In some papers and books we can see that authors using symbols to represent robot arms. My question is, is there a convention for such sketches? If so could you provide a reference which shows how these symbols should be used?
There are usually only two kinds of joints you would use in a robot - a revolute (rotational) joint and a prismatic (translational) joint. Every reference I've seen uses a cylinder to represent revolute joints and a cube or prism to represent a prismatic joint.
You might be able to argue that a cylinder should represent a cylindrical joint, but in reality a cylindrical joint is a combination revolute and prismatic joint.
There are spherical (ball) joints, but I have never seen an actuated spherical joint before. They're more used as a kinematic constraint in shoulder joints or suspension design, in which cases the joint is a pivot and the actuation is still done by prismatic joints.