Geometry, Kinematics, Workspace, and Singularities of a Novel 3-PRRS Parallel Manipulator
Baigunchekov Z. Carbone G. Laribi M.A. Kaiyrov R. Qian L. Zhumasheva Z.
January 2026Multidisciplinary Digital Publishing Institute (MDPI)
Robotics
2026#15Issue 1
“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.
direct and inverse kinematics , geometry , matrices of links and kinematic pairs , parallel manipulators , pose of moving platform , singularity , tripod , workspace
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Faculty of Mechanics and Mathematics, Department of Mechanics, Al-Farabi Kazakh National University, 71/23 Al-Farabi Avenue, Almaty, 050040, Kazakhstan
School of Engineering, Department of Mechanical, Energy and Management Engineering (DIMEG), University of Calabria, Via Bucci Cubo 45C, Rende, 87036, Italy
Department of GMSC, Prime Institute CNRS, ENSMA, University of Poitiers, UPR 3346, Poitiers, 86000, France
Laboratory of Applied Mechanics and Robotics, Karaganda Buketov University, Karaganda, 100001, Kazakhstan
Institute of Automation, Shandong Academy of Sciences, Jinan, 250000, China
Faculty of Mechanics and Mathematics
School of Engineering
Department of GMSC
Laboratory of Applied Mechanics and Robotics
Institute of Automation
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