The Planar Joint has two translational and one rotational degrees of freedom between the two components. Both components are free to translate relative to each other in a plane perpendicular to the axis of joint, and they are also free to rotate about this axis.

For a planar joint, the destination boundaries are free to translate relative to the source boundaries in a plane perpendicular to the joint axis and free to rotate relative to the source boundaries about this axis. The degrees of freedom are two relative displacements along the second and third axes of the joint (u2, u3) and one relative rotation about the joint axis (θ).

The joint formulation is similar to the cylindrical joint; the only difference is in the definition of the relative displacement vector (ur):