Unlike conventional manipulators where the robot is actuated at discrete joints, continuum robots are actuated continuously in smooth curves. These robots are often dexterous and compact, allowing them to operate in constrained environments during minimally invasive medical interventions. Since the unconventional robot structure often consists of elastic or flexible materials, the corresponding kinematics formulation is significantly more challenging to derive and simulate. This thesis introduces two different but related continuum robot designs: the concentric tube robot (CTR) and the eccentric tube robot (ETR). These designs utilize multiple pre-curved and superelastic nitinol tubes to actuate the robot. This mechanism also leads to an undesirable behavior called snapping . Based on Cosserat Rod theory, two separate kinematics models are derived, solved, and simulated for CTR and ETR. Additionally, an ETR prototype is designed and constructed for experimental validation. Compared to the simulation, the measured average tip error is about 3.8% of the robot length
