What is a robot ?
There are numerous types of modern "robot". You have robots that are moving, robots which remain stationary. You have industrial robots, military robots.. You have toy robots, that look like robots and only move. There are advanced biped and quadruped robots, made for amusement purposes. Medical robots doing surgery. Most of that would be completely out of reach for mechanical technology. Safety is an issue.. complexity, reliability..
But you also have windmills and looms, which are mechanical devices that can do a supervised task. In fact these are robot-like. Like a clock runs. Let's do a gradual buildup of the complexity, else, "mechanics" would will be out of reach soon..
Definition 1: A robot is a device with moving parts.
Any motor is a robot, any artificial motion is robotics. When we would apply this definition, anything goes. Trains are quite durable, some run 50-80 years. Electronics with moving parts, like record players and CD players have a shorter lifetime, but they tend to keep functioning. For the basic requirement of "moving and artificial" both technologies can be durable.
Toy robots, that only look like robots, mostly android robots, fall into this category too.. 20th century toy robots move and flicker their lights, 80% mechanics. They were not really durable, most ended up damaged. I kept them for years. Nowadays, you have robotics toolkits for computer savant kids. See definition 4 below, that's another league !
Definition 2: A robot is a device which can do a supervised task.
This will limit the number of "robots" considerably. But looking at the two aspects, "moving" and "supervised task", there are numerous devices we don't call "robot", which meet both requirements.
The power loom (1787) is an example of a 100% mechanical apparatus doing a quite complicated task. In fact you could call a clock a robot. As far as I know mechanical clocks and watches have proved to be - at least - as durable as electronic clocks and electronic watches. We actually don't know this yet. Generally available electric clocks (wrist watches) have existed for only 75 years or so, less than a century. Electronics could be more vulnerable on the long term, requiring a specific type of batteries to be replaced.. mechanics does not suffer from that issue.
Definition 3: A robot is a device performing a task unsupervised
Now we are in the realm of modern robots. A lot of industrial robots are actually deployed with this purpose. To perform a task previously done by a human, quicker and more hours in a row. An industrial robot can open up possibilities, enable certain processes that would not be possible with human hands only. Still, a 6 year old would hardly recognize a Mitutoyo arm as "robot".
This class of robots is not out of reach for a mechanical level of technology. In the age of "mechanization" it was the primary development goal. Before 1950, mass production existed.. very sophisticated mechanical work. But without the electronics, it is difficult to control it and dangerous to work with. During that age (1850-1950) there were numerous accidents with mechanical production lines, with mechanical solutions without safety limits. There were no prescribed safety limits and ISO-standards, like we have now.
Definition 4: A robot is a device that can autonomously perform a human task
An autopilot takes over control from the pilot. You could call it a robot, or you could call the autopilot-controlled aircraft a robot. In any case, it will take decisions, sometimes move around. Advanced industrial robots, or robots in hospitals can perform tasks previously done by humans. This area requires versatile, mobile robots that can be assigned tasks on the fly. Robots that assist industrial warehouses, robots that can pick up and transport goods inside a building. It could be done mechanically, with rails and tricks.. but it would become very complicated construction.
Definition 5: A robot is a device that can impersonate a human
In the virtual realm (games, films) there are numerous very credible designs. To create such a robot in real life remains a challenge, but some developments approach spectacular results. There exists no mechanical equivalent of this. A mechanical robot impersonating a human being would become too heavy to carry its own weight.