7R Darboux Linkages by Factorization of Motion Polynomials
This work addresses a problem in mechanical engineering by developing new linkage designs, but it appears incremental as it builds on existing factorization algorithms.
The paper constructs two types of 7R closed single loop linkages by factorizing a general Darboux motion, resulting in linkages with specific configuration components and degrees of freedom.
In this paper, we construct two types of 7R closed single loop linkages by combining different factorizations of a general (non-vertical) Darboux motion. These factorizations are obtained by extensions of a factorization algorithm for a generic rational motion. The first type of 7R linkages has several one-dimensional configuration components and one of them corresponds to the Darboux motion. The other type is a 7R linkage with two degrees of freedom and without one-dimensional component. The Darboux motion is a curve in an irreducible two dimensional configuration component.