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Let's restrict this question to rockets whose first stage :

  • run on liquid propellant
  • use turbopump (this may be too restrictive for this question, but it still restrict to many rockets in use today -in 2019- )
  • use gimbal for attitude control

Those restriction still let many rockets all over the world (PSLV, Ariane V,...)

As gimbal is used to orient the entire engine (or at least the combustion chamber and the nozzle), the feed pipes going from the tanks (fix relative to the rocket stage) to the combustion chamber (moving relative to the rocket stage), pipes must allow such movements. How is it done? Is it done through flexible pipes?

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For the engine configurations you list, the typical feedline application is rigid sections of duct connected by flexible joints. Here are a couple examples.

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The flex-joints are typically two sections connected by some kind of internal link and sealed using bellows. Again, examples.

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Everything in this answer is taken from the NASA document Liquid Rocket Lines, Bellows, Flexible Hoses, and Filters (which could not have a more descriptive name!) I urge you to consult this document for much more information and many more examples.

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