# Type Synthesis of 5-DOF Hybrid (Parallel-Serial) Manipulators Designed from Open Kinematic Chains

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Synthesis Method

- There are no coaxial P joints;
- The greatest number of (coplanar) P joints is three;
- There are no coaxial R joints;
- The greatest number of R joints with parallel axes is three;
- The greatest number of R joints with intersecting axes is three.

## 3. Results of Method Application

- For the 3T2R motion pattern, the axes of all R joints should remain parallel to a common plane;
- For the 3R2T motion pattern, the axes of all R joints should intersect a common line, orthogonal to the axes of all P joints.

#### 3.1. Type 5R, Subtype RRRRR

#### 3.2. Type 4R1P, Subtype RPRRR

#### 3.3. Type 3R2P, Subtype PPRRR

#### 3.4. Type 3P2R, Subtype PRRPP

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Correction Statement

## References

- Ye, W.; Li, Q. Type synthesis of lower mobility parallel mechanisms: A review. Chin. J. Mech. Eng.
**2019**, 32, 38. [Google Scholar] [CrossRef] - Li, Q.; Hervé, J.M.; Ye, W. Geometric Method for Type Synthesis of Parallel Manipulators; Springer: Singapore, 2020. [Google Scholar] [CrossRef]
- Gao, F.; Yang, J.; Ge, Q.J. Type synthesis of parallel mechanisms having the second class G
_{F}sets and two dimensional rotations. J. Mech. Robot.**2011**, 3, 011003. [Google Scholar] [CrossRef] - Zhang, J.; Jin, Z.; Feng, H. Type synthesis of a 3-mixed-DOF protectable leg mechanism of a firefighting multi-legged robot based on G
_{F}set theory. Mech. Mach. Theory**2018**, 130, 567–584. [Google Scholar] [CrossRef] - Yang, T.L.; Liu, A.X.; Shen, H.P.; Hang, L.B.; Luo, Y.F.; Jin, Q. Topology Design of Robot Mechanisms; Springer: Singapore, 2018. [Google Scholar] [CrossRef]
- Gogu, G. Structural Synthesis of Parallel Robots: Part 1—Methodology; Springer: Dordrecht, The Netherlands, 2008. [Google Scholar] [CrossRef]
- Sun, T.; Yang, S.; Lian, B. Finite and Instantaneous Screw Theory in Robotic Mechanism; Springer: Singapore, 2020. [Google Scholar] [CrossRef]
- Song, Y.; Han, P.; Wang, P. Type synthesis of 1T2R and 2R1T parallel mechanisms employing conformal geometric algebra. Mech. Mach. Theory
**2018**, 121, 475–486. [Google Scholar] [CrossRef] - Huang, Z.; Li, Q. Type synthesis of symmetrical lower-mobility parallel mechanisms using the constraint-synthesis method. Int. J. Robot. Res.
**2003**, 22, 59–79. [Google Scholar] [CrossRef] - Huang, Z.; Li, Q.; Ding, H. Theory of Parallel Mechanisms; Springer: Dordrecht, The Netherlands, 2013. [Google Scholar] [CrossRef]
- Borges Dos Santos, J.V.; Simoni, R.; Carboni, A.P.; Martins, D. A new method for type synthesis of parallel mechanisms using screw theory and features of genetic algorithms. J. Braz. Soc. Mech. Sci. Eng.
**2020**, 42, 615. [Google Scholar] [CrossRef] - Hu, B.; Bai, P. Type synthesis of serial kinematic chains with screw type terminal constraints based on an adding joint method. Mech. Mach. Theory
**2023**, 184, 105277. [Google Scholar] [CrossRef] - Kong, X.; Gosselin, C. Type Synthesis of Parallel Mechanisms; Springer: Berlin-Heidelberg, Germany, 2007. [Google Scholar] [CrossRef]
- Hopkins, J.B.; Culpepper, M.L. Synthesis of multi-degree of freedom, parallel flexure system concepts via freedom and constraint topology (FACT)—Part I: Principles. Precis. Eng.
**2010**, 34, 259–270. [Google Scholar] [CrossRef] - Hopkins, J.B.; Culpepper, M.L. Synthesis of multi-degree of freedom, parallel flexure system concepts via freedom and constraint topology (FACT). Part II: Practice. Precis. Eng.
**2010**, 34, 271–278. [Google Scholar] [CrossRef] - Xie, F.; Li, T.; Liu, X. Type synthesis of 4-DOF parallel kinematic mechanisms based on Grassmann line geometry and atlas method. Chin. J. Mech. Eng.
**2013**, 26, 1073–1081. [Google Scholar] [CrossRef] - Zhang, Y.; Huang, H.; Mei, T.; Li, B. Type synthesis of single-loop deployable mechanisms based on improved atlas method for single-DOF grasping manipulators. Mech. Mach. Theory
**2022**, 169, 104656. [Google Scholar] [CrossRef] - Kuo, C.H.; Dai, J.S. Structural synthesis of serial robotic manipulators subject to specific motion constraints. In Proceedings of the ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Montreal, QC, Canada, 15–18 August 2010; Volume 2, pp. 907–915. [Google Scholar] [CrossRef]
- Kuo, C.H.; Dai, J.S. Task-oriented structure synthesis of a class of parallel manipulators using motion constraint generator. Mech. Mach. Theory
**2013**, 70, 394–406. [Google Scholar] [CrossRef] - Tsai, L.W. Systematic enumeration of parallel manipulators. In Parallel Kinematic Machines; Boër, C.R., Molinari-Tosatti, L., Smith, K.S., Eds.; Springer: London, UK, 1999; pp. 33–49. [Google Scholar] [CrossRef]
- Lu, Y.; Leinonen, T. Type synthesis of unified planar–spatial mechanisms by systematic linkage and topology matrix-graph technique. Mech. Mach. Theory
**2005**, 40, 1145–1163. [Google Scholar] [CrossRef] - Ramirez, D. Automatic Generation of Task-Specific Serial Mechanisms Using Combined Structural and Dimensional Synthesis. Ph.D. Thesis, Gottfried Wilhelm Leibniz Universität, Hannover, Germany, 2018. [Google Scholar] [CrossRef]
- Meng, X.; Gao, F.; Wu, S.; Ge, Q.J. Type synthesis of parallel robotic mechanisms: Framework and brief review. Mech. Mach. Theory
**2014**, 78, 177–186. [Google Scholar] [CrossRef] - Xie, F.; Liu, X.J.; Li, T. Type synthesis and typical application of 1T2R-type parallel robotic mechanisms. Math. Probl. Eng.
**2013**, 2013, 206181. [Google Scholar] [CrossRef] - Lin, G.; Huang, P.; Wang, M.; Xu, Y.; Zhang, R.; Zhu, L. An inverse kinematics solution for a series-parallel hybrid banana-harvesting robot based on deep reinforcement learning. Agronomy
**2022**, 12, 2157. [Google Scholar] [CrossRef] - Pisla, D.; Gherman, B.; Vaida, C.; Suciu, M.; Plitea, N. An active hybrid parallel robot for minimally invasive surgery. Robot. Comp. Int. Manuf.
**2013**, 29, 203–221. [Google Scholar] [CrossRef] - Zhou, M.; Yu, Q.; Huang, K.; Mahov, S.; Eslami, A.; Maier, M.; Lohmann, C.P.; Navab, N.; Zapp, D.; Knoll, A.; et al. Towards robotic-assisted subretinal injection: A hybrid parallel–serial robot system design and preliminary evaluation. IEEE Trans. Ind. Electron.
**2020**, 67, 6617–6628. [Google Scholar] [CrossRef] - Chakarov, D.; Parushev, P. Synthesis of parallel manipulators with linear drive modules. Mech. Mach. Theory
**1994**, 29, 917–932. [Google Scholar] [CrossRef] - Campos, A.; Budde, C.; Hesselbach, J. A type synthesis method for hybrid robot structures. Mech. Mach. Theory
**2008**, 43, 984–995. [Google Scholar] [CrossRef] - Alizade, R.; Bayram, Ç. Structural synthesis of parallel manipulators. Mech. Mach. Theory
**2004**, 39, 857–870. [Google Scholar] [CrossRef] - Zeng, Q.; Fang, Y. Structural synthesis of serial-parallel hybrid mechanisms based on representation and operation of logical matrix. J. Mech. Robot.
**2009**, 1, 041003. [Google Scholar] [CrossRef] - Zeng, Q.; Fang, Y. Algorithm for topological design of multi-loop hybrid mechanisms via logical proposition. Robotica
**2012**, 30, 599–612. [Google Scholar] [CrossRef] - Zeng, Q.; Fang, Y. Structural synthesis and analysis of serial–parallel hybrid mechanisms with spatial multi-loop kinematic chains. Mech. Mach. Theory
**2012**, 49, 198–215. [Google Scholar] [CrossRef] - Shen, H.; Zhao, H.; Deng, J.; Meng, Q.; Zhu, W.; Yang, T. Type design method and the application for hybrid robot based on freedom distribution and position and orientation characteristic set. J. Mech. Eng.
**2011**, 47, 56–64. [Google Scholar] [CrossRef] - Antonov, A.; Fomin, A.; Glazunov, V.; Kiselev, S.; Carbone, G. Inverse and forward kinematics and workspace analysis of a novel 5-DOF (3T2R) parallel–serial (hybrid) manipulator. Int. J. Adv. Robot. Syst.
**2021**, 18. [Google Scholar] [CrossRef] - Wang, C.; Fang, Y.; Guo, S. Design and analysis of 3R2T and 3R3T parallel mechanisms with high rotational capability. J. Mech. Robot.
**2016**, 8, 011004. [Google Scholar] [CrossRef] - Kim, S.K.; Shin, W.H.; Ko, S.Y.; Kim, J.; Kwon, D.S. Design of a compact 5-DOF surgical robot of a spherical mechanism: CURES. In Proceedings of the 2008 IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Xi’an, China, 2–5 July 2008; pp. 990–995. [Google Scholar] [CrossRef]
- Pisla, D.; Plitea, N.; Gherman, B.G.; Vaida, C.; Pisla, A.; Suciu, M. Kinematics and design of a 5-DOF parallel robot used in minimally invasive surgery. In Advances in Robot Kinematics: Motion in Man and Machine; Lenarčič, J., Stanišić, M.M., Eds.; Springer: Dordrecht, The Netherlands, 2010; pp. 99–106. [Google Scholar] [CrossRef]
- Tsai, C.Y.; Wong, C.C.; Yu, C.J.; Liu, C.C.; Liu, T.Y. A hybrid switched reactive-based visual servo control of 5-DOF robot manipulators for pick-and-place tasks. IEEE Syst. J.
**2015**, 9, 119–130. [Google Scholar] [CrossRef] - Gao, F.; Peng, B.; Zhao, H.; Li, W. A novel 5-DOF fully parallel kinematic machine tool. Int. J. Adv. Manuf. Tech.
**2006**, 31, 201–207. [Google Scholar] [CrossRef] - Tian, W.; Mou, M.; Yang, J.; Yin, F. Kinematic calibration of a 5-DOF hybrid kinematic machine tool by considering the ill-posed identification problem using regularisation method. Robot. Comp. Int. Manuf.
**2019**, 60, 49–62. [Google Scholar] [CrossRef] - Li, Y.; Tan, D.; Wen, D.; Ji, S.; Cai, D. Parameters optimization of a novel 5-DOF gasbag polishing machine tool. Chin. J. Mech. Eng.
**2013**, 26, 680–688. [Google Scholar] [CrossRef] - Sun, T.; Wu, H.; Lian, B.; Qi, Y.; Wang, P.; Song, Y. Stiffness modeling, analysis and evaluation of a 5 degree of freedom hybrid manipulator for friction stir welding. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci.
**2017**, 231, 4441–4456. [Google Scholar] [CrossRef] - Cao, Y.; Qin, Y.; Chen, H.; Ge, S.; Zhou, H. Structural synthesis of 5-DOF hybrid mechanisms based on G
_{F}set. Trans. Chin. Soc. Agr. Mach.**2015**, 46, 392–398. [Google Scholar] [CrossRef] - Cao, Y.; Zhou, R.; Qin, Y.; Ge, S.; Ding, R. Structural synthesis of fully-isotropic five degree-of-freedom hybrid kinematic mechanisms. J. Mech. Eng.
**2018**, 54, 29–37. [Google Scholar] [CrossRef] - Zhou, H.; Qin, Y.; Chen, H.; Ge, S.; Cao, Y. Structural synthesis of five-degree-of-freedom hybrid kinematics mechanism. J. Eng. Des.
**2016**, 27, 390–412. [Google Scholar] [CrossRef] - Shen, H.; Yin, H.; Li, J.; Deng, J.; Liu, A. Position and orientation characteristic based method and enlightenment for topology characteristic analysis of typical parallel mechanisms and its application. J. Mech. Eng.
**2015**, 51, 101–115. [Google Scholar] [CrossRef] - Xu, Y.; Yao, J.; Zhao, Y. Type synthesis of spatial mechanisms for forging manipulators. Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci.
**2012**, 226, 2320–2330. [Google Scholar] [CrossRef] - Xu, Y.; Zhao, Y.; Yue, Y.; Xi, F.; Yao, J.; Zhao, Y. Type synthesis of overconstrained 2R1T parallel mechanisms with the fewest kinematic joints based on the ultimate constraint wrenches. Mech. Mach. Theory
**2020**, 147, 103766. [Google Scholar] [CrossRef] - Zhang, D.; Zheng, Y.; Wei, L.; Wu, J.; Xu, Y.; Zhao, Y. Type synthesis of 2T1R planar parallel mechanisms and their moduling development applications. IEEE Access
**2021**, 9, 72217–72227. [Google Scholar] [CrossRef] - Zhang, D.; Xu, Y.; Yao, J.; Zhao, Y. Design of a novel 5-DOF hybrid serial-parallel manipulator and theoretical analysis of its parallel part. Robot. Comp. Int. Manuf.
**2018**, 53, 228–239. [Google Scholar] [CrossRef] - Merlet, J.P. Parallel Robots, 2nd ed.; Springer: Dordrecht, The Netherlands, 2006. [Google Scholar] [CrossRef]
- Fang, Y.; Tsai, L.W. Enumeration of a class of overconstrained mechanisms using the theory of reciprocal screws. Mech. Mach. Theory
**2004**, 39, 1175–1187. [Google Scholar] [CrossRef] - Riordan, J. Introduction to Combinatorial Analysis, Dover ed.; Dover Publications: Mineola, NY, USA, 2002; Available online: https://scholar.google.com/scholar?cluster=17160231405262501443 (accessed on 10 July 2023).
- He, P.; Kantu, N.T.; Xu, B.; Swami, C.P.; Saleem, G.T.; Kang, J. A novel 3-RRR spherical parallel instrument for daily living emulation (SPINDLE) for functional rehabilitation of patients with stroke. Int. J. Adv. Robot. Syst.
**2021**, 18. [Google Scholar] [CrossRef] - Khoshnoodi, H.; Rahmani Hanzaki, A.; Talebi, H.A. Kinematics, singularity study and optimization of an innovative spherical parallel manipulator with large workspace. J. Intell. Robot. Syst.
**2018**, 92, 309–321. [Google Scholar] [CrossRef] - Si, G.; Chen, F.; Zhang, X. Comparison of the dynamic performance of planar 3-DOF parallel manipulators. Machines
**2022**, 10, 233. [Google Scholar] [CrossRef] - Bonev, I.A.; Yu, A.; Zsombor-Murray, P. XY-Theta positioning table with parallel kinematics and unlimited theta rotation. In Proceedings of the 2006 IEEE International Symposium on Industrial Electronics, Montreal, QC, Canada, 9–13 July 2006; Volume 4, pp. 3113–3117. [Google Scholar] [CrossRef]
- Li, Q.; Xu, L.; Chen, Q.; Ye, W. New family of RPR-equivalent parallel mechanisms: Design and application. Chin. J. Mech. Eng.
**2017**, 30, 217–221. [Google Scholar] [CrossRef] - Li, Q.; Hervé, J.M. Type synthesis of 3-DOF RPR-equivalent parallel mechanisms. IEEE Trans. Robot.
**2014**, 30, 1333–1343. [Google Scholar] [CrossRef] - Kong, X.; Gosselin, C.M. Type synthesis of 3-DOF PPR-equivalent parallel manipulators based on screw theory and the concept of virtual chain. J. Mech. Des.
**2005**, 127, 1113–1121. [Google Scholar] [CrossRef] - Xie, F.; Liu, X.J.; You, Z.; Wang, J. Type synthesis of 2T1R-type parallel kinematic mechanisms and the application in manufacturing. Robot. Comp. Int. Manuf.
**2014**, 30, 1–10. [Google Scholar] [CrossRef] - Yao, Y.; Wu, W.; Li, R.; Zhao, Y. Parasitic motions of 3-PRS parallel mechanisms with two different branch chain arrangements. Appl. Sci.
**2023**, 13, 5425. [Google Scholar] [CrossRef] - Hu, B.; Huang, Z. A family of 2R1T parallel manipulators with intersecting rotational axes. In Advances in Reconfigurable Mechanisms and Robots II; Ding, X., Kong, X., Dai, J.S., Eds.; Springer: Cham, Switzerland, 2016; pp. 287–295. [Google Scholar] [CrossRef]
- Sun, P.; Li, Y.B.; Wang, Z.S.; Chen, K.; Chen, B.; Zeng, X.; Zhao, J.; Yue, Y. Inverse displacement analysis of a novel hybrid humanoid robotic arm. Mech. Mach. Theory
**2020**, 147, 103743. [Google Scholar] [CrossRef] - Prause, I.; Charaf Eddine, S.; Corves, B. Comparison of parallel kinematic machines with three translational degrees of freedom and linear actuation. Chin. J. Mech. Eng.
**2015**, 28, 841–850. [Google Scholar] [CrossRef] - Ye, W.; Li, Q.; Chai, X.X. New family of 3-DOF UP-equivalent parallel mechanisms with high rotational capability. Chin. J. Mech. Eng.
**2018**, 31, 12. [Google Scholar] [CrossRef] - Zhang, Z.; Wang, L.; Shao, Z. Improving the kinematic performance of a planar 3-RRR parallel manipulator through actuation mode conversion. Mech. Mach. Theory
**2018**, 130, 86–108. [Google Scholar] [CrossRef] - Laryushkin, P.; Antonov, A.; Fomin, A.; Essomba, T. Velocity and singularity analysis of a 5-DOF (3T2R) parallel-serial (hybrid) manipulator. Machines
**2022**, 10, 276. [Google Scholar] [CrossRef] - Antonov, A.V.; Fomin, A.S. Inverse kinematics of a 5-Dof hybrid manipulator. Autom. Remote Control
**2023**, 84, 281–293. [Google Scholar] [CrossRef] - Antonov, A.; Fomin, A. Velocity analysis of a 5-DOF hybrid manipulator. In New Advances in Mechanisms, Transmissions and Applications; Laribi, M.A., Nelson, C.A., Ceccarelli, M., Zeghloul, S., Eds.; Springer: Cham, Switzerland, 2023; pp. 161–170. [Google Scholar] [CrossRef]
- Wu, X.; Bai, S. Analytical determination of shape singularities for three types of parallel manipulators. Mech. Mach. Theory
**2020**, 149, 103812. [Google Scholar] [CrossRef] - Gosselin, C.; Schreiber, L.T. Redundancy in parallel mechanisms: A review. Appl. Mech. Rev.
**2018**, 70, 010802. [Google Scholar] [CrossRef]

**Figure 1.**5R type, RRRRR subtype (# 1 in Table 2): (

**a**) primary open kinematic chain; (

**b**,

**c**) synthesized 5-DOF 3R2T hybrid manipulators with a 3-DOF spherical parallel mechanism.

**Figure 2.**5R type, RRRRR subtype (# 1 in Table 2): (

**a**) primary open kinematic chain; (

**b**,

**c**) synthesized 5-DOF 3T2R hybrid manipulators with a 3-DOF planar parallel mechanism.

**Figure 3.**4R1P type, RPRRR subtype (# 7 in Table 2): (

**a**) primary open kinematic chain; (

**b**,

**c**) synthesized 5-DOF 3R2T hybrid manipulators with a 3-DOF RPR-equivalent parallel mechanism.

**Figure 4.**3R2P type, PPRRR subtype (# 19 in Table 2): (

**a**) primary open kinematic chain; (

**b**,

**c**) synthesized 5-DOF 3T2R hybrid manipulators with a 3-DOF PPR-equivalent parallel mechanism.

**Figure 5.**3P2R type, PRRPP subtype (# 64 in Table 2): (

**a**) primary open kinematic chain; (

**b**,

**c**) synthesized 5-DOF 3T2R hybrid manipulators with a 3-DOF PU-equivalent parallel mechanism.

**Figure 6.**5R type, RRRRR subtype (# 1 in Table 2): (

**a**) primary open kinematic chain; (

**b**) synthesized 5-DOF 3T2R hybrid manipulator, whose parallel part has a motion pattern different from the replaced subchain.

**Figure 7.**Virtual prototypes of two 5-DOF 3T2R hybrid manipulators developed by the proposed method: (

**a**) manipulator with a 3-DOF PU-equivalent parallel mechanism and a PP serial chain; (

**b**) manipulator with a redundantly actuated 3-DOF planar parallel mechanism and a PR serial chain.

(1) RRRRR | (2) PRRRR | (3) RPRRR | (4) RRPRR | (5) RRRPR | (6) RRRRP |

(7) PPRRR | (8) PRPRR | (9) PRRPR | (10) PRRRP | (11) RPPRR | (12) RPRPR |

(13) RPRRP | (14) RRPPR | (15) RRPRP | (16) RRRPP | (17) PPPRR | (18) PPRPR |

(19) PPRRP | (20) PRPPR | (21) PRPRP | (22) PRRPP | (23) RPPPR | (24) RPRPP |

(25) RPPRP | (26) RRPPP |

5R Type | |||||
---|---|---|---|---|---|

(1) RRRRR | (2) RRRRR | (3) RRRRR | |||

4R1P type | |||||

(4) PRRRR | (5) PRRRR | (6) PRRRR | (7) RPRRR | (8) RPRRR | (9) RPRRR |

(10) RRPRR | (11) RRPRR | (12) RRPRR | (13) RRRPR | (14) RRRPR | (15) RRRPR |

(16) RRRRP | (17) RRRRP | (18) RRRRP | |||

3R2P type | |||||

(19) PPRRR | (20) PPRRR | (21) PPRRR | (22) PRPRR | (23) PRPRR | (24) PRPRR |

(25) PRRPR | (26) PRRPR | (27) PRRPR | (28) PRRRP | (29) PRRRP | (30) PRRRP |

(31) RPPRR | (32) RPPRR | (33) RPPRR | (34) RPRPR | (35) RPRPR | (36) RPRPR |

(37) RPRRP | (38) RPRRP | (39) RPRRP | (40) RRPPR | (41) RRPPR | (42) RRPPR |

(43) RRPRP | (44) RRPRP | (45) RRPRP | (46) RRRPP | (47) RRRPP | (48) RRRPP |

3P2R type | |||||

(49) PPPRR | (50) PPPRR | (51) PPPRR | (52) PPRPR | (53) PPRPR | (54) PPRPR |

(55) PPRRP | (56) PPRRP | (57) PPRRP | (58) PRPPR | (59) PRPPR | (60) PRPPR |

(61) PRPRP | (62) PRPRP | (63) PRPRP | (64) PRRPP | (65) PRRPP | (66) PRRPP |

(67) RPPPR | (68) RPPPR | (69) RPPPR | (70) RPRPP | (71) RPRPP | (72) RPRPP |

(73) RPPRP | (74) RPPRP | (75) RPPRP | (76) RRPPP | (77) RRPPP | (78) RRPPP |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Antonov, A.; Fomin, A.; Glazunov, V.; Petelin, D.; Filippov, G.
Type Synthesis of 5-DOF Hybrid (Parallel-Serial) Manipulators Designed from Open Kinematic Chains. *Robotics* **2023**, *12*, 98.
https://doi.org/10.3390/robotics12040098

**AMA Style**

Antonov A, Fomin A, Glazunov V, Petelin D, Filippov G.
Type Synthesis of 5-DOF Hybrid (Parallel-Serial) Manipulators Designed from Open Kinematic Chains. *Robotics*. 2023; 12(4):98.
https://doi.org/10.3390/robotics12040098

**Chicago/Turabian Style**

Antonov, Anton, Alexey Fomin, Victor Glazunov, Daniil Petelin, and Gleb Filippov.
2023. "Type Synthesis of 5-DOF Hybrid (Parallel-Serial) Manipulators Designed from Open Kinematic Chains" *Robotics* 12, no. 4: 98.
https://doi.org/10.3390/robotics12040098