7R Darboux Linkages by Factorization of Motion Polynomials

TL;DR

This paper introduces a method to construct 7R closed linkages based on factorizing motion polynomials representing Darboux motions, expanding the design possibilities for such linkages.

Contribution

It extends factorization algorithms for rational motions to create new 7R linkage types with specific configuration properties.

Findings

Constructed 7R linkages with one-dimensional configuration components.

Developed 7R linkages with two degrees of freedom and no one-dimensional components.

Demonstrated Darboux motion as a curve in a two-dimensional configuration space.

Abstract

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.