In this paper, a novel six degrees-of-freedom (DOF) hybrid kinematic machine (HKM) is designed, analyzed, and evaluated for precision polishing. The design adopts a 3-DOF tripod-based parallel mechanism (PM) to locate the workpiece, a 2-DOF serial mechanism (SM) to orient the polishing tool, and a functional extension limb to provide a redundant DOF when polishing the workpieces with axially symmetrical shapes. Compared with the existing HKMs, the most distinctive feature is that the position and orientation adjustments of the tool with respect to the workpiece are decoupled during the synchronous machining, thus allowing the rotational tool center point (RTCP) function to be conveniently realized. For the developed HKM, the kinematics are studied systematically, including position, velocity, acceleration, and workspace. The dynamic model of the PM is derived by employing the principle of virtual work. For a pre-defined trajectory, the required driving forces are obtained through dynamic simulation. Based on these analyses, a laboratory prototype of the HKM is designed and developed. A preliminary accuracy assessment of the HKM is implemented with a double ball-bar, and a series of polishing experiments are conducted to show the capacity and feasibility of the developed HKM.