Abbreviations |
CDCR | Cable-driven continuum robot |
D‒H | Denavit‒hartenberg |
DC | Direct current |
DOF | Degree of freedom |
ESC | Electronic speed controller |
FEM | Finite element method |
LPC | Low-pressure compressor |
MAE | Mean absolute error |
MAPE | Mean absolute percentage error |
PC | Personal computer |
PCC | Piecewise constant curvature |
Variables |
Ci | Cable number |
Di | Disc number |
E | Young’s modulus of Ni‒Ti rod |
| Friction generated by the jth cable on the ith disc |
| Value of the jth cable tension in the ith joint |
| Value of the jth cable tension on the force sensor |
| Lumped force of actuating forces on the ith disc expressed in frame |
| Actuating force vector applied by the jth cable to the ith disc expressed in frame |
| Lumped forces on the ith disc expressed in frame |
FEX | Matrix of |
| External force applied to the ith disc expressed in frame |
| jth cable tension in the ith joint expressed in frame |
| Matrix of |
| Gravity of the jth cable-locking device on the ith disc expressed in frame |
| Gravity of the ith disc expressed in frame |
| Gravity of the jth cable of the ith joint expressed in frame |
| Gravity of the Ni‒Ti rod of the ith joint expressed in frame |
g | Gravitational acceleration |
h | Thickness of disc |
, | jth cable holes on the ith disc |
Iz | Moment of inertia of Ni‒Ti rod |
K | Number of sections |
, | jth cable length in the ith segment |
, | jth cable variations in the ith segment |
L | Length of Ni‒Ti rod |
| Sum of the jth cable variation from the ith joint to the th joint |
| Mass of the jth cable-locking device on the ith disc |
| Mass of the ith disc |
| Mass of the jth cable of the ith joint |
| Mass of the ith compliant backbone |
| Moment of the jth cable-locking device gravity relative to the point expressed in frame |
| Lumped moments relative to the point expressed in frame |
| Lumped moment of relative to point expressed in frame |
| Moment of actuating force relative to point expressed in frame |
| Matrix of |
| External moment applied to the ith disc expressed in frame |
| Moment of the lumped force relative to point expressed in frame |
| Moment of the external force relative to point expressed in frame |
| Moment of the ith disc gravity relative to the point expressed in frame |
| Moment of the jth cable gravity relative to the point expressed in frame |
| Bending moment of the ith joint expressed in frame |
| Moment of Ni‒Ti rod gravity relative to the point expressed in frame |
N | Number of segments |
| Pressure generated by the jth cable on the ith disc expressed in frame |
| Normal unit vector of the plane, expressed in frame |
| Gravity center of the jth cable-locking device on the ith disc, expressed in frame |
| Gravity center of the ith disc, expressed in frame |
| Point expressed in frame |
| Gravity center of the jth cable of the (2i − 1)th joint, expressed in frame |
| Gravity center of the ith compliant backbone, expressed in frame |
| Revolute joint frame with origin at the axial intersection point of the (2i ‒ 1)th disc and the 2ith disc |
| World frame and YG-axis is considered to be along the gravity direction |
| ith disc frame with origin at the center of the ith disc |
rj | Distance of the center of disc and the jth cable hole |
| Rotation matrix (around the xi-axis and the bending angle is ) |
| Homogeneous transformation matrix from to |
| Translation matrix |
| Linear density of cables |
, | Joint angles of the ith segment |
| Results of the bending angle matrix |
| Bending angle matrix during solving the kinetostatic equations |
| Matrix of and |
| Angle of the jth cable hole and Yi-axis |
, | Friction coefficient of the 2ith disc |
| Cable-hole angle |
, | Angel between the 2ith disc and cables |
| Degree of the deviation of the center of the gravity of the Ni‒Ti rod in the ith segment |