Page 343 - Flexible Robotics in Medicine

334 Chapter 14

Our CTR (Fig. 14.6) is two-tubed, so N 5 2 (nested tubes), and our input values will be
ðθ 1 ; L 1 ; θ 2 ; L 2 Þ, representing the four degrees of freedom, where θ is the tube rotation angle,
and L is the tube extension length (Figs. 14.6 and 14.7). For tip-based control with
coordinate inputs ðx; y; zÞ, we can obtain the coordinate outputs ðL 1 ; h; θ 2 Þ. The θ 1 will
remain fixed.
We define the following variables: θ 5 axial angle; α 5 angle of curvature; r 5 radius of
curvature; h 5 length of the arc.

α r
x
X z
t
h
L 1
Y Z
Reference axis L 2

Figure 14.6
Reference model of concentric tubes.

x

y x

t

Θ 2 X
y

Z
Y
Figure 14.7
Alternate reference plane for the inner tube.