Table 2.
The parameters for the analytical expression of the boundary, ai, (i = 0, 1, 2), the correlation coefficients (R2) between the fitted analytical boundary and the baseline, and the root of mean square (RMS) of the residual error between the fitted analytical boundary and baseline for all boundaries. The baseline boundary is established by interpolating the computer derived points shown in Table 1 using cubic spline with 10−5 as the increment in x, the COM position.
| Boundary | x | a2 | a1 | a0 | R2 | RMS | |
|---|---|---|---|---|---|---|---|
| 2-link model | non-slip | [−0.5 0] | 2.3140 ×10−4 | −1.8827 ×10−1 | −8.5327 ×10−5 | 0.999 | 4×10−5 |
| [−1.25 −0.5] | 2.4801 ×10−3 | −1.8008 ×10−1 | 3.4997 ×10−3 | 0.999 | 2×10−4 | ||
| slip | [−0.5 0] | −3.2984 ×10−2 | −5.9022 ×10−1 | −2.5810 ×10−3 | 0.999 | 1×10−3 | |
| [−1.25 −0.5] | −1.8213 ×10−1 | −6.3270 ×10−1 | 1.1219 ×10−2 | 0.999 | 5×10−4 | ||
| 7-link model | non-slip | [−0.5 0] | 2.1441 ×10−3 | −3.0251 ×10−1 | −7.8846 ×10−4 | 0.999 | 3×10−4 |
| [−1.25 −0.5] | −1.2952 ×10−1 | −4.1240 ×10−1 | −2.3666 ×10−2 | 0.999 | 3×10−4 | ||
| slip | [−0.5 0] | −4.7109 ×10−1 | −8.0771 ×10−1 | 2.6057 ×10−3 | 0.999 | 1×10−3 | |
| [−1.25 −0.5] | −1.3135 ×10−1 | −5.3269 ×10−1 | 5.9536 ×10−2 | 0.999 | 7×10−4 | ||
The analytical boundary is expressed as ẋ = a0 + a1x + a2x2.