This paper proposes a novel three-legged (6+3)-degree-of-freedom kinematically redundant parallel robot, where each of the legs of the robot consists of a Delta parallel mechanism and a spherical-revolute kinematically redundant link. Kinematic modeling, singularity analysis, and workspace evaluation of the proposed robot are performed. Using modules in the legs ensures that all actuators are fixed on the base, hence the global robot has a low moving inertia, making it suitable for some applications, such as physical human-robot interaction. Moreover, the structure of the Delta module is rearranged, in which the axes of two of the three rotational actuators are collinear and are perpendicular to the axis of the third rotational actuator. It is shown that such an arrangement can reduce the possibility of mechanical interferences and improve the workspace of the kinematically redundant parallel robot.