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Table 2 Key fitting parameters of each waist twisting cycle in Y direction

From: Smooth Trajectory Planning for a Cable Driven Parallel Waist Rehabilitation Robot Based on Rehabilitation Evaluation Factors

Waist twisting cycles

Key fitting parameters

R-squares

\({a}_{0}\)

\({a}_{1}\)

\({b}_{1}\)

ω

\({a}_{x}^{^{\prime}}\)

1st

10.0903

40.5181

− 45.6060

0.0502

61.0051

0.9967

2nd

9.7610

45.2876

1.4728

0.0531

45.3116

0.9977

3rd

1.6601

56.3211

7.5311

0.0497

56.8224

0.9992

4th

3.5996

58.8380

7.3858

0.0507

59.2998

0.9976

5th

10.7859

57.8365

1.6622

0.0487

57.8603

0.9978

6th

9.6217

54.5511

0.4017

0.0501

54.5526

0.9997

7th

13.1768

56.8928

− 7.5860

0.0485

57.3963

0.9987

8th (min)

11.6342

57.4316

13.8960

0.0506

59.0888

0.9986

9th

14.2717

57.2698

− 2.0050

0.0527

57.3049

0.9926

10th (max)

16.0207

61.1319

− 2.9088

0.0484

61.2011

0.9986

11th

14.2903

54.8039

− 18.0752

0.0474

57.7077

0.9901

12th

16.1964

55.7053

3.0875

0.0503

55.7908

0.9959

13th

13.1907

46.6916

6.4250

0.0564

47.1316

0.9990