In the present study, the kinematics of a class of parallel manipulators with two translational and one rotational degrees-of freedom are addressed through the analysis of HALF robot. A detailed kinematic and constraint analysis of the robot is conducted. In addition, an exhaustive singularity characterization is presented with interpretation of the robot’s behavior in singular poses. The implications of this study will initiate further investigations on the design of parallel manipulators belonging to the class of manipulators under consideration.