Design and analysis of rehabilitation training mechanism based on upper limb rehabilitation movements

Rehabilitation movement	Shoulder coronal plane ROM	Shoulder sagittal plane ROM	Shoulder transverse plane ROM	Elbow coronal plane ROM	Elbow sagittal plane ROM	Elbow transverse plane ROM
Elbow flexion	0°	0°	0°	0°	0–91.5°	0°
Horizontal adduction/abduction	0°	0°	0–91.3°	0°	0°	0–93.5°
Vertical abduction/adduction	0°	−30.6–89.1°	0°	0°	0°	0°
Flexion/extension	0–92.1°	0°	0°	0°	0°	0°
Shoulder internal/external rotation	0°	0°	0°	0–62.4°	0°	0°
Elbow internal/external rotation	0°	0°	0°	0–29.5°	0°	0°

Table 3

Summary of the DAS3 model

Category	Item	Description
General information	Model name	DAS3
	Original source	DAS project
	Primary references	Chadwick et al., 2014
Skeletal structure	Segments	Thorax, clavicle, scapula, humerus, ulna, radius
Joint definition	Shoulder complex	Multi–joint system (SC, AC, GH joints)
	Elbow joint	1 degrees of freedom (DOF) (flexion/extension)
	Forearm joint	1 DOF (pronation/supination)
Musculotendon units	Muscle type	Hill–type muscle model
Applications	Biomechanics	Muscle force estimation, joint load analysis
	Clinical	Rehabilitation assessment
	Engineering	Exoskeleton and prosthesis design

Simulation analysis of movement process: (a) elbow flexion, (b) horizontal adduction/abduction, (c) vertical abduction/adduction, and (d) flexion/extension.

Table 4

Shoulder joint IK

Shoulder joint IK	Elbow flexion movement	Horizontal adduction/abduction movement	vertical abduction/adduction movement	Flexion/extension movement
0–1	0°–0°	0°–18.26°	−30.6°–6.66°	0°–18.42°
1–3	0°–0°	18.26°–54.78°	6.66°–41.22°	18.42°–55.26°
3–5	0°–0°	54.78°–91.3°	41.22°–89.1°	55.26°–92.1°

Table 5

Elbow joint IK

Elbow joint IK	Elbow flexion movement	Horizontal adduction/abduction movement	vertical abduction/adduction movement	Flexion/extension movement
0–1	0°–18.3°	0°–18.7°	0°–0°	0°–0°
1–3	18.3°–54.9°	18.7°–56.1°	0°–0°	0°–0°
3–5	54.9°–91.5°	56.1°–93.5°	0°–0°	0°–0°

Table 6

Horizontal adduction/abduction trajectory data

Time	Human X	Human Y	Exo X	Exo Y	End X	End Y
0	0.5500	0.0000	0.5497	0.0174	0.5470	−0.0519
0.25	0.5499	0.0088	0.5493	0.0267	0.5487	−0.0335
0.5	0.5488	0.0348	0.5479	0.0459	0.5499	0.0073
0.75	0.5439	0.0771	0.5438	0.0778	0.5459	0.0650
1	0.5315	0.1335	0.5343	0.1231	0.5338	0.1267
1.25	0.5070	0.2006	0.5133	0.1861	0.5112	0.1928
1.5	0.4669	0.2728	0.4739	0.2620	0.4785	0.2564
1.75	0.4089	0.3431	0.4099	0.3422	0.4324	0.3197
2	0.3341	0.4042	0.3229	0.4113	0.3639	0.3848
2.25	0.2462	0.4492	0.2220	0.4578	0.2684	0.4421
2.5	0.1516	0.4740	0.1184	0.4777	0.1482	0.4769
2.75	0.0580	0.4776	0.0240	0.4739	0.0212	0.4763
3	−0.0275	0.4625	−0.0528	0.4544	−0.0844	0.4450
3.25	−0.0999	0.4337	−0.1105	0.4280	−0.1563	0.4026
3.5	−0.1569	0.3975	−0.1546	0.3992	−0.1974	0.3668
3.75	−0.1984	0.3602	−0.1905	0.3682	−0.2185	0.3434
4	−0.2265	0.3268	−0.2183	0.3373	−0.2321	0.3256
4.25	−0.2439	0.3008	−0.2373	0.3111	−0.2404	0.3133
4.5	−0.2531	0.2845	−0.2484	0.2930	−0.2435	0.3085
4.75	−0.2559	0.2790	−0.2527	0.2851	−0.2409	0.3124
5	−0.2600	0.2751	−0.2517	0.2844	−0.2379	0.3129

Table 7

Flexion/extension trajectory data

Time	Human X	Human Y	Exo X	Exo Y	End X	End Y
0	−0.2800	−0.4734	−0.2648	−0.4820	−0.3173	−0.4490
0.25	−0.2732	−0.4773	−0.2574	−0.4860	−0.3027	−0.4590
0.5	−0.2527	−0.4885	−0.2428	−0.4935	−0.2703	−0.4789
0.75	−0.2183	−0.5048	−0.2176	−0.5051	−0.2226	−0.5029
1	−0.1698	−0.5231	−0.1801	−0.5197	−0.1696	−0.5232
1.25	−0.1076	−0.5394	−0.1232	−0.5360	−0.1090	−0.5391
1.5	−0.0334	−0.5490	−0.0465	−0.5480	−0.0462	−0.5480
1.75	0.0499	−0.5477	0.0485	−0.5479	0.0235	−0.5494
2	0.1382	−0.5323	0.1517	−0.5287	0.1096	−0.5389
2.25	0.2264	−0.5012	0.2512	−0.4892	0.2107	−0.5080
2.5	0.3091	−0.4549	0.3388	−0.4330	0.3189	−0.4481
2.75	0.3817	−0.3960	0.4087	−0.3678	0.4157	−0.3597
3	0.4409	−0.3288	0.4589	−0.3031	0.4827	−0.2623
3.25	0.4856	−0.2583	0.4922	−0.2453	0.5196	−0.1777
3.5	0.5161	−0.1900	0.5149	−0.1933	0.5363	−0.1195
3.75	0.5348	−0.1286	0.5311	−0.1428	0.5429	−0.0866
4	0.5445	−0.0776	0.5417	−0.0953	0.5463	−0.0633
4.25	0.5486	−0.0397	0.5471	−0.0564	0.5479	−0.0479
4.5	0.5498	−0.0165	0.5492	−0.0300	0.5483	−0.0428
4.75	0.5499	−0.0086	0.5497	−0.0184	0.5475	−0.0501
5	0.5501	−0.0089	0.5504	−0.0094	0.5575	−0.0511

Changes in upper limb muscle force: (a) elbow flexion, (b) horizontal adduction/abduction, (c) vertical abduction/adduction, and (d) flexion/extension.

Table 8

Muscle strength RMS data

Time (s)	Elbow flexion		Horizontal adduction/abduction		Vertical abduction/adduction		Flexion/extension
	Upper (N)	Fount (N)	Upper (N)	Fount (N)	Upper (N)	Fount (N)	Upper (N)	Fount (N)
0	12.40	12.40	4.26	4.13	6.00	0.49	7.00	10.00
0.25	12.45	13.50	11.18	6.27	6.00	0.65	7.00	10.05
0.5	12.35	16.80	18.10	8.41	8.50	0.75	9.50	9.95
0.75	12.48	16.70	25.02	10.55	12.50	0.68	13.20	10.08
1	12.32	15.70	31.94	12.69	17.50	0.72	18.50	9.92
1.25	12.43	15.11	38.86	14.83	18.50	0.63	19.20	10.03
1.5	12.37	14.50	45.78	16.97	27.40	0.75	28.50	9.97
1.75	12.41	13.40	55.20	19.80	28.50	0.69	29.80	10.01
2	12.39	14.41	55.74	18.80	37.50	0.71	39.80	9.99
2.25	12.46	16.19	55.76	18.61	39.20	0.66	41.50	10.06
2.5	12.34	18.53	55.73	18.34	47.80	0.74	50.80	9.94
2.75	12.44	20.21	55.74	18.20	53.10	0.67	52.60	10.02
3	12.36	18.50	55.75	18.20	59.40	0.73	54.40	9.98
3.25	12.42	16.80	55.77	18.17	59.30	0.64	56.20	10.04
3.5	12.38	15.10	55.74	18.15	59.50	0.76	58.00	9.96
3.75	12.40	12.60	55.73	18.14	59.60	0.70	58.40	10.07
4	12.41	15.80	55.52	18.11	59.70	0.70	59.60	9.93
4.25	12.39	19.82	55.71	18.09	59.80	0.68	59.70	10.00
4.5	12.40	27.35	55.78	18.04	59.80	0.72	60.20	10.00
4.75	12.40	34.18	55.76	18.01	59.70	0.69	61.50	10.00
5	12.40	39.23	55.72	18.01	59.70	0.71	62.40	10.00
RMS	12.401	19.200	45.997	15.848	42.840	0.691	42.727	10.010

Upper limb model motion trajectory: (a) Horizontal Adduction/abduction trajectory and (b) flexion/extension trajectory.

Table 9

Number of mechanism components

Mechanism type	Movable links in mechanism (n)	Lower pairs (PL)	Higher pairs (PH)	DOF (F)
Exoskeleton	2	2	0	2
End–effector	3	2	2	2

End of mechanism trajectories: (a) end–effector during flexion/extension, (b) end–effector trajectory during adduction/abduction, (c) exoskeleton–type during flexion/extension, and (d) exoskeleton during horizontal adduction/abduction.

Trajectory fitting: (a) end–effector during flexion/extension, (b) end–effector during horizontal adduction/abduction, (c) exoskeleton during flexion/extension, and (d) exoskeleton during horizontal adduction/abduction.

Comparison of R ² data trajectories at the end of mechanisms: (a) horizontal adduction/abduction comparison and (b) flexion/extension comparison.

Variation in joint torque: (a) flexion/extension with end–effector mechanism, (b) horizontal adduction/abduction with end–effector mechanism, (c) flexion/extension with exoskeleton mechanisms, and (d) horizontal adduction/abduction with exoskeleton mechanisms.

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DOI: https://doi.org/10.37190/abb/220943 | Journal eISSN: 2450-6303 | Journal ISSN: 1509-409X

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Language: English

Page range: 136 - 151

Submitted on: Mar 10, 2026

Accepted on: Apr 21, 2026

Published on: Oct 28, 2026

Published by: Wroclaw University of Science and Technology

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

Mechanism analysis,

Mechanism design,

Rehabilitation device,

Rehabilitation training,

Trajectory fitting

Related subjects:

Engineering,

Bioengineering and biomedical engineering,

Cellular and tissue engineering,

Biomechanics,

Medicine,

Biomedical engineering,

Materials sciences,

Biomaterials and natural materials

© 2026 Haoyu Han, Qinghui Zhu, Li Feng, published by Wroclaw University of Science and Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 28 (2026): Issue 1 (March 2026)

Design and analysis of rehabilitation training mechanism based on upper limb rehabilitation movements

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