Beyond Constant Curvature: A New Mechanics Model for Unidirectional Notched-Tube Continuum Wrists

Area of Science:

• Robotics
• Mechanical Engineering
• Biomedical Engineering

Background:

• Continuum wrists are crucial for distal steering in minimally invasive surgical robots.
• Existing models assume constant curvature, limiting tracking accuracy.
• Notched-tube wrists, often made of Nitinol, exhibit complex behavior.

Purpose of the Study:

• Develop a more accurate mechanics model for notched-tube continuum wrists.
• Improve kinematic prediction for surgical robotic instruments.
• Enhance steering precision in needle-sized robotic applications.

Main Methods:

• Utilized Castigliano's second theorem for deflection modeling.
• Incorporated a capstan friction term to account for tendon losses.
• Applied local linearization for Nitinol's nonlinear stress-strain properties.
• Solved a system of nonlinear equations numerically.

Main Results:

• The new model relaxes the constant curvature assumption.
• Experimental validation demonstrates superior accuracy compared to prior models.
• The model accurately predicts wrist configuration based on actuation force.

Conclusions:

• The proposed mechanics model offers enhanced accuracy for continuum wrist kinematics.
• This advancement can lead to improved control and precision in surgical robotics.
• The model provides a more realistic representation of notched-tube wrist behavior.