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33 pages, 1458 KB

Open AccessArticle

Design of a New 3-UPU/S Parallel Ankle Rehabilitation Mechanism

by Assia Abdi, Ridha Kelaiaia, Brahmia Allaoua, Adlen Kerboua and Ameur Latreche

Designs 2026, 10(4), 87; https://doi.org/10.3390/designs10040087 - 13 Aug 2026

Viewed by 164

Ankle injuries may lead to severe complications, including chronic instability and reduced mobility. Rehabilitation therefore plays a critical role in restoring normal ankle function and preventing long-term impairment. However, conventional manual physiotherapy presents several limitations, such as limited availability of therapists, variability in [...] Read more.

Ankle injuries may lead to severe complications, including chronic instability and reduced mobility. Rehabilitation therefore plays a critical role in restoring normal ankle function and preventing long-term impairment. However, conventional manual physiotherapy presents several limitations, such as limited availability of therapists, variability in treatment, and reduced accessibility for home-based rehabilitation. Consequently, significant research efforts have been devoted to the development of robotic and mechatronic devices for ankle rehabilitation. In this work, we propose the design of a simple and cost-effective parallel mechanism dedicated to ankle rehabilitation. The proposed device is based on a closed-chain kinematic architecture capable of reproducing the three principal rotational degrees of freedom of the ankle joint. This configuration enables controlled and repeatable rehabilitation exercises while ensuring mechanical stability and compactness. Furthermore, the device is designed to allow patients to perform rehabilitation exercises autonomously, without the continuous assistance of a physiotherapist, both in clinical environments and in home-based rehabilitation settings. Full article

(This article belongs to the Section Mechanical Engineering Design)

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23 pages, 6911 KB

Open AccessArticle

Configuration Design and Kinematic Analysis of RUPU/2UPU Reconfigurable Parallel Mechanism

by Shuwei Qu, Hongfu Wang, Shengquan Feng, Xiaoguang Tian, Zhike Qian, Wei Yao, Chaochao Li and Shenlin Gao

Mathematics 2026, 14(7), 1205; https://doi.org/10.3390/math14071205 - 3 Apr 2026

Viewed by 504

Abstract

The configuration synthesis and kinematic analysis of reconfigurable parallel mechanisms are performed for two motion modes: three-translation (3T) and three-translation-one-rotation (3T1R). Firstly, the degrees of freedom and constraint conditions of the moving platform and the limbs of the mechanism are analyzed. The limb [...] Read more.

The configuration synthesis and kinematic analysis of reconfigurable parallel mechanisms are performed for two motion modes: three-translation (3T) and three-translation-one-rotation (3T1R). Firstly, the degrees of freedom and constraint conditions of the moving platform and the limbs of the mechanism are analyzed. The limb configurations satisfying the degrees of freedom are synthesized by using the equivalent motion screw method, and the RUPU/2UPU reconfigurable parallel mechanism is synthesized by reasonably arranging the limbs. The degrees of freedom and motion continuity of the mechanism are analyzed by using the geometric constraint method based on screw theory. It has been proved that the mechanism can switch motion modes via the revolute joint R. The inverse position solution and workspace of the mechanism are analyzed, and its full Jacobian matrix is established. Based on this matrix, the reconfigurability and singularity of the mechanism were analyzed. At the same time, the dexterity of the mechanism is evaluated based on the velocity Jacobian matrix and the actuation Jacobian matrix. The results of the two methods are consistent. Finally, the mechanism’s degrees of freedom, motion continuity, and reconfigurable characteristics are verified through virtual simulation experiments. The experimental results are consistent with the theoretical analysis. Full article

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18 pages, 2160 KB

Open AccessArticle

Kinematic Analysis and Workspace Evaluation of a New Five-Axis 3D Printer Based on Hybrid Technologies

by Azamat Mustafa, Rustem Kaiyrov, Yerik Nugman, Mukhagali Sagyntay, Nurtay Albanbay, Algazy Zhauyt, Zharkynbek Turgunov, Ilyas Dyussebayev and Yang Lei

Robotics 2026, 15(1), 16; https://doi.org/10.3390/robotics15010016 - 7 Jan 2026

Viewed by 1632

Abstract

Additive manufacturing technologies for metals are developing rapidly. Among them, wire arc additive manufacturing (WAAM) has become widespread due to its accessibility. However, parts produced using WAAM require surface post-processing; therefore, hybrid technologies have emerged that combine additive and subtractive processes within a [...] Read more.

Additive manufacturing technologies for metals are developing rapidly. Among them, wire arc additive manufacturing (WAAM) has become widespread due to its accessibility. However, parts produced using WAAM require surface post-processing; therefore, hybrid technologies have emerged that combine additive and subtractive processes within a single compact manufacturing complex. Such systems make it possible to organize single-piece and small-batch production, including for the repair and restoration of equipment in remote areas. For this purpose, hybrid equipment must be lightweight, compact for transportation, provide sufficient workspace, and be capable of folding for transport. This paper proposes the concept of a multifunctional metal 3D printer based on hybrid technology, where WAAM is used for printing, and mechanical post-processing is applied to obtain finished parts. To ensure both rigidity and low mass, a 3-UPU parallel manipulator and a worktable with two rotational degrees of freedom are employed, enabling five-axis printing and machining. The printer housing is foldable for convenient transportation. The kinematics of the proposed 3D printer are investigated as an integrated system. Forward and inverse kinematics problems are solved, the velocities and accelerations of the moving platform center are calculated, singular configurations are analyzed, and the workspace of the printer is determined. Full article

(This article belongs to the Section Industrial Robots and Automation)

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27 pages, 4375 KB

Open AccessArticle

Dynamic Modeling and Performance Analysis of a Novel Dual-Platform Biped Robot Based on a 4-UPU Parallel Mechanism

by Zhaofeng Shi, Shengtao Song, Ruiqin Li, Fengping Ning, Lei Zhang and Lianzheng Deng

Machines 2025, 13(12), 1094; https://doi.org/10.3390/machines13121094 - 26 Nov 2025

Viewed by 863

Abstract

Biped robots based on parallel mechanisms hold great potential for applications in complex terrains. Based on a 4-UPU parallel mechanism, this paper proposes a novel biped robot that achieves alternating bipedal locomotion and turning with only six actuators by employing fixed/moving platform switching [...] Read more.

Biped robots based on parallel mechanisms hold great potential for applications in complex terrains. Based on a 4-UPU parallel mechanism, this paper proposes a novel biped robot that achieves alternating bipedal locomotion and turning with only six actuators by employing fixed/moving platform switching and following an “upper platform + lower foot” continuous gait strategy. Using the influence coefficient method, the first order and second order kinematic influence coefficient matrices of the biped robot were derived. Based on the principle of virtual work, a dynamic model of the robot was formulated, and its validity was verified through numerical simulations. The dynamic performance of the robot was further evaluated using the Dynamic Manipulability Ellipsoid (DME) index, while its stability during step-climbing and turning was analyzed using the Zero-Moment Point (ZMP) method. The results demonstrate that the dual-platform biped robot features a rational structure and exhibits robust stability during step-climbing and turning. Full article

(This article belongs to the Special Issue The Kinematics and Dynamics of Mechanisms and Robots)

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24 pages, 12784 KB

Open AccessArticle

A Fiber-Optic Six-Axis Force Sensor Based on a 3-UPU-Compliant Parallel Mechanism

by Jiachen Ma, Siyi Chen, Haiting Di and Ke Liu

Appl. Sci. 2025, 15(13), 7548; https://doi.org/10.3390/app15137548 - 4 Jul 2025

Cited by 1 | Viewed by 1299

Abstract

Traditional six-axis force sensors are mostly based on resistance strain, piezoelectricity and capacitors, which have poor resistance to electromagnetic interference. In this paper, a six-axis force sensor based on bending-sensitive optical fibers is proposed. A 3-UPU-(universal joint–prismatic joint–universal joint) compliant parallel mechanism is [...] Read more.

Traditional six-axis force sensors are mostly based on resistance strain, piezoelectricity and capacitors, which have poor resistance to electromagnetic interference. In this paper, a six-axis force sensor based on bending-sensitive optical fibers is proposed. A 3-UPU-(universal joint–prismatic joint–universal joint) compliant parallel mechanism is adopted in the sensor. The bending-sensitive optical fiber is encapsulated to form a fiber encapsulation module (FEM). The configuration of the FEMs within the six-axis force sensor is investigated. Static and stiffness analyses of the sensor are conducted and a force mapping matrix for the sensor is established. Simulation experiments are performed to verify the correctness of the established force mapping matrix. The detection system of the sensor is fabricated and the experiments are carried out to evaluate the performance of the sensor. The experiment results show that the maximum values of type-I errors and type-II errors are 4.52%FS and 3.26%FS, respectively. The maximum hysteresis and repeatability errors are 2.78% and 3.27%. These results verify the effectiveness of the proposed sensor. Full article

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16 pages, 4261 KB

Open AccessArticle

Research on the Conditions and Optimization of 3-UPU Parallel Manipulators That Naturally Realize Three Translational Degrees of Freedom

by Bo Hu and Peng Bai

Machines 2025, 13(4), 265; https://doi.org/10.3390/machines13040265 - 24 Mar 2025

Cited by 2 | Viewed by 1821

Abstract

The characteristics of the degrees of freedom (DOFs) of the 3-UPU parallel mechanisms (PMs) are closely related to the orientations of the ending R joints fixed connected with the platforms. The orientations of the ending revolute (R) joints in the Tsai 3-UPU PM [...] Read more.

The characteristics of the degrees of freedom (DOFs) of the 3-UPU parallel mechanisms (PMs) are closely related to the orientations of the ending R joints fixed connected with the platforms. The orientations of the ending revolute (R) joints in the Tsai 3-UPU PM cannot naturally realize three translational DOFs. First, this paper gives and proves the geometric conditions of the ending R joint fixed to the platforms that can naturally ensure three translational DOFs of the 3-UPU PMs. Second, based on the common motion/force index and good transmission workspace volume of the 3-UPU translational PMs, the performance map of the PMs is drawn, and the corresponding optimization design area of the PMs is obtained. Finally, combined with the obtained optimization design area, in view of the differences in the constraint and stiffness performance of the 3-UPU translational PMs, the multi-objective optimization is carried out using the game theory algorithm, and the orientations of the ending R joints for the 3-UPU translational PMs with good constraint and stiffness performance are obtained. Full article

(This article belongs to the Section Machine Design and Theory)

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17 pages, 6995 KB

Open AccessEditor’s ChoiceArticle

Kinematics and Dynamics Analysis of a 3UPS-UPU-S Parallel Mechanism

by Jing-Shan Zhao, Xiao-Cheng Sun and Song-Tao Wei

Machines 2023, 11(8), 840; https://doi.org/10.3390/machines11080840 - 18 Aug 2023

Cited by 2 | Viewed by 3019

Abstract

In this paper, a two-rotational degrees of freedom parallel mechanism with five kinematic subchains (3UPS-UPU-S) (U, P, and S stand for universal joints, prismatic joints, and spherical joints) for an aerospace product is introduced, and its kinematic and dynamic characteristics are subsequently analyzed. [...] Read more.

In this paper, a two-rotational degrees of freedom parallel mechanism with five kinematic subchains (3UPS-UPU-S) (U, P, and S stand for universal joints, prismatic joints, and spherical joints) for an aerospace product is introduced, and its kinematic and dynamic characteristics are subsequently analyzed. The kinematic and dynamic analyses of this mechanism are carried out in screw coordinates. Firstly, the inverse kinematics is performed through the kinematic equations established by the velocity screws of each joint to obtain the position, posture, and velocity of each joint within the mechanism. Then, a dynamic modeling method with screw theory for multi-body systems is proposed. In this method, the momentum screws are established by the momentum and moment of momentum according to the fundamentals of screws. By using the kinematic parameters of joints, the dynamic analysis can be carried out through the dynamic equations formed by momentum screws and force screws. This method unifies the kinematic and dynamic analyses by expressing all parameters in screw form. The approach can be employed in the development of computational dynamics because of its simplified and straightforward analysis procedure and its high adaptability for different kinds of multi-body systems. Full article

(This article belongs to the Section Automation and Control Systems)

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18 pages, 8601 KB

Open AccessArticle

Dynamics of a 3-UPS-UPU-S Parallel Mechanism

by Jing-Shan Zhao, Song-Tao Wei and Xiao-Cheng Sun

Appl. Sci. 2023, 13(6), 3912; https://doi.org/10.3390/app13063912 - 19 Mar 2023

Cited by 8 | Viewed by 3462

Abstract

In this paper, a parallel mechanism with two rotational degrees of freedom is proposed. It could rotate freely and continuously around the two coordinate axes at the fixed origin of the coordinate frame. The structure of the mechanism is a second-order over constraint [...] Read more.

In this paper, a parallel mechanism with two rotational degrees of freedom is proposed. It could rotate freely and continuously around the two coordinate axes at the fixed origin of the coordinate frame. The structure of the mechanism is a second-order over constraint parallel structure and the moving platform and base platform are connected by five kinematic chains. The motion characteristics of this structure are analyzed by reciprocal screw equation. Then, the kinematics and dynamics modelling are carried out systematically in a unified way. The kinematics of the mechanism is established by means of screws, the displacements and accelerations of each joint and any point on a link could be calculated by the kinematic screw equation directly. The analysis of acceleration and its mathematical expression in screw form are given, and the acceleration matrix could be applied into the dynamic analysis based on the Newton–Euler equation. All the constraint forces and torques could be obtained by a single set of Newton–Euler equations. Full article

(This article belongs to the Collection Recent Advances in Mechanical Systems Dynamics)

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23 pages, 14955 KB

Open AccessArticle

Kinematic Analysis and Verification of a New 5-DOF Parallel Mechanism

by Yesong Wang, Changhuai Lyu and Jiang Liu

Appl. Sci. 2021, 11(17), 8157; https://doi.org/10.3390/app11178157 - 2 Sep 2021

Cited by 12 | Viewed by 4761

Abstract

This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU, and then analyses its DOF by traditional Grubler–Kutzbach and motion spiral theory. It theoretically shows that the mechanism meets the requirement of five dimensions of freedoms including three-dimensional movement and two-dimensional rotation. [...] Read more.

This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU, and then analyses its DOF by traditional Grubler–Kutzbach and motion spiral theory. It theoretically shows that the mechanism meets the requirement of five dimensions of freedoms including three-dimensional movement and two-dimensional rotation. Based on this, the real mechanism is built, but unfortunately it is found unstable in some positions. Grassmann line geometry method is applied to analyze its unstable problem caused by singular posture, and then an improving method is put forward to solve it. With the improved mechanism, closed loop vector method is employed to establish the inverse position equation of the parallel mechanism, and kinematics analysis is carried out to get the mapping relationships between position, speed, and acceleration of moving and fixed platform. Monte Carlo method is used to analyze the workspace of the mechanism, to explore the influencing factors of workspace, and then to get the better workspace. Finally, an experiment is designed to verify the mechanism working performance. Full article

(This article belongs to the Topic Industrial Robotics)

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19 pages, 4675 KB

Open AccessArticle

Concept Design and Load Capacity Analysis of a Novel Serial-Parallel Robot for the Automatic Charging of Electric Vehicles

by Han Yuan, Qiong Wu and Lili Zhou

Electronics 2020, 9(6), 956; https://doi.org/10.3390/electronics9060956 - 8 Jun 2020

Cited by 12 | Viewed by 5320

Abstract

The automatic charging of electric vehicles is an important but challenging problem. Recently, various charging robots are proposed for electric vehicles. Most previous researches do not pay enough attention to the robots’ load capacities. Actually, providing the charging connector with adequate pushing and/or [...] Read more.

The automatic charging of electric vehicles is an important but challenging problem. Recently, various charging robots are proposed for electric vehicles. Most previous researches do not pay enough attention to the robots’ load capacities. Actually, providing the charging connector with adequate pushing and/or pulling forces is vital to guarantee a reliable electrical connection, which is a key issue for charging robot design. In this paper, we present a novel serial-parallel robot for the automatic charging of electric vehicles. This robot is based on the 3 universal-prismatic-universal (3UPU) parallel mechanism and featured by high-load capacity. We firstly address the kinematic and static models of the proposed robot, then analyze its load capacity. It is shown that the robot’s maximum load capacity depends not only on the driving ability of the prismatic joints, but also on the robot’s structural parameters and the robot’s configuration. Finally, optimizations are made and results show that the robot’s load capacity along the desired trajectory has more than doubled. Results of this paper could be useful for the development of automatic electric-vehicle-charging devices. Full article

(This article belongs to the Special Issue Robots in Assisted Living)

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9 pages, 1095 KB

Open AccessArticle

Reconfiguration Analysis of a 3-DOF Parallel Mechanism

by Maurizio Ruggiu and Xianwen Kong

Robotics 2019, 8(3), 66; https://doi.org/10.3390/robotics8030066 - 2 Aug 2019

Cited by 4 | Viewed by 8763

Abstract

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains [...] Read more.

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified. Full article

(This article belongs to the Special Issue Kinematics and Robot Design II, KaRD2019)

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17 pages, 4066 KB

Open AccessArticle

Stability and Gait Planning of 3-UPU Hexapod Walking Robot

by Ruiqin Li, Hongwei Meng, Shaoping Bai, Yinyin Yao and Jianwei Zhang

Robotics 2018, 7(3), 48; https://doi.org/10.3390/robotics7030048 - 31 Aug 2018

Cited by 14 | Viewed by 11091

Abstract

The paper presents an innovative hexapod walking robot built with 3-UPU parallel mechanism. In the robot, the parallel mechanism is used as both an actuator to generate walking and also a connecting body to connect two groups of three legs, thus enabling the [...] Read more.

The paper presents an innovative hexapod walking robot built with 3-UPU parallel mechanism. In the robot, the parallel mechanism is used as both an actuator to generate walking and also a connecting body to connect two groups of three legs, thus enabling the robot to walk with simple gait by very few motors. In this paper, forward and inverse kinematics solutions are obtained. The workspace of the parallel mechanism is analyzed using limit boundary search method. The walking stability of the robot is analyzed, which yields the robot’s maximum step length. The gait planning of the hexapod walking robot is studied for walking on both flat and uneven terrains. The new robot, combining the advantages of parallel robot and walking robot, has a large carrying capacity, strong passing ability, flexible turning ability, and simple gait control for its deployment for uneven terrains. Full article

(This article belongs to the Special Issue Mechanism Design for Robotics)

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