Is it possible to design and construct a Robot which can solder components using a Soldering iron on printed circuit boards?
If No, What are the limitations?
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Yes. There are many soldering robots in existence today. Unfortunately, they don't look very humanoid. They are usually simply gantry style robot arms. They are common on manufacturing lines.
Remember that a robot is just a machine. And machines are designed to do a specific task, usually as efficiently as possible. And this usually means simple, straightforward, and with the fewest extra degrees of freedom. So a humanoid robot doesn't really make sense for this task.
Some quick google searches turn up many examples: