Page 320 - Flexible Robotics in Medicine

310 Chapter 13

where N is the number of repeating main conduit segments 1 connector segments.
Substituting the following values:

H 5 3:6 mm and N 5 4;
we get:

L 0 5 24:8mm:

Therefore theoretical tendon lengths after bending are

θ max θ max
L short 5 h 0 Ucos 2 dUsin ;
2 2

θ max θ max
L long 5 h 0 Ucos 1 dUsin :
2 2

Therefore the total changes in tendon length are

Total L short 5 L 0 2 NdUsin θ max 1 2h 0 Usin 2 θ max ;
2 4

θ max 2 θ max
Total L long 5 L 0 1 NdUsin 2 2h 0 Usin :
2 4
Substituting the following values:

θ max 5 46:4degrees; L 0 5 24:8mm; H 5 3:6mm; d 5 3:9mm;

we get:
Total L short 5 15:6mm:

Total L long 5 27:6mm:

We use the total reduction in total L short from L 0 to determine the stress delivered by the
stepper motor to the flexible manipulator system:

L tension 5 L 0 2 L short 5 9:2 3 10 23 m;
Stepper motor holding torque 5 0:23 Nm;

0:23 Nm
Stress 5 ;
L tension UA
where A is the cross-sectional area of nylon thread;

23 2
A 5 πð0:4 3 10 Þ ;