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I am seeing on some videos robots picking items and putting them somewhere in order.

Here are some examples:

How are these types of manipulators called and where can I find schematic illustration explaining principles of its work?

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They are parallel manipulators.

You may find chapters on parallel manipulators in robotics textbooks, for example, A Mathematical Introduction to Robotic Manipulation, useful. There are also a number of articles related to kinematics analysis of those manipulators (such as this article).

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