New 6-screw linkage with circular translation and its variants

• Circular translation generators of articulated parallelograms are introduced.
• A mechanical generator of spherical translation is revealed.
• A new family of 6-screw paradoxical linkages with circular translation is proposed.
• The published 6R linkages having circular translation are special types of 6H.
• Combining three 6R linkages produces a new 3-UU platform with circular translation.

The circular translation generated by a pseudo-planar parallelogram with four screw pairs having equal pitches and parallel axes is introduced and a special Delassus parallelogram producing the same motion is obtained through the addition of a second pseudo-planar parallelogram with another value of its equal pitches. A mechanical generator of spherical translation stemming from the circular translation generator is revealed. Combining a spherical translation generator and a pseudo-planar or special Delassus parallelogram leads to a new family of 6-screw (6H) paradoxical linkages with circular translation in a purely geometric way. Their architectural type belongs to the structural group with two alternate pairs of joint-axes parallel and one pair of opposite joint-axes parallel. Moreover, the one-degree-of-freedom (1-DoF) movability is conditioned by metric constraints. The already published 6R linkages having circular translation are special types of 6H with all screw-pitches zero. The parallel arrangement of three special 6R linkages produces a 3-UU parallel platform with circular translation (U denotes a universal joint with intersecting joint axes of revolute pairs). A more overconstrained m-UU case (m ≥ 4) with special joint-axes arrangements is disclosed too.