Axodes of a spatial mechanism can reveal plenty of information about its motion characteristic. Through the research of the axodes, the mechanism's motion patterns can be more intuitively understood, which provides lots of help to exploring its further application. However, compared with one-DOF (degree of freedom) spatial mechanism, the research on axodes of multi-DOF PMs (parallel mechanisms) is scarce. Thus, this paper mainly investigates the axodes of a typical 2-DOF rotational PM, i.e.The 4-4R pointing mechanism, also called as Omni Wrist III, and further discloses its distinctive rolling characteristics. The final objective is to extend the application of the 4-4R pointing mechanism based on its axode characteristic. For this purpose, a rapid graphic-based algorithm for calculating the fixed and moving axodes of the 4-4R pointing mechanism is presented considering its particular geometrical arrangement. Based on the algorithm and further axode analysis, three special motion patterns existing in the mechanism, i.e. pure conical rolling, pure cylindrical rolling and pure spherical rolling, are disclosed. According to its axodes characteristic, the application of the 4-4R pointing mechanism can be extended to design of new spherical gears and constant-velocity couplings, etc.