This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel\nmanipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed\nof a base and a moving platform shaped as equilateral triangles connected by three serial kinematic\nchains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint.\nThe third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal\njoint in sequence. A set of constraint equations of the 1-RPU-2-UPU PM is derived and solved\nin terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the\norientation of the moving platform and of the Cartesian coordinates of the reference point on\nthe moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF\nplanar operation mode only when the base and the moving platform are identical. The transition\nconfiguration between the operation modes is also identified.
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