Table 1 List of valuables and parameters used in the mathematical models

\(d_{n}\) [mm]

Rod segment’s length between the nth disc and the \(n+1\)th disc.

\(L_{n}\) [mm]

Natural length of the tendon between nth disc and \(n+1\)th disc.

\(l_{n}\) [mm]

Actual length of the tendon between nth disc and \(n+1\)th disc.

\(T_{n}\) [N]

Tension generated in the tendon between nth disc and \(n+1\)th disc.

w [mm]

Length of the tendon to be wound.

L [mm]

Total length of the rod.

R [mm]

Radius of the disc.

E [N/mm\(^{2}\)]

Young’s modulus of the rod.

I [mm\(^{4}\)]

The rod’s cross-sectional secondary moment.

\(N+1\)

Number of discs.

M

Number of representative points and target points.

\(k_{\text {T},\text {r}}\) [N\(\cdot\)m/rad]

Torsion spring constant of the rod.

\(k_{\text {L},\text {r}}\) [N/mm]

Linear spring constant of the rod.

\(k_{\text {L},\text {t}}\) [N/mm]

Linear spring constant of the tendon.