A New Mechanics Model for Continuum Notched-Tube Wrists that Accounts for Tendon Friction and Material Nonlinearities

Pacheco, Nicholas E.

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A New Mechanics Model for Continuum Notched-Tube Wrists that Accounts for Tendon Friction and Material Nonlinearities

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In this thesis, we present a new mechanics model for notched-tube continuum wrists, a class of mechanisms frequently used to implement distal steering in needle-sized surgical robotic instruments. Existing kinematic models available for these devices use two simplifying assumptions, namely (i) frictionless actuation and (ii) linear material properties, so that wrist bending can be treated as a purely geometric problem. This approach is analytically attractive, but, as we show in this thesis, it can sometimes fail to provide good tracking accuracy. The model proposed in this thesis relaxes both of the assumptions above and provides superior accuracy compared to previous models. Wrist deflection is estimated using Castigliano's second theorem, with the addition of a capstan friction term that models frictional losses on the actuation tendon. Because notched-tube wrists are typically made of Nickel-Titanium (Nitinol), which has nonlinear stress-strain characteristics, we introduce a technique to obtain a local linearized approximation of the material modulus, suitable for use in the deflection model. The result of our modeling is a system of nonlinear equations that can be solved numerically to predict the wrist configuration based on the applied actuation force. Experimental validation was performed on manufactured notched-tube continuum wrists. Our model had an average Root-Mean-Square error of only 1 degree per notch and we show that our model has an average tip position Root-Mean-Square error of only 0.3 millimeters where models with tighter assumptions have greater errors around 0.73 millimeters on average.

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