This paper focuses on parallel mechanisms (PMs) that can perform two translations and two rotations (2T2R). Two sufficient conditions for eliminating parasitic motion in 2T2R PMs are presented. A motion expression satisfying those two conditions is identified and several kinematic bonds containing that motion are found. To achieve symmetrical structures, a configurable platform that generates an instantaneous translation motion is presented, to which four limbs having identical structures are connected, leading to the construction of novel 2T2R PMs. Several designs that may have good practical values are identified and form a mechanism family. A typical mechanism is selected with its position model, workspace, singularity thoroughly investigated. Redundant limbs are added to eliminate the singularities, which then ensure the rotational capability. The proposed mechanisms have the advantages of identical limbs, no parasitic motion, and relatively high rotational capability, which can be used in several applications such as in five-axis machine.

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