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.