Parasitic motion is a major drawback of the general 1T2R parallel mechanism (PM), where T denotes a translation degree of freedom (DOF) and R a rotational DOF. This paper investigates the type synthesis of the 1T2R PM without parasitic motion. First, a brief review on the planar–spherical bond and its mechanical generators is presented. Then, the difference between the general and special $a$T $b$R motion is discussed. Relations between the parasitic motion and the general and special $a$T$b$ R motion are revealed. An infinitesimal 1T2R PM with rotation bifurcation is presented as a special case. Further, the definition of the 1T2R PM without parasitic motion is presented, and the limb bond { ${\bf G}$(${\bf u}$ )}{${\bf S}$($N$ )} is identified. Geometrical conditions to construct an 1T2R PM without parasitic motion are presented, and nonoverconstrained 1T2R PMs without parasitic motion are synthesized. Idle pairs in the nonoverconstrained 1T2R PMs without parasitic motion are detected. Finally, overconstrained 1T2R PMs without parasitic motion are obtained by removing the idle pairs in the nonoverconstrained 1T2R PMs.

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