Mass and damping are associated with the motion of a dynamic system. Degrees-of-freedom with mass or damping are often called dynamic degrees-of-freedom; degrees-of-freedom with stiffness are called static degrees-of-freedom. It is possible (and often desirable) in models of complex systems to have fewer dynamic degrees-of-freedom than static degrees-of-freedom.

By degrees of freedom, I believe you meant dimensions. Everything in this universe has 3 degrees of freedom.

A scara robot uaually have 4 degrees of freedom

The knee has 2 degrees of freedom. Flexion/Extension and varus/valgus rotation.

A rigid object has up to 6 degrees of freedom:

3 degrees of freedom of location:

In both directions of x,y,z axis

3 degrees of freedom of rotation (attitude):

pitch, roll, and yaw,

rotation about the x,y,z axis.