Why would robots take over? Are we really so stupid as to give them deudly firearms without knowing how they feel about us? Would they even want to? I mean, humans are an integral part of a lot of the production processes that go into making machine parts. If they killed us all, they would eventually decay and break.
Of course, if you consider the possibility of robots like those in The Terminator, then they're quite capable of making new parts and fixing themselves.
Designing a concious entity using mechanical parts is one thing. It is definitely physically possible, and is a thought process more than anything. Processor limitations can be easily overcome by throwing more CPUs at it.
But designing and building a replica or superior body to the human one using only mechanical parts has proven to be a nightmare. There are so many minute things that need to be constantly changed, and making something with the properties that allow it to be lightweight, strong, and fast is a challenge against the very materials we are able to use.
Muscles can work because of various protein reactions, that are replenished by the rest of the body as it synthesises them from other living matter, but robots would take in only electricity and hydraulic fluids maybe, and have no biological functions to speak of.
An example of this being so difficult is that one Japanese robot that falls down stairs.
Edit: Yes, robots are involved in the manufacture of machines, but they are nowhere to be seen in silicon mines, or driving transport trucks around. Or having overall control of power generation. There's always a failsafe to have a human override it if they feel the automated systems are not doing it right.
Stockpiled materials will only last so long. And when you have no biological clock, maintenance will have to come at some point before they become inoperable.