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

Chinese Journal of Mechanical Engineering

Table 1 Key fitting parameters of each waist twisting cycle in X direction

Waist twisting cycles	Key fitting parameters					R-squares	Removal conditions
Waist twisting cycles	\({a}_{0}\)	\({a}_{1}\)	\({b}_{1}\)	ω	\({a}_{x}^{^{\prime}}\)	R-squares	Removal conditions
1st	7.6832	38.4680	− 4.8989	0.0536	38.7787	0.9806	Excessive fitting residual
2nd	8.2234	44.8662	0.5078	0.0446	44.8691	0.9935
3rd	9.3725	38.0859	− 6.5433	0.0501	38.6439	0.9963
4th	6.2964	35.6410	− 2.1783	0.0477	35.7075	0.9821	Excessive fitting residual
5th	9.3321	30.8377	− 2.6001	0.0553	30.9472	0.9967
6th	8.9843	30.2105	1.8983	0.0510	30.2701	0.9950
7th	6.6655	33.2023	− 2.3185	0.0453	33.2832	0.9992
8th (min)	4.6415	31.8730	− 10.8424	0.0476	33.6667	0.9888	Excessive fitting residual
9th	6.5133	30.2323	− 0.9434	0.0568	30.2470	0.9962
10th (max)	13.9039	29.7146	− 10.1172	0.0473	31.3897	0.9932	>3σ
11th	8.3610	36.1557	3.4668	0.0484	36.3216	0.9943
12th	9.7264	28.8197	5.8161	0.0542	29.4007	0.9885	Excessive fitting residual
13th	11.2816	34.8355	− 6.7973	0.0487	35.4925	0.9969
14th	8.2762	39.7236	− 4.3227	0.0486	39.9581	0.9939
15th	9.8185	33.7732	− 3.2430	0.0556	33.9285	0.9996