A Multi-Bennett 8R Mechanism Obtained From Factorization of Bivariate Motion Polynomials

TL;DR

This paper introduces a novel 8R closed-loop mechanism with unique properties, derived from factorization of bivariate motion polynomials, revealing special configurations and joint behaviors.

Contribution

It presents a new 8R mechanism with specific geometric properties, derived through factorization of bivariate motion polynomials, expanding the understanding of linkage configurations.

Findings

Mechanism exhibits fixed second joints with one degree of freedom.

Presence of four 'totally aligned' configurations with coinciding normals.

Opposite distances and angles are equal, with zero offsets.

Abstract

We present a closed-loop 8R mechanism with two degrees of freedom whose motion exhibits curious properties. In any point of a two-dimensional component of its configuration variety it is possible to fix every second joint while retaining one degree of freedom. This shows that the even and the odd axes, respectively, always form a Bennett mechanism. In this mechanism, opposite distances and angles are equal and all offsets are zero. The 8R mechanism has four "totally aligned" configurations in which the common normals of any pair of consecutive axes coincide.