Closed-form Kinematic Model and Workspace Characterization for Magnetic Ball Chain Robots

Magnetic ball chains are well suited to serve as the steerable tips of endoluminal robots. While it has been demonstrated that these robots produce a larger reachable workspace than magnetic soft continuum robots designed using either distributed or lumped magnetic material, here we investigate the orientational capabilities of these robots. To increase the range of orientations that can be produced at each point in the workspace, we introduce a comparatively-stiff outer sheath from which the steerable ball chain is extended. We present an energy-based kinematic model and also derive an approximate expression for the range of achievable orientations at each point in the workspace. Experiments are used to validate these results.