Quadruped robot, 3 DOF vs 4 DOF Legs

Hi all,

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I need opinions/advice, I was planning to make a quadruped robot and I’m trying to figure out a design.

Mostly need to understand the differences between using 3dof for legs vs 4dof.

I see robots like the phantomX (https://www.trossenrobotics.com/p/PhantomX-AX-12-Quadruped.aspx) which use 3 and still maintain a decent gait so I wonder what adding another DOF does. (other than hike up the cost)

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Thanks!