There's a great variety of videos and slide shows on robotics basics. Thanks to those teams that created these documents.
If you are new to FIRST and want to learn about some of the basic approaches and tools we have, watch these:
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The game we played in 2016:
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Manipulators (ways to move something to do something)
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http://www.slideshare.net/oregonfirst/first-fare-2013-manipulators-firstfare-2013
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More on manipulators from founder of AndyMark, FRC main supplier:
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Ways to lift a robot:
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Drive trains:
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then click on DRIVE systems
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Control system (older system but basics ideas still run true):
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The physics of getting your robot to turn (complex, not for beginners): then download via the link
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Basics of building something mechanical:
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General FRC thoughts and designs:
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FRC subreddit: