Singularity Conditions of Concentric Tube Robots

Abstract

This paper derives singularity conditions for concentric tube robots (CTRs). To the scope, we build the CTR geometrico-static model using discretization techniques, which are suitable for several currentlyused CTRs models. Then, we obtain singularity conditions by performing a linearization of the geometrico-static model. We define Type-1 and Type-2 singularities, which are related to the unsolvability of the inverse and forward kinematostatic problems, respectively. Moreover, we also show the link between Type-2 singularities and CTR equilibrium stability. A case study with a two-tube CTR is proposed to illustrate our results.