Mobility Characteristics Analysis of a Dual-Continuum-Joint Translator

Abstract

A design library of continuum mechanisms, which consists of various mechanism modules with different motion characteristics, can greatly facilitate design tasks. A recent addition to this design library is a dual-continuum-joint translator. This translator is composed of two continuum joints and a multi-lumen tube. The two continuum joints are identical in size and coupled by connecting their corresponding backbones inside the multi-lumen tube. This translator was previously used in constructing a continuum delta robot with a parallel structure and three translation DoFs (Degrees of Freedom). Even though the validity of the dual-continuum-joint translator was experimentally demonstrated, a theoretical characterization is still missing. This paper hence presents a mobility characteristics analysis of the dual-continuum-joint translator. Cosserat rod theory and screw theory are used to analyze the mobility characteristics of this translator. First, the deflected shapes and the compliance matrices of the translator are calculated using Cosserat rod theory. Then, the mobility characteristics of the translator is investigated using screw theory by quantifying the primary mobility. Results of the calculated deflected shapes show that under external wrenches exerted on the translator, the two coupled continuum joints have the bending shapes close to circular curves with similar bending angles. The calculated compliance matrices indicate that translation is the translator's primary mobility.