New Schoenflies-Motion Manipulator Implementing Isosceles Triangle and Delassus Parallelogram

Schoenflies (X) motion is a 4D displacement Lie group including a spatial translation and any rotation whose axis is parallel to a given direction. Delassus parallelogram has four parallel screw (H) pairs with related pitches and the isosceles triangle is a special HHHP. After merging these two chains, an HHH-//-HHH generator of 2-DoF translation along a right helicoid is derived. It produces a 2-DoF motion mathematically modeled by a 2D submanifold of a 4D group of X-motion. Because of the product closure in an X-group, the 4-DoF generator with HHH-//-HHH loop serving as a subchain is revealed by adding two H pairs with axes parallel to fixed H axes. Parallel arrangement of two generators of the same X motion results in a new Schoenflies-motion manipulator with hybrid topology for 4-DoF pick-and-place operations. Four fixed H pairs (two double Hs) can actuate this manipulator and the two coaxial Hs must have distinct pitches. In addition, the possible design choices of special architectures are introduced for practical applications. Computer simulations of the new parallel manipulator with Schoenflies motion verify the effectiveness.