Translational parallel manipulators with doubly planar limbs

Based on the Lie-group-algebraic properties of the displacement set, the 3-dof generators of planar gliding motion (G) are introduced. Two serial generators of 3-dof planar gliding produce a 5-dof motion including 3 translations and 2 rotations (3T–2R) as it is established using the composition product of two Lie subgroups of G-motion. All possible 3T–2R 5-dof limbs generating double-planar (G–G) kinematic bonds are comprehensively enumerated. There are a total of 21 mechanical generators of G–G motion with distinct architectures. The parallel setting of three 5-dof G–G limb make up a translational parallel manipulator (TPM), which produces a motion subset of spatial translations. Moreover, related families of TPMs are also deducted using the commutation of factors in any products of spatial translations and rotations around an axis. By that way, some novel examples of 3-dof TPM including doubly planar kinematic chains are synthesized systematically.