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Robotics
Volume 15
Issue 1
10.3390/robotics15010010
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Geometry, Kinematics, Workspace, and Singularities of a Novel 3-PRRS Parallel Manipulator

by
Zhumadil Baigunchekov
1,
Giuseppe Carbone
2,
Med Amine Laribi
3,
Rustem Kaiyrov
4,*,
Li Qian
5 and
Zhadyra Zhumasheva
1
1
Faculty of Mechanics and Mathematics, Department of Mechanics, Al-Farabi Kazakh National University, 71/23 Al-Farabi Avenue, Almaty 050040, Kazakhstan
2
School of Engineering, Department of Mechanical, Energy and Management Engineering (DIMEG), University of Calabria, Via Bucci Cubo 45C, 87036 Rende, Italy
3
Department of GMSC, Prime Institute CNRS, ENSMA, University of Poitiers, UPR 3346, Poitiers 86000, France
4
Laboratory of Applied Mechanics and Robotics, Karaganda Buketov University, Karaganda 100001, Kazakhstan
5
Institute of Automation, Shandong Academy of Sciences, Jinan 250000, China
*
Author to whom correspondence should be addressed.
Robotics 2026, 15(1), 10; https://doi.org/10.3390/robotics15010010 (registering DOI)
Submission received: 6 November 2025 / Revised: 22 December 2025 / Accepted: 24 December 2025 / Published: 29 December 2025
(This article belongs to the Section Industrial Robots and Automation)
Versions Notes

Abstract

“Experiments were conducted at DIMEG, University of Calabria, located in the main campus in Arcavacata di Rende, Italy.” This article focuses on the study of the geometry, direct and inverse kinematics, workspace, and singularity of a novel 3-PRRS parallel manipulator (PM) with a redundantly actuated architecture. The PM consists of three active revolute joints and three passive prismatic redundant input joints, all located on a fixed platform. The constant and variable parameters characterizing the PM’s geometry and kinematics are determined. The direct kinematics problem is formulated as a 16th-degree polynomial, while the inverse kinematics problem is solved in closed form. A comparison of the direct and inverse kinematics is provided, and the correctness of the solutions is validated through numerical examples. The equations of motion for the moving platform are derived, and the PM’s workspace is defined based on the inverse kinematics. This work demonstrates how the passive prismatic input joints, specifically included in the design, contribute to an enlarged workspace—particularly in the vertical direction—compared to traditional 3-RRS PM architecture.
Keywords: parallel manipulators; tripod; geometry; matrices of links and kinematic pairs; direct and inverse kinematics; pose of moving platform; workspace; singularity parallel manipulators; tripod; geometry; matrices of links and kinematic pairs; direct and inverse kinematics; pose of moving platform; workspace; singularity

Share and Cite

MDPI and ACS Style

Baigunchekov, Z.; Carbone, G.; Laribi, M.A.; Kaiyrov, R.; Qian, L.; Zhumasheva, Z. Geometry, Kinematics, Workspace, and Singularities of a Novel 3-PRRS Parallel Manipulator. Robotics 2026, 15, 10. https://doi.org/10.3390/robotics15010010

AMA Style

Baigunchekov Z, Carbone G, Laribi MA, Kaiyrov R, Qian L, Zhumasheva Z. Geometry, Kinematics, Workspace, and Singularities of a Novel 3-PRRS Parallel Manipulator. Robotics. 2026; 15(1):10. https://doi.org/10.3390/robotics15010010

Chicago/Turabian Style

Baigunchekov, Zhumadil, Giuseppe Carbone, Med Amine Laribi, Rustem Kaiyrov, Li Qian, and Zhadyra Zhumasheva. 2026. "Geometry, Kinematics, Workspace, and Singularities of a Novel 3-PRRS Parallel Manipulator" Robotics 15, no. 1: 10. https://doi.org/10.3390/robotics15010010

APA Style

Baigunchekov, Z., Carbone, G., Laribi, M. A., Kaiyrov, R., Qian, L., & Zhumasheva, Z. (2026). Geometry, Kinematics, Workspace, and Singularities of a Novel 3-PRRS Parallel Manipulator. Robotics, 15(1), 10. https://doi.org/10.3390/robotics15010010

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