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Robotics and Parallel Kinematic Machines

Swaminath Venkateswaran

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Swaminath Venkateswaran. Robotics and Parallel Kinematic Machines. Robotics, 2025, 14 (9), pp.125. 10.3390/robotics14090125. hal-05240680

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Editorial

# Special Issue: Robotics and Parallel Kinematic Machines

Swaminath Venkateswaran ID

De Vinci Higher Education, De Vinci Research Center, 92916 Paris, France; swaminath.venkateswaran@devinci.fr

Parallel kinematic machines (PKMs) are a class of robots that have long been recognized for their higher stiffness and high payload-to-weight ratio and precision compared to their serial counterparts [1,2]. Their applications are suitable in various areas such as high-speed machining, medical robotics, and space. Despite their advantages and widespread applications, PKMs suffer from various inherent challenges in design and control owing to complexities in kinematics, limited workspaces, and intricate singularity conditions [3]. Recent industrial developments and research work have focused on improving modeling techniques, the analysis of singular configurations, and reconfigurable architecture. Significant attention has been paid to domains such as the optimization of workspaces [4], the singularity avoidance approach [5], robust design procedures [6], and the integration of compliant components for PKM structures [7] in order to meet evolving application demands. However, several theoretical and practical aspects remain underexplored. For example, cuspidal configurations whereby a robot can transition between multiple inverse kinematic solutions without encountering singularities remain less documented [8,9]. Another interesting phenomenon includes self-motion conditions where the end-effector exhibits mobility even when all actuators are locked, thereby posing design challenges and difficulties in control [10,11]. Furthermore, emerging topics such as modular PKM architectures [12], dynamic performance evaluation [13], and control-aware design optimization [14] continue to attract the attention of the research community, especially for high-precision applications under uncertain or varying load conditions. The following Special Issue features eight articles in the field of PKMs and their potential applications to meet the present era's growing industrial demands.

In paper [15], the authors propose an approach for the 3D modeling of spatial manipulators using Maple 2023 software. This approach enables the creation of three-dimensional computer models of manipulators with clear visual representation of links, cross sections, kinematic pairs, and loads, differing in structure and degrees of freedom, while ensuring a comprehensive view from spatial perspectives. Using the Denavit-Hartenberg method for motion control of 3D models and the recursive Newton-Euler algorithm for calculating distributed dynamic loads, algorithms were developed for generating distribution diagrams of all dynamic loads in each link of a moving manipulator. This approach proves vital, especially during the design of new, innovative manipulators.

In paper [16], the author proposes a computationally efficient approach for dimensional synthesis using multi-objective particle swarm optimization with hierarchical constraints. The approach demonstrates the broad applicability of combined structural and dimensional synthesis for symmetric parallel robots with rigid links and serial-kinematic leg chains. The approach also allows for extension as an open-source MATLAB toolbox 2024b.

In paper [17], the authors present the design and analysis of a novel three-degrees-of-freedom parallel robot with self-sensing Nitinol actuators. The method is a continuation of a previous work and was extended to a 20 mm actuator length. The manipulator was

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updates

Received: 16 June 2025

Revised: 28 August 2025

Accepted: 2 September 2025

Published: 3 September 2025

**Citation:** Venkateswaran, S. Special Issue: Robotics and Parallel Kinematic Machines. *Robotics* **2025**, *14*, 125. https://doi.org/10.3390/robotics14090125

**Copyright:** © 2025 by the author. 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/).
realized, and the control strategy was validated experimentally. The work highlights the importance of self-sensing Nitinol actuators for the design of small parallel manipulators.

In paper [18], the authors propose a flexible surgical stapler mechanism for laparoscopic rectal cancer surgery. By performing workspace analysis and synthesizing kinematic equations, precise control of the mechanism was possible during surgical procedures in the rectal region. The singularities were also examined, considering the influential eyelet friction parameter. A preliminary design was presented, which facilitates the identification of the friction parameter.

In paper [19], the authors propose a neural network model to approximate the task time function of a generic multi-DOF robot. The method proposed a uniform interface that can be adapted to generic robots and tasks. The results presented an accurate model with evaluation times compatible with real-time process optimization.

In paper [20], the authors present the analysis of a spherical parallel mechanism of type 3-SPS-U. The usual singularity approach involves using Euler angles. However, this method is computationally expensive, especially when working with stacked models. Using the Tilt and Torsion approach, the singularity analysis was carried out successfully, which also enabled the work to be extended for stacked models. An experimental platform also aided in validating the approach.

In paper [21], the authors present a novel walking hybrid-kinematics robot that can be reconfigured to have three, five, or six degrees of freedom. A symmetric 3PRPR/3PRRR parallel manipulator with three translational DOFs was used to perform machining tasks. A serial module with two rotational DOFs was added to the 3T parallel mechanism to provide five DOFs. Similarly, a parallel 3SPR or 3SU mechanism can also be combined with the 3T parallel mechanism to provide six DOFs. The mobility, pose, kinematics, differential kinematics, singularities, and workspace of the parallel configuration are discussed in detail. The analysis showed that by making the moving platform of 3SPR or 3SU smaller than the base, the singularities can be easily avoided.

Lastly, in paper [22], the authors present a detailed review covering the fields of rehabilitation, assistive technologies, and humanoid robots. The authors focus on the study of parallel robots designed for human body joints with three degrees of freedom, particularly the neck, shoulder, wrist, hip, and ankle. The review authors discuss the timeline and advancements of parallel robots, focusing on technology readiness levels (TRLs), degrees of freedom, kinematic structure, workspace analysis, performance evaluation methods, and material selection for the design.

The Guest Editor would like to sincerely thank all of the contributors for taking a keen interest in our Special Issue. All of the articles included herein were subjected to rigorous peer review to ensure the production of a high-quality publication. We also thank all of the reviewers for their valuable comments and revisions. In addition, we would like to thank the editors from MDPI for their support in the organization and publication of this Special Issue.

It is our belief that this Special Issue will help fellow researchers and industrial experts to gain an in-depth understanding of the analysis of parallel kinematic machines and their applications based on their architecture.

**Conflicts of Interest:** The author declares no conflicts of interest.

## References

1. Merlet, J.P. *Parallel Robots*; Springer: Dordrecht, The Netherlands, 2006.

2. Tsai, L.W. *Robot Analysis: The Mechanics of Serial and Parallel Manipulators*; John Wiley & Sons: Hoboken, NJ, USA, 1999.

3. Miller, K. *Optimal design and modeling of spatial parallel manipulators*. *Int. J. Robot. Res.* **2004**, *23*, 127–140. [CrossRef]
4. Soltanov, S.; Roberts, R. Design of a Novel Bio-Inspired Three Degrees of Freedom (3DOF) Spherical Robotic Manipulator and Its Application in Human-Robot Interactions. *Robotics* **2025**, *14*, 8. [CrossRef]

5. Di Gregorio, R. Dimensional synthesis of a novel 3-URU translational manipulator implemented through a novel method. *Robotics* **2022**, *11*, 10. [CrossRef]

6. Riabtsev, M.; Guilhem, J.M.; Petuya, V.; Urizar, M.; Laribi, M.A. A Cartesian Parallel Mechanism for Initial Sonography Training. *Robotics* **2025**, *14*, 95. [CrossRef]

7. Feller, D.; Siemens, C. Mechanical design and analysis of a novel three-legged, compact, lightweight, omnidirectional, serial-parallel robot with compliant agile legs. *Robotics* **2022**, *11*, 39. [CrossRef]

8. Wenger, P. Cuspidal robots. In *Singular Configurations of Mechanisms and Manipulators*; Springer International Publishing: Cham, Switzerland, 2019; pp. 67–99.

9. Wenger, P.; Chablat, D. A review of cuspidal serial and parallel manipulators. *J. Mech. Robot.* **2023**, *15*, 040801. [CrossRef]

10. Briot, S.; Arakelian, V.; Bonev, I.A.; Chablat, D.; Wenger, P. Self-motions of general 3-r pr planar parallel robots. *Int. J. Robot. Res.* **2008**, *27*, 855–866. [CrossRef]

11. Chablat, D.; Ottaviano, E.; Venkateswaran, S. Self-motion conditions for a 3-PPPS parallel robot with delta-shaped base. *Mech. Mach. Theory* **2019**, *135*, 109–114. [CrossRef]

12. Cammarata, A.; Maddio, P.D.; Sinatra, R.; Tian, Y.; Zhao, Y.; Xi, F. Elastostatic analysis of a module-based shape morphing snake-like robot. *Mech. Mach. Theory* **2024**, *194*, 105580. [CrossRef]

13. Elsamanty, M.; Faidallah, E.M.; Hossameldin, Y.H.; Rabbo, S.A.; Maged, S.A.; Yang, H.; Guo, K. Workspace analysis and path planning of a novel robot configuration with a 9-DOF serial-parallel hybrid manipulator (SPHM). *Appl. Sci.* **2023**, *13*, 2088. [CrossRef]

14. Maloisel, G.; Knoop, E.; Thomaszewski, B.; Bächer, M.; Coros, S. Singularity-Aware Design Optimization for Multi-Degree-of-Freedom Spatial Linkages. *IEEE Robot. Autom. Lett.* **2021**, *6*, 6585–6592. [CrossRef]

15. Utenov, M.; Sobh, T.; Temirbekov, Y.; Zhilkibayeva, S.; Patel, S.; Baltabay, D.; Zhumasheva, Z. Analysis of Distributed Dynamic Loads Induced by the Own Mass of Manipulator Links and Their Visualization on Interactive 3D Computer Models. *Robotics* **2025**, *14*, 46. [CrossRef]

16. Schappler, M. Dimensional Synthesis of Parallel Robots Using Bilevel Optimization for Design Optimization and Resolution of Functional Redundancy. *Robotics* **2025**, *14*, 29. [CrossRef]

17. Durante, F.; Raparelli, T.; Beomonte Zobel, P. Three-Degree-of-Freedom Cable-Driven Parallel Manipulator with Self-Sensing Nitinol Actuators. *Robotics* **2024**, *13*, 93. [CrossRef]

18. Khanzode, D.; Jha, R.; Thomieres, A.; Duchalais, E.; Chablat, D. Surgical staplers in laparoscopic colectomy: A new innovative flexible design perspective. *Robotics* **2023**, *12*, 156. [CrossRef]

19. Righettini, P.; Strada, R.; Cortinovis, F. Neural network mapping of industrial robots’ task times for real-time process optimization. *Robotics* **2023**, *12*, 143. [CrossRef]

20. Venkateswaran, S.; Chablat, D. Mapping the Tilt and Torsion Angles for a 3-SP SU Parallel Mechanism. *Robotics* **2023**, *12*, 50. [CrossRef]

21. Rosyid, A.; Stefanini, C.; El-Khasawneh, B. A reconfigurable parallel robot for on-structure machining of large structures. *Robotics* **2022**, *11*, 110. [CrossRef]

22. Abarca, V.E.; Elias, D.A. A review of parallel robots: Rehabilitation, assistance, and humanoid applications for neck, shoulder, wrist, hip, and ankle joints. *Robotics* **2023**, *12*, 131. [CrossRef]

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