Two-degree-of-freedom (2-DOF) rotational parallel manipulators (RPMs) have been widely used in pointing devices and robot wrists. This paper focuses on a class of 2-DOF RPMs achieving an equal-diameter spherical pure rolling motion (ESPRM) around the base. At first, a theoretical model of spherical pure rolling motion is analyzed and the characteristic of the associated constraint space is derived. Taking the Omni-Wrist III as a typical 2-DOF RPMs with an equal-diameter spherical pure rolling motion, mappings between the geometry and the motion are established and eight useful constraint conditions are derived which will be instructive for the type synthesis. Then, with focus on symmetrical structures, nine classes of 2-DOF RPMs with equal-diameter spherical pure rolling motion are synthesized based on the graphic method. Most of these RPMs have already been used in practice. Unlike the conventional type synthesis of lower-mobility parallel manipulators in literatures, some geometrical parameters of links, in addition to the distributions of joints and limbs, are taken into consideration in the type synthesis in this paper. This proposed research may help produce novel architectures.

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