Kinematics of the translational 3-URC mechanism

A new 3-DOF spatial parallel mechanism, named translational 3-URC, is presented. The translational 3-URC makes the platform translate with respect to the base. The new mechanism belongs to a set of mechanisms with topologically equal architectures, called 3-URC, which contains another mechanism behaving as a spherical parallel wrist. The translational 3-URC position and mobility analyses are addressed and solved in closed form and the singularity conditions are written in explicit form and interpreted