Figure 1:
![A two-phase HSM, (A) Whole motor, (B) Rotor, and (C) Stator [28]. HSM, hybrid stepper motor.](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLY5XLEKT%2F20260316%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260316T232748Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBcaDGV1LWNlbnRyYWwtMSJGMEQCIC%2FAFpH7xU48k%2B28kz%2BvHlRGhbG7ijNDvuP%2B81YOYX%2FHAiB7WV76L5NcUEIL9iImoJvLD71ooqeIxyNt1TD1gJ5kkirEBQjg%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMkwVTBMTnbeFx8OxSKpgFYmAG6lZaf12wdld1XcMhpf7NvNZj323BcpudCMAloAvGedmms2JTXhbbQbeEHzxr5RlXaQWQ47dBY1bnicZaus88W5XdDY15ALFVwPpu3E7YpVOHm6xhnTi82rr7z1Y0vrsJ%2FQFJ41rDZMX8SyYGX8%2Ft57weeP5YpoEqdUkjliiEZAdYuzA5KvwY3zg6wy9RVQZpq9ZEEhBcJ8HapW3UxIaxx3FRz2Ub9O5y0hRmhdJtOHdKfTsKxbp2YKUbH3ynh%2BtW%2FW3%2BBG5pxQh45iWkzf5Nkb0pGBoHeX1Dks74NOaCLdXkAuDvgyarKKWMO4q08%2BP7kSQJfR3iOrw5Z0S724PtwQag4UA%2FfWdlF93%2BG8W%2B6RQq3IoyF2R%2FJcsK%2BObxhGzS6TbD%2BlEPDhv5LcAz7lqMfB1xgc1a0aAVuw6wKAFbHGKcyMCUc5fOKPzrXUfXGAOOoj7g0VxF9LSd9EnlXXI0O5LVWog3bY%2Fly%2BQwIc3nvesW2Ix27g72ck0%2FlnCdAfRpycVVfF9G2Ypn4QikPf8pgUrtATIUahF%2Ft5YSQspnXAnLzyF9BTiJwJB2puFHXwysBuF4vuH3rvbycvmT8cAKu9U5R7M3k6A9bXM1bnI7CjC56Ox9kIM5OnL1NRdh%2F0IunBdbCT8%2Fox3rSq8tTRh20%2BXrIB9jAq6DIHDxejJcGYHpyN2wQoOHyPexhEu3PKwAFquFqu8%2FdIdy5WRr1Y70MfEv%2FP1mOPUJP6OsqhIK8SM%2BOBzLSIzO7MX6Q0Rrabo%2Bssz7F7wsnTZcCwfB06rr3USWR86j3KPLJyoRBC5J5uvpxdsZ73cp7n%2BzMuxP7VbGB9JiuePQGLd1gKw2esXyVblHiMZgkBlq%2FUqrCFXNdNuVrbjIjDDjiuLNBjqyAZORb1z0SOFyKnXuDMY4DZMGrJrNEMKYyToBfoCvA72u%2Foo0jEBvuY%2BLmvmKgTrXsobb1IRylpmEyRJ4IJ51LD9Wfq5S9dq1RphJAa6CzSCWmmOvAvt%2FFCViaBUnU5xEbvqO6LjhipcUIy3sueU82Ls%2FxdE97AoKHjrPtCWLsCr47FxvnT4DU6F09YWSsehFemcsf%2FpwgyQc%2BC1f7oFQn%2B%2FMGMnfDcpcAiINEe31%2B9SU1l4%3D&X-Amz-Signature=7235eb43e33abcd2beabfa3da791b0daa571c4055331e6806a1be7fa4ed6c7b3&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 2:
![Stepper motor testbed, (A) Front view, (B) Back view, 1: Stepper motor, 2: Weights carrier arm, 3: Arduino and LCD shield, 4: Load cell, 5: Weights [28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_002.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLY5XLEKT%2F20260316%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260316T232748Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBcaDGV1LWNlbnRyYWwtMSJGMEQCIC%2FAFpH7xU48k%2B28kz%2BvHlRGhbG7ijNDvuP%2B81YOYX%2FHAiB7WV76L5NcUEIL9iImoJvLD71ooqeIxyNt1TD1gJ5kkirEBQjg%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMkwVTBMTnbeFx8OxSKpgFYmAG6lZaf12wdld1XcMhpf7NvNZj323BcpudCMAloAvGedmms2JTXhbbQbeEHzxr5RlXaQWQ47dBY1bnicZaus88W5XdDY15ALFVwPpu3E7YpVOHm6xhnTi82rr7z1Y0vrsJ%2FQFJ41rDZMX8SyYGX8%2Ft57weeP5YpoEqdUkjliiEZAdYuzA5KvwY3zg6wy9RVQZpq9ZEEhBcJ8HapW3UxIaxx3FRz2Ub9O5y0hRmhdJtOHdKfTsKxbp2YKUbH3ynh%2BtW%2FW3%2BBG5pxQh45iWkzf5Nkb0pGBoHeX1Dks74NOaCLdXkAuDvgyarKKWMO4q08%2BP7kSQJfR3iOrw5Z0S724PtwQag4UA%2FfWdlF93%2BG8W%2B6RQq3IoyF2R%2FJcsK%2BObxhGzS6TbD%2BlEPDhv5LcAz7lqMfB1xgc1a0aAVuw6wKAFbHGKcyMCUc5fOKPzrXUfXGAOOoj7g0VxF9LSd9EnlXXI0O5LVWog3bY%2Fly%2BQwIc3nvesW2Ix27g72ck0%2FlnCdAfRpycVVfF9G2Ypn4QikPf8pgUrtATIUahF%2Ft5YSQspnXAnLzyF9BTiJwJB2puFHXwysBuF4vuH3rvbycvmT8cAKu9U5R7M3k6A9bXM1bnI7CjC56Ox9kIM5OnL1NRdh%2F0IunBdbCT8%2Fox3rSq8tTRh20%2BXrIB9jAq6DIHDxejJcGYHpyN2wQoOHyPexhEu3PKwAFquFqu8%2FdIdy5WRr1Y70MfEv%2FP1mOPUJP6OsqhIK8SM%2BOBzLSIzO7MX6Q0Rrabo%2Bssz7F7wsnTZcCwfB06rr3USWR86j3KPLJyoRBC5J5uvpxdsZ73cp7n%2BzMuxP7VbGB9JiuePQGLd1gKw2esXyVblHiMZgkBlq%2FUqrCFXNdNuVrbjIjDDjiuLNBjqyAZORb1z0SOFyKnXuDMY4DZMGrJrNEMKYyToBfoCvA72u%2Foo0jEBvuY%2BLmvmKgTrXsobb1IRylpmEyRJ4IJ51LD9Wfq5S9dq1RphJAa6CzSCWmmOvAvt%2FFCViaBUnU5xEbvqO6LjhipcUIy3sueU82Ls%2FxdE97AoKHjrPtCWLsCr47FxvnT4DU6F09YWSsehFemcsf%2FpwgyQc%2BC1f7oFQn%2B%2FMGMnfDcpcAiINEe31%2B9SU1l4%3D&X-Amz-Signature=0a67cc459367657f542fab54af403f000c88757551884258193e06363653c6d2&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 3:
![Real motor and simulated model output torque [28].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLY5XLEKT%2F20260316%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260316T232748Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBcaDGV1LWNlbnRyYWwtMSJGMEQCIC%2FAFpH7xU48k%2B28kz%2BvHlRGhbG7ijNDvuP%2B81YOYX%2FHAiB7WV76L5NcUEIL9iImoJvLD71ooqeIxyNt1TD1gJ5kkirEBQjg%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMkwVTBMTnbeFx8OxSKpgFYmAG6lZaf12wdld1XcMhpf7NvNZj323BcpudCMAloAvGedmms2JTXhbbQbeEHzxr5RlXaQWQ47dBY1bnicZaus88W5XdDY15ALFVwPpu3E7YpVOHm6xhnTi82rr7z1Y0vrsJ%2FQFJ41rDZMX8SyYGX8%2Ft57weeP5YpoEqdUkjliiEZAdYuzA5KvwY3zg6wy9RVQZpq9ZEEhBcJ8HapW3UxIaxx3FRz2Ub9O5y0hRmhdJtOHdKfTsKxbp2YKUbH3ynh%2BtW%2FW3%2BBG5pxQh45iWkzf5Nkb0pGBoHeX1Dks74NOaCLdXkAuDvgyarKKWMO4q08%2BP7kSQJfR3iOrw5Z0S724PtwQag4UA%2FfWdlF93%2BG8W%2B6RQq3IoyF2R%2FJcsK%2BObxhGzS6TbD%2BlEPDhv5LcAz7lqMfB1xgc1a0aAVuw6wKAFbHGKcyMCUc5fOKPzrXUfXGAOOoj7g0VxF9LSd9EnlXXI0O5LVWog3bY%2Fly%2BQwIc3nvesW2Ix27g72ck0%2FlnCdAfRpycVVfF9G2Ypn4QikPf8pgUrtATIUahF%2Ft5YSQspnXAnLzyF9BTiJwJB2puFHXwysBuF4vuH3rvbycvmT8cAKu9U5R7M3k6A9bXM1bnI7CjC56Ox9kIM5OnL1NRdh%2F0IunBdbCT8%2Fox3rSq8tTRh20%2BXrIB9jAq6DIHDxejJcGYHpyN2wQoOHyPexhEu3PKwAFquFqu8%2FdIdy5WRr1Y70MfEv%2FP1mOPUJP6OsqhIK8SM%2BOBzLSIzO7MX6Q0Rrabo%2Bssz7F7wsnTZcCwfB06rr3USWR86j3KPLJyoRBC5J5uvpxdsZ73cp7n%2BzMuxP7VbGB9JiuePQGLd1gKw2esXyVblHiMZgkBlq%2FUqrCFXNdNuVrbjIjDDjiuLNBjqyAZORb1z0SOFyKnXuDMY4DZMGrJrNEMKYyToBfoCvA72u%2Foo0jEBvuY%2BLmvmKgTrXsobb1IRylpmEyRJ4IJ51LD9Wfq5S9dq1RphJAa6CzSCWmmOvAvt%2FFCViaBUnU5xEbvqO6LjhipcUIy3sueU82Ls%2FxdE97AoKHjrPtCWLsCr47FxvnT4DU6F09YWSsehFemcsf%2FpwgyQc%2BC1f7oFQn%2B%2FMGMnfDcpcAiINEe31%2B9SU1l4%3D&X-Amz-Signature=628247eac4a39b3483c1225e1e14c2a0f77b3861c9fb193716b403eb6285856d&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4:

Figure 5:
![Linearized tooth to tooth arrangement and flux tubes [14, 15].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLY5XLEKT%2F20260316%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260316T232748Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBcaDGV1LWNlbnRyYWwtMSJGMEQCIC%2FAFpH7xU48k%2B28kz%2BvHlRGhbG7ijNDvuP%2B81YOYX%2FHAiB7WV76L5NcUEIL9iImoJvLD71ooqeIxyNt1TD1gJ5kkirEBQjg%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMkwVTBMTnbeFx8OxSKpgFYmAG6lZaf12wdld1XcMhpf7NvNZj323BcpudCMAloAvGedmms2JTXhbbQbeEHzxr5RlXaQWQ47dBY1bnicZaus88W5XdDY15ALFVwPpu3E7YpVOHm6xhnTi82rr7z1Y0vrsJ%2FQFJ41rDZMX8SyYGX8%2Ft57weeP5YpoEqdUkjliiEZAdYuzA5KvwY3zg6wy9RVQZpq9ZEEhBcJ8HapW3UxIaxx3FRz2Ub9O5y0hRmhdJtOHdKfTsKxbp2YKUbH3ynh%2BtW%2FW3%2BBG5pxQh45iWkzf5Nkb0pGBoHeX1Dks74NOaCLdXkAuDvgyarKKWMO4q08%2BP7kSQJfR3iOrw5Z0S724PtwQag4UA%2FfWdlF93%2BG8W%2B6RQq3IoyF2R%2FJcsK%2BObxhGzS6TbD%2BlEPDhv5LcAz7lqMfB1xgc1a0aAVuw6wKAFbHGKcyMCUc5fOKPzrXUfXGAOOoj7g0VxF9LSd9EnlXXI0O5LVWog3bY%2Fly%2BQwIc3nvesW2Ix27g72ck0%2FlnCdAfRpycVVfF9G2Ypn4QikPf8pgUrtATIUahF%2Ft5YSQspnXAnLzyF9BTiJwJB2puFHXwysBuF4vuH3rvbycvmT8cAKu9U5R7M3k6A9bXM1bnI7CjC56Ox9kIM5OnL1NRdh%2F0IunBdbCT8%2Fox3rSq8tTRh20%2BXrIB9jAq6DIHDxejJcGYHpyN2wQoOHyPexhEu3PKwAFquFqu8%2FdIdy5WRr1Y70MfEv%2FP1mOPUJP6OsqhIK8SM%2BOBzLSIzO7MX6Q0Rrabo%2Bssz7F7wsnTZcCwfB06rr3USWR86j3KPLJyoRBC5J5uvpxdsZ73cp7n%2BzMuxP7VbGB9JiuePQGLd1gKw2esXyVblHiMZgkBlq%2FUqrCFXNdNuVrbjIjDDjiuLNBjqyAZORb1z0SOFyKnXuDMY4DZMGrJrNEMKYyToBfoCvA72u%2Foo0jEBvuY%2BLmvmKgTrXsobb1IRylpmEyRJ4IJ51LD9Wfq5S9dq1RphJAa6CzSCWmmOvAvt%2FFCViaBUnU5xEbvqO6LjhipcUIy3sueU82Ls%2FxdE97AoKHjrPtCWLsCr47FxvnT4DU6F09YWSsehFemcsf%2FpwgyQc%2BC1f7oFQn%2B%2FMGMnfDcpcAiINEe31%2B9SU1l4%3D&X-Amz-Signature=fafbd08ce81044cd5eff49240e83903b00f76af5bf4af664768cc68433c66baa&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 6:
![Construction of a two-phase hybrid stepping motor [14].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/65ccbc5b3bc2d770e76b839c/j_ijssis-2024-0020_fig_006.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKLY5XLEKT%2F20260316%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260316T232748Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEBcaDGV1LWNlbnRyYWwtMSJGMEQCIC%2FAFpH7xU48k%2B28kz%2BvHlRGhbG7ijNDvuP%2B81YOYX%2FHAiB7WV76L5NcUEIL9iImoJvLD71ooqeIxyNt1TD1gJ5kkirEBQjg%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIMkwVTBMTnbeFx8OxSKpgFYmAG6lZaf12wdld1XcMhpf7NvNZj323BcpudCMAloAvGedmms2JTXhbbQbeEHzxr5RlXaQWQ47dBY1bnicZaus88W5XdDY15ALFVwPpu3E7YpVOHm6xhnTi82rr7z1Y0vrsJ%2FQFJ41rDZMX8SyYGX8%2Ft57weeP5YpoEqdUkjliiEZAdYuzA5KvwY3zg6wy9RVQZpq9ZEEhBcJ8HapW3UxIaxx3FRz2Ub9O5y0hRmhdJtOHdKfTsKxbp2YKUbH3ynh%2BtW%2FW3%2BBG5pxQh45iWkzf5Nkb0pGBoHeX1Dks74NOaCLdXkAuDvgyarKKWMO4q08%2BP7kSQJfR3iOrw5Z0S724PtwQag4UA%2FfWdlF93%2BG8W%2B6RQq3IoyF2R%2FJcsK%2BObxhGzS6TbD%2BlEPDhv5LcAz7lqMfB1xgc1a0aAVuw6wKAFbHGKcyMCUc5fOKPzrXUfXGAOOoj7g0VxF9LSd9EnlXXI0O5LVWog3bY%2Fly%2BQwIc3nvesW2Ix27g72ck0%2FlnCdAfRpycVVfF9G2Ypn4QikPf8pgUrtATIUahF%2Ft5YSQspnXAnLzyF9BTiJwJB2puFHXwysBuF4vuH3rvbycvmT8cAKu9U5R7M3k6A9bXM1bnI7CjC56Ox9kIM5OnL1NRdh%2F0IunBdbCT8%2Fox3rSq8tTRh20%2BXrIB9jAq6DIHDxejJcGYHpyN2wQoOHyPexhEu3PKwAFquFqu8%2FdIdy5WRr1Y70MfEv%2FP1mOPUJP6OsqhIK8SM%2BOBzLSIzO7MX6Q0Rrabo%2Bssz7F7wsnTZcCwfB06rr3USWR86j3KPLJyoRBC5J5uvpxdsZ73cp7n%2BzMuxP7VbGB9JiuePQGLd1gKw2esXyVblHiMZgkBlq%2FUqrCFXNdNuVrbjIjDDjiuLNBjqyAZORb1z0SOFyKnXuDMY4DZMGrJrNEMKYyToBfoCvA72u%2Foo0jEBvuY%2BLmvmKgTrXsobb1IRylpmEyRJ4IJ51LD9Wfq5S9dq1RphJAa6CzSCWmmOvAvt%2FFCViaBUnU5xEbvqO6LjhipcUIy3sueU82Ls%2FxdE97AoKHjrPtCWLsCr47FxvnT4DU6F09YWSsehFemcsf%2FpwgyQc%2BC1f7oFQn%2B%2FMGMnfDcpcAiINEe31%2B9SU1l4%3D&X-Amz-Signature=75a7a5cbbb2faf490025789914918f3c23b8a0a04d1f0d94821970c82d818368&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 7:

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Figure 27:

Stepper motor experiment results [28]
| Current [A] | Weights mass [g] | Torque [mN/m] |
|---|---|---|
| 1.05 | 218 | 130.8 |
| 1.53 | 297 | 178.2 |
| 1.96 | 373 | 223.8 |
| 2.35 | 433 | 259.8 |
| 2.73 | 477 | 286.2 |
Motor specifications [28]
| Motor outer diameter | 56.5 mm |
| Motor body height | 52 mm |
| Stator outer diameter | 54.1 mm |
| Stator inner diameter | 30 mm |
| Number of teeth in each stator pole | 5 |
| Stator teeth depth | 1.25 mm |
| Stator height | 23 mm |
| Air gap | 0.1 mm |
| Rotor outer diameter | 29.8 mm |
| Each half-rotor height | 10 mm |
| Distance between two half-rotors | 3 mm |
| Number of teeth in each half-rotor | 50 |
| Rotor teeth depth | 1.5 mm |
| Magnet diameter | 20.8 mm |
| Magnet height | 13 mm |
| Number of wire-turns per coil | 32 |
| Wire diameter | 0.6 mm |
| Stator and rotor material | Steel 1,008 |
| Magnet material | NdFe35 (1.3 T) |
| Stator and rotors teeth fillet radius | 0.125 mm |
| Maximum nominal current | 3A |
| Angle per step | 1.8° |
| Rotor and stator teeth angle (pitch) | 7.2° |
| Rotor and stator teeth width | 3.6°(0.94 mm) |
| Stator pole thickness | 2 mm |
The motor parameters
| Absolute permeability | μ0 | 4π × 10−7 H/m |
| Slot thickness | t | 0.939 mm |
| Air gap length | g | 0.1 mm |
| Rotor and stator teeth depth | d | 1.375 mm |
| Tooth thickness | s | 0.939 mm |
| Number of teeth per stator pole | Zs | 5 |
| Number of rotor teeth | Zr | 50 |
| Number of wire-turns per stator winding | Ns | 32 |
| Excitation current | i | 1.5 A |
| Rotor height | h | 20 mm |