Attached is a good reference image set to study on a pulley block from a youtube video called "Why Snatch Blocks are Awesome" - By SmarterEveryDay. It is a good example of a complex pulley block system worth studying imo.
Above is my design drawing of a bearing based pulley. The bearing is in the middle and a plastic disc is on both sides sandwiching in the bearing. These discs prevent the string from coming off the outer race of the bearing. The top rope comes down, wraps around the outer race of the bearing, then goes back up. The bottom rope goes through the center of the bearing and then ties off on the bottom. This handoff between the forces of the top rope and bottom rope is where the magic happens of the mechanical advantage doubling. Trading speed for torque. The plastic discs on either side of the bearing I am able to tie snug to the bearing by threading a string through the center of both discs and the bearing and then wrapping that around the top half of the whole pulley and tying it off. I do this with another wrap going around the bottom half too. These don't interfere with rope travel and hold everything together solidly.
Below is a diagram where you can see the two ties I'm talking about from a side view with the two discs and the bearing spread apart so you can see everything better - this is called an "exploded view" where the parts are spread out for easier visibility.
Note: the ties that hold it together are nylon upholstery thread. The glue I'm using is 401 glue generic stuff off ebay. The plastic discs are clear plastic I salvaged from blueberry, strawberry, and sushi produce containers. That type of plastic is perfect for this. The same plastic is also found in coffee cake, other cakes, etc. It's like plastic "display" plastic that is very clear and fairly firm but very flexible. It seems ideal for pulley making. These can be cut to size with little 4" titanium straight embroidery scissors. Wearing a magnification visor for accuracy is recommended for this.
Note: I have to make custom pulleys because there are none commercially available at these tiny sizes from the shopping attempts I did (if I'm wrong on this, let me know)
I put a little super glue onto these strings pictured above to stiffen them and prevent their knot from untying and solidify everything more generally. But you should apply the glue by dipping the tip of a sewing needle into the glue so you just apply a tiny amount at a time so none gets into the bearing or any other unwanted area.
Now I am working on the actuation of a index finger first as actuating the hands is a hard challenge in robotics and has never been done with human level strength, accuracy, speed, and range of motion while simultaneously keeping all actuators within the confine constraints of a human arm between the bones and skin where muscle would be. At best, we've seen people greatly increase the size of the forearm to be the size of a thigh in order to cram in enough motors and electronics to pull this off. So they "cheated" in some sense by just upping the size rather than solving the miniaturization challenges required to fit this all inside a human form factor. So I might be the first to downsize to fit the human form factor. Anyways, that all said, the pulleys must then be very small for the fingers to pull this off as we'll need to fit a ton of pulleys into the forearms. So for this, I went with 1x3x1mm ball bearings I bought on aliexpress. They're only like $25 for 200 of them so very cheap. I will bump up to larger bearings once the torque conversion demands it. These tiny bearings can only handle I think like 3lb of force on them. So once the forces multiply in the down-gearing system enough, I will switch to bigger pulleys as needed. The next size bearings I'm using are 2x5x2.5mm bearings. These can handle around 22lb placed onto them. I'll finally switch to custom made plain bearings once I exceed 22lb of force for the last couple pulleys of the 64:1 down-gearing Archimedes compact pulley system. Each bearing in the down-gearing process has twice the forces placed onto it than the previous bearing upstream of it. So the motor is like .42lb of force coming off its shaft at 0.25cm away from its central axis point which is about where our string wrap will average, so the first bearing ups that to .84lb of force so a 1x3x1mm bearing can handle that. Next doubling is 1.68lb of force. Again, 1x3x1mm bearing can handle that. Next doubling puts us at 3.36lb force. again a 1x3x1mm bearing can handle that (although it's pushing it - we'll see in testing...). Next doubling is 6.72lb force. 1x3x1mm bearing cannot handle that much so we switch to 2x5x2.5mm bearing for that pulley. And on it goes till we hit the last couple bearings which exceed the force even the 2x5x2.5mm ball bearings can handle. For those two bearings we are going to make custom stainless steel plain bearings using stainless steel tubing I bought that just has to be cut to the length we want with a dremel to make a simple plain bearing that has no balls in it. This type of bearing can handle much higher forces because it doesn't have little balls that can be crushed. It will have more friction internally though but that's the tradeoff we have to make to keep the sizes tiny as possible. The final force the pulley system outputs is around 27lb. So 27lb of force will bend the two most distal joints of the index finger. Due to the mechanical advantage loss that happens at the joint itself, I estimate around 5.4lb of force will be all the finger joint can finally lift. So if the robot were to put its hand palm up and pull its index finger back and forth signalling a person to come over here - that movement - for that movement it should be able to pull a 5.4lb weight. That is about the same amount of weight I think my index finger could lift and with great difficulty. So it will be as strong or stronger than me on this joint pair. I say joint pair because the index finger distal two joints share the same muscle for their actuation. They move together at the same time and so just need the one motor.
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