This paper investigates the mobility of a family of 3-DOF parallel manipulators using screw theory. Based on the 3-PSP, 3-PPS and 3-PCU manipulators and a new 3-CUP parallel manipulator, the paper obtains the branch motion-screws for these architectures and determines the sets of platform constraint-screws. The constraints are identified to be the forces acting on the S and U joints fixed in the platform and the couples acting about an axis perpendicular to the base. The mobility of a manipulator platform is thus obtained by determining the reciprocal screws to the platform constraint screw sets and the platforms are identified to have three instantaneous independent degrees of freedom which are: (i) a translation along an axis perpendicular to the base; and (ii) two rotations about two skew axes.

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