Traction of the head-neck is important in the treatment of patients suffering from neck pain due to degeneration of the intervertebral discs. Conventional neck traction is provided manually by experienced physical therapists who maintain a desired orientation of the head-neck relative to the trunk while applying the traction. It is postulated that innovative designs of neck exoskeletons can provide the same function both flexibly and accurately. This article presents a novel architecture of a parallel mechanism whose base sits on the human shoulders with 4 parallel chains, each chain having a revolute-revolute-universal-revolute (RRUR) structure, while the end-effector is connected rigidly to the human head. Each chain has five degrees-of-freedom (DOF) and applies a constraint on the motion of the end-effector. As a result, this parallel mechanism allows two DOFs to the end-effector. These are (i) forward flexion or lateral bending of the head and (ii) vertical translation. An important motivation for the current design with RRUR structure is to characterize the range of forward flexion/lateral bending of the head-neck with this structure and the vertical translation to the end-effector. A physical prototype was constructed and tested to evaluate the performance of this mechanism in hardware for the proposed application.