A Dual-Vector Method to Derive the Equivalent Screw of Two Successive Finite Screw Displacements for Line Segments

For finite rigid body motion, every two successive screw displacements can be represented by one equivalent screw displacement. However, such phenomenon should not be considered naturally to be valid for incompletely specified displacements (ISDs). There is neither a precise statement for such phenomenon nor an understanding of its range of validity within ISD, such as line segment displacements. As one of the main contributions in this paper, based on dual vector algebra and screw theory, an algorithm is provided to prove the existence of the subset within the scope of the line segment motion, which expresses the similar relation as shown in finite rigid body motion. A numerical example is presented for illustrative purpose.