Two-degree-of-freedom (2DOF) pointing mechanisms have been widely used in areas such as stabilized platforms, tracking devices, etc. Besides the commonly used serial gimbal structures, another two types of parallel pointing mechanisms, i.e., spherical parallel manipulators (SPMs) and equal-diameter spherical pure rolling (ESPR) parallel manipulators, are increasingly concerned. Although all these pointing mechanisms have two rotational DOFs, they exhibit very different motion characteristics. A typical difference existing in these three pointing mechanisms can be found from their characteristics of self-motion, also called spinning motion by the authors. In this paper, the spinning motions of three pointing mechanisms are modeled and compared via the graphical approach combined with the vector composition theorem. According to our study, the spinning motion is essentially one component of the moving platform's real rotation. Furthermore, image distortions caused by three spinning motions are identified and distinguished when the pointing mechanisms are used as tracking devices. Conclusions would facilitate the design and control of the pointing devices and potentially improve the measuring accuracy for targets pointing and tracking.