Dexterous continuum manipulators (DCMs) have been widely adopted for minimally- and less-invasive surgery. During the operation, these DCMs interact with surrounding anatomy actively or passively. The interaction force will inevitably affect the tip position and shape of DCMs, leading to potentially inaccurate control near critical anatomy. In this paper, we demonstrated a 2D mechanical model for a tendon actuated, notched DCM with compliant joints. The model predicted deformation of the DCM accurately in the presence of tendon force, friction force, and external force. A partition approach was proposed to describe the DCM as a series of interconnected rigid and flexible links. Beam mechanics, taking into consideration tendon interaction and external force on the tip and the body, was applied to obtain the deformation of each flexible link of the DCM. The model results were compared with experiments for free bending as well as bending in the presence of external forces acting at either the tip or body of the DCM. The overall mean error of tip position between model predictions and all of the experimental results was 0.62±0.41mm. The results suggest that the proposed model can effectively predict the shape of the DCM.
Keywords: Cosserat rod theory; Dexterous continuum manipulators; compliant joints; partition approach.