crank and more horsepower going through it, the more tightly you have to hold the gears together. But it's going to be some fraction compared to a bearing that is directly driven.)
The note only alludes to this mechanism being used to elude a patent claim, not mentioning any advantages. Someone had patented cranks in such a way that you can weasel your way out with this arrangement. I'm guessing that the patent's drawings and descriptions specifically indicated a rotating bushing on the crank wheel where the arm is attached, and this has no such arm attachment.
Avoiding patent infringement.
James Pickard modified the Newcomen steam engine to deliver rotary motion using a crank (and patented it). So James Watt used the sun and planet for his steam engine to avoid infringing the patent.
The Picard patent specifies that the crank is fixed to the driveshaft, but it is free to rotate in the sun and planet setup
Looks like there's contact between the outer diameter of the sun-gear and a surface close to the center of the planet-gear? The link arm is pulling them together and this contact keeps them apart I guess. The rotation speeds are different so you'd need a bearing? I dunno tbh - I'm not sure what the colors represent and I'm not even sure if I'm using the correct words to describe what I see.