I am currently taking my first robotics class and I found it curious that all serial manipulators have single dof joints. Why not use joints with more dof and reduce the number of components? Will that increase the error?
Conceptually multiple-dof join is a series of 1-dof joints in sequence. Such decomposition allows you to model your control system and do stuff like inverse- and forward kinematics.
For example - if you have something like a 'ball-joint', 2-dof, you will still need two motors to control it, two control signals to calculate (and transmit), each of them might have their own errors, etc. And you will use two encoders to read this joint position. And still you can model such joint as two 1-dof in sequence.