- Starts with current situation
- Prosthesis able to replace limbs 1 on 1 without any disadvantages
I think that this step needs to be split in at least two steps. The first is "without any disadvantages, but the limbs need replacing every 2 to 3 years", the second is "without any disadvantages, the limbs will have decade-long lifespans". At this point you should also wonder how these limbs will be treated. Cars for example are a consumer item. VolksWagen tried to promote cars that lasted decades and were sturdy and capable throughout those years. Other car companies build cars that lasted only a couple of years, but by then the consumer wanted a newer, shinier model anyway, which caused VolksWagen to lose out despite qualitatively superior cars. If the latter is true, then no one will ever want or need something that lasts more than around 5 to 7 years, although if the recuperation process behind every adaptation takes a while people will want longer lasting prosthetics.
This would really only apply to the limbs. While limbs have complex systems that allow for example 90% of the energy from the previous step to be used in the next step, such systems are all mechanical in nature and would be relatively easy to reproduce (relatively, it's still incredibly hard). But other biological functions like the Liver won't be surpassed for some time.
As for the exact timeline, this is a link to something that gives you some idea but paints the current status quo much more rose-colored than it is: https://share.upmc.com/2015/03/timeline-prosthetic-limbs-years/
In recent years, we've started building things like ultra-light carbon prosthetics. These are extremely detrimental to the wearer except in extreme sports conditions. Our legs are pretty heavy for a reason, because when we move we basically throw our legs forwards to drag our bodies after it, then "fall" forwards until our heels touch the ground. Lightweight Carbon prosthetics don't have that weight, and require high speeds before you can re-use some of the energy of your previous step. Basically, the general prosthetic of today is no better at walking than the wooden peg, the only advances have been easier to clean, easier attachment and less wounds from extensive usage (and the ability to hang a shoe off of it). Some electrical designs are now in play that can mimic certain movements, but they run out of energy quickly and the user must manually change it's settings each time. Having a computer that knows that the user is doing is still a bit away and would leech even more energy. So my quesstimate is that it's going to take until 2030 at least before we have anything approaching a "normal" limb functionality that lasts the entire day. (this has been my area of study).
If you look around the internet, you'll find advanced electrical hands and legs up the whazoo (some as early as 2010, maybe earlier), each claiming they can now let someone walk around or grab stuff as if it's a normal leg/hand. These things also cost immense amounts of money, and while they all have a gimmick they are good at they aren't close to mimicing the complexity and capabilities of a real leg or hand like they claim.
- Prosthesis surpass the level of functioning of normal limbs.
First the "throwaway" prosthetics with a short lifespan will surpass the normal limbs. But just like a Car, it'll likely come at a price. Having to recharge every day, or refill the fuel. As someone else mentioned, it's more likely that at this point they will start 3D printing biological limbs first (https://www.theverge.com/2018/1/31/16954712/growing-ear-3-d-printing-regenerative-medicine-microtia), assuming we solve the problem of creating capillary bloodvessles for larger organs, and then start combining these 3D printed limbs with synthetic materials first, like a spidersilk tendon and improved muscle attachments so we can use a higher muscle force without ripping it out of the bone. Then these start being combined with robotic/cyborg elements to improve the limb overall.
On the timeline, I expect this to be fairly close to having the limbs be on equal footing with normal limbs, around 2030 to 2035.
Here's actually a (not super-accurate) source: https://www.futuretimeline.net/21stcentury/2036.htm
I expect that they paint it far more rose-colored than it will actually be. But if the Olympics assume that a "super-athlete" category is feasible between 2036 to 2040, it should be possible somewhat feasible. I've personally worked with an (unfinished) idea to help blind people skate on the ice through the use of triangulation of a phone the participant is carrying, and then using earphones for simulating a soundsource a distance away from the participant that follows the track. So they are nothing but ambitious and trying to make such things a reality.
- These prosthesis become available to the general public.
Probably within a year or two after these limbs become better than current limbs you would see people actively pursuing gaining such limbs, it could be longer if the legal issue's drag on. At first it might be some half-crazy person who will happily cut his arms and legs off in an attempt to become elegible for advanced prosthetics, and quickly people will have trials in court to receive such limbs if only because some idiot who had an accident at work now outperforms his peers and everyone else wants it too.
- People start replacing eyes too instead of just limbs.
At this point I can't comment anymore. It depends on how fast we can start 3D printing full-scale organs, how advanced genetic alterations are at that point to create biological super-organs, and how much research they still put into creating mechanical versions while they have potentially biological super-versions already available or in the pipeline. A heart might still be mechanically replaceable, but something as complex as the chemical factory liver? I wouldn't be able to predict a timeline at this point, not even with my experience in this field.
