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Machines
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The Kinematics and Dynamics of Mechanisms and Robots
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The Kinematics and Dynamics of Mechanisms and Robots

A special issue of Machines (ISSN 2075-1702). This special issue belongs to the section "Automation and Control Systems".

Deadline for manuscript submissions: 31 December 2026 | Viewed by 12142

Special Issue Editor

Dr. Shuofei Yang

E-Mail Website
Guest Editor
College of Engineering, China Agricultural University, Beijing 100083, China
Interests: type synthesis of mechanisms; kinematics and dynamics of mechanisms; robotic prototype building; stiffness modeling and experiments; error modeling and calibration; innovation and optimal design of robots; rigid and compliant mechanisms; flexible polyhedral mechanisms; mobile robots; agricultural robots
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

It is our great honor to organize this Special Issue of Machines, which is an outstanding academic journal focused on Mechanical Engineering and Science.

Mechanisms and robots play increasingly important roles in numerous areas, such as industry, agriculture, and medical treatment. This Special Issue aims to publish high-quality papers investigating the kinematic and dynamic problems of robotic mechanisms. It calls for papers to discuss ideas on the innovation, design, and application of various mechanisms and robots. Potential contributions may include, but are not limited to, the following topics:

  • Parallel and hybrid mechanisms;
  • Metamorphic mechanisms;
  • Deployable mechanisms and origami;
  • Compliant mechanisms;
  • Robotic systems in machining, manufacturing, and mining;
  • Mobile robots, field robots, and agricultural robots.

Your consideration will be appreciated. We look forward to receiving your submissions and will arrange a timely review.

Yours sincerely,

Dr. Shuofei Yang
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Machines is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • kinematics and dynamics
  • parallel and hybrid mechanisms
  • metamorphic mechanisms
  • deployable mechanisms and origami
  • compliant mechanisms
  • applications of mechanisms and robots

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Published Papers (8 papers)

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Research

22 pages, 5879 KB  
Article
An Obstacle-Negotiation Wheel with Hybrid Active–Passive Mechanism for Mechanical Augmentation
by Peixiang Wang, Xinyuan Wen, Hongjun Yin, Meiru Li and Pingyi Liu
Machines 2026, 14(3), 334; https://doi.org/10.3390/machines14030334 - 16 Mar 2026
Viewed by 1162
Abstract
To address the limitation of wheeled mobile robots in traversing unstructured terrain, this paper proposes an Active–Passive Hybrid Obstacle-Crossing Wheel (APHOCW). The mechanism integrates an active angle-adjustment mechanism and a lever-assist mechanism. While maintaining low system complexity and high reliability, it utilizes periodically [...] Read more.
To address the limitation of wheeled mobile robots in traversing unstructured terrain, this paper proposes an Active–Passive Hybrid Obstacle-Crossing Wheel (APHOCW). The mechanism integrates an active angle-adjustment mechanism and a lever-assist mechanism. While maintaining low system complexity and high reliability, it utilizes periodically telescoping assist levers that rotate with the wheel to overcome obstacles. By actively adjusting the eccentric angle, the trajectory of the assist levers can be modified to optimize the crossing posture. Through geometric and quasi-static mechanical modeling, dynamic simulation, and prototype experiments, this study systematically validated the robot’s obstacle-crossing capability and continuous step-climbing performance under different eccentric angles. Simulation and experimental results demonstrate that in the lever-assisted obstacle-crossing mode, the robot can stably overcome obstacles with a height up to 2.1 times its wheel radius and accomplish continuous step ascent. A smaller eccentric angle helps increase the maximum obstacle-crossing height, while a larger eccentric angle exhibits superior energy efficiency under sufficient ground-friction conditions. Full article
(This article belongs to the Special Issue The Kinematics and Dynamics of Mechanisms and Robots)
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24 pages, 5595 KB  
Article
Online End Deformation Calculation Method for Mill Relining Manipulator Based on Structural Decomposition and Kolmogorov-Arnold Network
by Mingyuan Wang, Yujun Xue, Jishun Li, Shuai Li and Yunhua Bai
Machines 2026, 14(1), 21; https://doi.org/10.3390/machines14010021 - 23 Dec 2025
Viewed by 507
Abstract
Due to the large mass, high end load, and long action distance of a mill relining manipulator, gravity effects inevitably lead to a reduction in end effector positioning accuracy. To solve this problem, an online calculation method is proposed to realize real-time end [...] Read more.
Due to the large mass, high end load, and long action distance of a mill relining manipulator, gravity effects inevitably lead to a reduction in end effector positioning accuracy. To solve this problem, an online calculation method is proposed to realize real-time end effector deformation prediction. First, a manipulator is simplified into two cantilever beams: the upper arm and the forearm. Second, a reaction force and moment transformation model is established based on the coupling relationship between the forearm and upper arm. Third, finite element (FE) static analysis and simulation are carried out to obtain the end deformation. A total of 3528 discrete joint configurations are selected to cover the entire joint space, and their corresponding FE solutions are used to establish the end deformation offline dataset. Finally, an online deformation calculation algorithm based on Kolmogorov–Arnold networks (KANs) is developed to predict end deformation in any working condition. Visualization analysis and validation experiments are conducted and demonstrate the superiority of the proposed method in reducing gravity effects and improving computational efficiency. In summary, the proposed method provides support for end position compensation, especially for heavy-duty manipulators. Full article
(This article belongs to the Special Issue The Kinematics and Dynamics of Mechanisms and Robots)
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27 pages, 4375 KB  
Article
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 656
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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31 pages, 11720 KB  
Article
A New Integrated Method to Improve the Computation of the Robotics’ Inverse Kinematics in a Simple and Unified Formula
by Abubaker Ahmed, Hehua Ju, Yang Yang, Hosham Wahballa and Ghazally I. Y. Mustafa
Machines 2025, 13(12), 1073; https://doi.org/10.3390/machines13121073 - 21 Nov 2025
Viewed by 790
Abstract
Formulating mathematical models and deriving efficient algorithms are crucial for meeting the requirements of future robotics applications. This paper proposes a novel approach for analyzing kinematic systems and computing inverse kinematics (IK) solutions for serial robotic arms. The aim is to reduce modeling [...] Read more.
Formulating mathematical models and deriving efficient algorithms are crucial for meeting the requirements of future robotics applications. This paper proposes a novel approach for analyzing kinematic systems and computing inverse kinematics (IK) solutions for serial robotic arms. The aim is to reduce modeling complexity and the computational cost of IK solution algorithms, while enhancing accuracy and efficiency by reformulating the kinematic equations using simplified constraints. This is achieved by integrating the rotation matrix and the unit quaternion to represent kinematic equations in a simple and unified form without compromising the degrees of freedom or raising the order of the kinematic equations, as in traditional approaches. The method combines analytical and numerical techniques to obtain an exact IK solution in two steps: first, the wrist joint variables are substituted into the position equations, resulting in a modified position vector equation obtained analytically; second, numerical iteration is applied to compensate for the error between the current and desired positions, leading to the ultimate exact inverse solution. The method is tested on a 5R robot and a 6R (UR-10) robot with an offset wrist to demonstrate the mathematical process and real-time algorithm performance. The results demonstrate that the absolute position error is less than 10−15 m, with no orientation error, and the mean calculation time for the IK solution is less than 5 ms. Furthermore, the results indicate higher accuracy and reduced computational time compared to other common IK methods. Moreover, the algorithm’s improved performance in processing continuous paths demonstrates its advantages in both simulation and practical applications. Finally, the proposed methodology is expected to advance further research in kinematic modeling and enhance polynomial-based numerical iterative algorithms. Full article
(This article belongs to the Special Issue The Kinematics and Dynamics of Mechanisms and Robots)
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50 pages, 23293 KB  
Article
Optimal Dimensional Synthesis of Ackermann and Watt-I Six-Bar Steering Mechanisms for Two-Axle Four-Wheeled Vehicles
by Yaw-Hong Kang, Da-Chen Pang and Dong-Han Zheng
Machines 2025, 13(7), 589; https://doi.org/10.3390/machines13070589 - 7 Jul 2025
Cited by 1 | Viewed by 1804
Abstract
This study investigates the dimensional synthesis of steering mechanisms for front-wheel-drive, two-axle, four-wheeled vehicles using two metaheuristic optimization algorithms: Differential Evolution with golden ratio (DE-gr) and Improved Particle Swarm Optimization (IPSO). The vehicle under consideration has a track-to-wheelbase ratio of 0.5 and an [...] Read more.
This study investigates the dimensional synthesis of steering mechanisms for front-wheel-drive, two-axle, four-wheeled vehicles using two metaheuristic optimization algorithms: Differential Evolution with golden ratio (DE-gr) and Improved Particle Swarm Optimization (IPSO). The vehicle under consideration has a track-to-wheelbase ratio of 0.5 and an inner wheel steering angle of 70 degrees. The mechanisms synthesized include the Ackermann steering mechanism and two variants (Type I and Type II) of the Watt-I six-bar steering mechanisms, also known as central-lever steering mechanisms. To ensure accurate steering and minimize tire wear during cornering, adherence to the Ackermann steering condition is enforced. The objective function combines the mean squared structural error at selected steering positions with a penalty term for violations of the Grashoff inequality constraint. Each optimization run involved 100 or 200 iterations, with numerical experiments repeated 100 times to ensure robustness. Kinematic simulations were conducted in ADAMS v2015 to visualize and validate the synthesized mechanisms. Performance was evaluated based on maximum structural error (steering accuracy) and mechanical advantage (transmission efficiency). The results indicate that the optimized Watt-I six-bar steering mechanisms outperform the Ackermann mechanism in terms of steering accuracy. Among the Watt-I variants, the Type II designs demonstrated superior performance and convergence precision compared to the Type I designs, as well as improved results compared to prior studies. Additionally, the optimal Type I-2 and Type II-2 mechanisms consist of two symmetric Grashof mechanisms, can be classified as non-Ackermann-like steering mechanisms. Both optimization methods proved easy to implement and showed reliable, efficient convergence. The DE-gr algorithm exhibited slightly superior overall performance, achieving optimal solutions in seven cases compared to four for the IPSO method. Full article
(This article belongs to the Special Issue The Kinematics and Dynamics of Mechanisms and Robots)
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25 pages, 7569 KB  
Article
Virtual Prototyping of a Novel Manipulator for Efficient Laser Processing of Complex Large Parts
by Antonio Pandolfi, Sergio Ferrarini, Pietro Bilancia and Marcello Pellicciari
Machines 2025, 13(3), 176; https://doi.org/10.3390/machines13030176 - 23 Feb 2025
Viewed by 1830
Abstract
Traditional industrial robots offer significant operational flexibility and adapt well to reconfigurable production systems, although they face limitations in applications demanding high motion performance and spatial positional accuracy. While novel manufacturing solutions supporting small batch productions of custom products are widely researched, they [...] Read more.
Traditional industrial robots offer significant operational flexibility and adapt well to reconfigurable production systems, although they face limitations in applications demanding high motion performance and spatial positional accuracy. While novel manufacturing solutions supporting small batch productions of custom products are widely researched, they are not yet fully available at industrial level. With the aim to advance in this domain, the present work, conducted in the context of the EU project OPeraTIC, reports the development of a novel manipulator for advanced three-dimensional laser surface treatment of large industrial components. The proposed robotic platform presents a decoupled kinematic architecture, with direct drive actuation in all axes. Its open control ensures adaptability to diverse manufacturing scenarios, making it a versatile tool for modern production lines. Starting from the description of its embodiment design and mechanical layout, the paper delves into robot virtual prototyping focusing on kinematic and dynamics aspects. In particular, a detailed behavioral model covering direct and inverse kinematic calculations, also allowing the precise evaluation of all actuation forces/torques, has been developed using analytical approaches. The model is validated with a commercial solver imposing different spatial motions. The generated performance maps illustrate the robot operational capabilities across a range of work scenarios. Full article
(This article belongs to the Special Issue The Kinematics and Dynamics of Mechanisms and Robots)
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22 pages, 15193 KB  
Article
First- and Second-Order Centrodes of Both Coupler Links of Stephenson III Six-Bar Mechanisms
by Giorgio Figliolini, Chiara Lanni and Luciano Tomassi
Machines 2025, 13(2), 93; https://doi.org/10.3390/machines13020093 - 24 Jan 2025
Cited by 5 | Viewed by 1152
Abstract
The subject of this paper is the formulation of a general algorithm that is aimed to obtain and analyze the first- and second-order centrodes of both coupler links of Stephenson III six-bar mechanisms, along with the corresponding pairs of Bresse’s circles. The position [...] Read more.
The subject of this paper is the formulation of a general algorithm that is aimed to obtain and analyze the first- and second-order centrodes of both coupler links of Stephenson III six-bar mechanisms, along with the corresponding pairs of Bresse’s circles. The position vectors of both pairs of instantaneous centers of rotation and acceleration centers are expressed as vector functions of the driving input angle of the mechanism and apply the fundamental theorems for velocities and accelerations, respectively. Thus, the proposed algorithm has been formulated by using vector algebra and validated through significant numerical and graphical results by devoting particular attention to the cases in which the second coupler link shows an instantaneous stop configuration, along with those where the first four-bar linkage reaches an asymptotic configuration. These results can be useful for designing and analyzing specific mechanisms for practical applications, such as composing the jaw-crusher machine, which has been selected as an example. Full article
(This article belongs to the Special Issue The Kinematics and Dynamics of Mechanisms and Robots)
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13 pages, 1035 KB  
Article
A New Method for Displacement Modelling of Serial Robots Using Finite Screw
by Feiyang Xue, Zhengjun Fang, Jiahao Song, Qi Liu and Shuofei Yang
Machines 2024, 12(9), 658; https://doi.org/10.3390/machines12090658 - 20 Sep 2024
Cited by 1 | Viewed by 1524
Abstract
Kinematics is a hot topic in robotic research, serving as a foundational step in the synthesis and analysis of robots. Forward kinematics and inverse kinematics are the prerequisite and foundation for motion control, trajectory planning, dynamic simulation, and precision guarantee of robotic manipulators. [...] Read more.
Kinematics is a hot topic in robotic research, serving as a foundational step in the synthesis and analysis of robots. Forward kinematics and inverse kinematics are the prerequisite and foundation for motion control, trajectory planning, dynamic simulation, and precision guarantee of robotic manipulators. Both of them depend on the displacement models. Compared with the previous work, finite screw is proven to be the simplest and nonredundant mathematical tool for displacement description. Thus, it is used for displacement modelling of serial robots in this paper. Firstly, a finite-screw-based method for formulating displacement model is proposed, which is applicable for any serial robot. Secondly, the procedures for forward and inverse kinematics by solving the formulated displacement equation are discussed. Then, two typical serial robots with three translations and two rotations are taken as examples to illustrate the proposed method. Finally, through Matlab simulation, the obtained analytical expressions of kinematics are verified. The main contribution of the proposed method is that finite-screw-based displacement model is highly related with instantaneous-screw-based kinematic and dynamic models, providing an integrated modelling and analysis methodology for robotic mechanisms. Full article
(This article belongs to the Special Issue The Kinematics and Dynamics of Mechanisms and Robots)
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