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This paper presents a mathematical model of forward and inverse kinematics for a manipulator composed of joints with one degree of freedom allowing only the rotation of a Cartesian coordinate system around one axis. The manipulator is controlled by means of internal ties running from the point of connection with the controlled arm to the place of connection with the mechanism regulating the length of the individual tie. This length is the basis in derived equations, and its change is the direct cause of the movement of the described robot. In contrast to the commonly used arm drives, the articulated variable in derived kinematic equations is the length of the tie, which affects the change in the angle between the arms, while it is not the same value of this angle. In addition, these joints are arranged parallel to each other, which results in the working space of the manipulator in one plane. The kinematic chain, which is the object of the described research, consisted of three series connected joints enabling rotation around one axis of the coordinate system. However, the dependencies and formulas enabling their application to the description of forward kinematics and inverse kinematic chains built from a larger number of similarly arranged joints were demonstrated. The kinematics model presented in the paper proves that it is possible to independently control each of the serially connected joints using internal ties. [ABSTRACT FROM AUTHOR]

In rigid lower-mobility parallel manipulators the motion of the end-effector is partially constrained due to a combination of passive kinematic pairs and rigid components. Translational mechanisms, such as the Delta manipulator, are the most common ones among this type of mechanisms. When flexible elements are introduced, as in Parallel Continuum Manipulators, the constraint is no longer rigid, and new challenges arise in performing certain motions depending on the degree of compliance. Mobility analysis shifts from being purely a geometric issue to one that heavily relies on force distribution within the mechanism. Simply converting classical lower-mobility rigid parallel mechanisms into Parallel Continuum Mechanisms may yield unexpected outcomes. This work, making use of a planar parallel continuum Delta manipulator, on the one hand, presents two different approaches to solve the Forward Kinematics of planar continuum manipulators, and, on the other hand, explores some challenges and issues in assessing the resultant workspace for different design alternatives of this kind of flexible manipulators. [ABSTRACT FROM AUTHOR]

A single input and multi-dimensional output 2RRS-S parallel mechanism was proposed based on the position and orientation characteristics (POC), and its topological structure, degree of freedom, and coupling degree were analyzed. A forward motion solution model of the mechanism was established by using the topological feature motion modeling method based on the coupling degree and verified through simulation models. According to the material mixing requirements, a three-dimensional model of a multi-dimensional mixing machine based on the 2RRS-S parallel mechanism was designed, and its motion trajectory and motion characteristics of attitude angles were simulated. Taking the variation change of the attitude angles of the moving platform as the objective function, the differential evolution algorithm was used to optimize the scale parameters of the mechanism, and the obtained mechanism has better mixing motion performance than that before the optimization.

Redundant degree-of-freedom (DOF) manipulators offer increased flexibility and are better suited for obstacle avoidance, yet precise control of these systems remains a significant challenge. This paper addresses the issues of slow training convergence and suboptimal stability that plague current deep reinforcement learning (DRL)-based control strategies for redundant DOF manipulators. We propose a novel DRL-based intelligent control strategy, FK-DRL, which integrates the manipulator's forward kinematics (FK) model into the control framework. Initially, we conceptualize the control task as a Markov decision process (MDP) and construct the FK model for the manipulator. Subsequently, we expound on the integration principles and training procedures for amalgamating the FK model with existing DRL algorithms. Our experimental analysis, applied to 7-DOF and 4-DOF manipulators in simulated and real-world environments, evaluates the FK-DRL strategy's performance. The results indicate that compared to classical DRL algorithms, the FK-DDPG, FK-TD3, and FK-SAC algorithms improved the success rates of intelligent control tasks for the 7-DOF manipulator by 21%, 87%, and 64%, respectively, and the training convergence speeds increased by 21%, 18%, and 68%, respectively. These outcomes validate the proposed algorithm's effectiveness and advantages in redundant manipulator control using DRL and FK models. [ABSTRACT FROM AUTHOR]

Nowadays, various Delta-type robots are widely used in many technological fields. In this work, we propose a novel 5-DOF Delta-type parallel robot with four linear and one rotational actuators. The major part of the article is devoted to the kinematic analysis of the robot, including solving its inverse and forward kinematic problems. To demonstrate the developed techniques, we consider two numerical examples. In the first one, we solve the inverse kinematics and determine the actuator displacements required to realize a spatial trajectory of the output link. The forward kinematic analysis, presented in the second example, results in six different assembly modes of the robot for the given set of the actuator displacements. The proposed algorithms represent the basis for subsequent velocity, acceleration, and dynamic analysis of the robot, and they can be adapted to other Delta-type parallel robots. [ABSTRACT FROM AUTHOR]

In this paper, a kind of hybrid kinematics chain with variable constraints is constructed by using a 6R spatial bifurcated chain and 4-DOF serial limbs, by using them, a 3-DOF Reconfigurable Parallel Mechanisms (RPM) was constructed, which has four motion modes: 3T, 2T1R, 2R1T, and 3R motion modes. Using screw theory, the change of wrench system in the hybrid kinematics chain caused by the reconfiguration of the 6R bifurcated chain is analyzed, which affects the wrench system of the moving platform (MP), and thus causes the reconfiguration of the parallel mechanism (PM). The triangular pyramid fixed to the MP was found as auxiliary geometry and used to intuitively describe the constraint relationship between joint axes in limbs. The latter was used to establish a unified forward kinematics model of the RPM in four motion modes. The general forward kinematics solution procedure for this type of RPM is given. The overall Jacobian matrix was obtained by screw theory for singularity analysis. The condition number of the Jacobian matrix measures the degree to which the mechanism is close to the singular configuration. Based on the Monte Carlo simulation, point cloud images representing the workspace of RPM were obtained. [ABSTRACT FROM AUTHOR]

Robotics includes complex mathematical calculations and coordinate transformations in forward and inverse kinematics, path planning, and robot dynamics. Students may experience a high cognitive load and lose learning motivation because robotics can be complex and challenging to understand. This study applied virtual reality (VR) technology in robotics education to simplify and visualize complex robot kinematics, aiming to increase learning motivation and reduce cognitive load. This study incorporated real and virtual robot control to develop an integrated robot learning system. This system enables learners to control the digital twin of a physical robot and observe the synchronized motion of both the virtual and physical robots. Users can operate the virtual robot to achieve the target position by setting joint parameters or using values calculated from inverse kinematics. They can also understand the principle of digital twins by observing the synchronous motion of both robots. A teaching experiment was conducted to explore the performance of applying VR in robotics education and its impacts on cognitive load and learning motivation. The system was improved based on user responses to facilitate subsequent promotional activities. VR can transform complex robotics into easily understandable learning experiences and provide an interactive user interface, making the system a suitable learning tool for STEM education. [ABSTRACT FROM AUTHOR]

The redundant manipulators have more DOFs (degree of freedoms) than it requires to perform specified task. The inverse kinematic (IK) of such robots are complex and high nonlinear with multiple solutions and singularities. As such, modern Artificial Intelligence (AI) techniques have been used to address these problems. This study proposed two AI techniques based on Neural Network Genetic Algorithm (NNGA) and Particle Swarm Optimization (PSO) algorithm to solve the inverse kinematics (IK) problem of 3DOF redundant robot arm. Firstly, the forward kinematics for 3 DOF redundant manipulator has been established. Secondly, the proposed schemes based on NNGA and PSO algorithm have been presented and discussed for solving the inverse kinematics of the suggested robot. Thirdly, numerical simulations have been implemented to verify the effectiveness of the proposed methods. Three scenarios based on triangle, circular, and sine-wave trajectories have been used to evaluate the performances of the proposed techniques in terms of accuracy measure. A comparison study in performance has been conducted and the simulated results showed that the PSO algorithm gives 7% improvement compared to NNGA technique for triangle trajectory, while 2% improvement has been achieved by the PSO algorithm for circular and sine-wave trajectories. [ABSTRACT FROM AUTHOR]

In this paper, the solution of a 4-axis selective compliance assembly robot arm (SCARA) for picking & placing an IC component onto the PCB is presented along with the simulation results. The SCARA robot arm, known for its horizontal movement and accurate positioning, presents a versatile platform for assembly tasks in various industries, particularly in electronics manufacturing. The main goal is to get the forward kinematics equations required to precisely calculate the end-effector's location and orientation using the 4-axis SCARA robot arm's joint angles. The mathematical model explaining the link between the robot's joint variables and the position/orientation of the end-effector is developed by specifying the DenavitHartenberg (DH) parameters and using transformation matrices. The work intends to simulate and test the computed end-effector locations and orientations against experimental or simulated data using the obtained forward kinematics equations. The forward kinematics approach will be implemented using code developed as part of the project, enabling systematic investigation and testing of the pick-and-place capabilities of the SCARA robot. Additionally, it also provides a brief overview of the possible uses and consequences of using this SCARA-based solution for accurate and efficient assembly jobs in industrial settings. The incorporation of a graphical user interface (GUI) has the potential to enhance user engagement and aid in the real-time management and observation of the pick-and-place processes. By offering a methodical solution to the direct kinematics problem of a 4-axis SCARA robot arm for the purpose of picking and placing IC components onto PCBs, it advances robotic assembly technologies and highlights their potential to increase productivity and accuracy in manufacturing processes. [ABSTRACT FROM AUTHOR]

Accurate calibration of a Stewart platform is important for their precise and efficient operation. However, the calibration of these platforms using forward kinematics is a challenge for researchers because forward kinematics normally generates multiple feasible and unfeasible solutions for any pose of the moving platform. The complex kinematic relations among the six actuator paths connecting the fixed base to the moving platform further compound the difficulty in establishing a straightforward and efficient calibration method. The authors developed a new forward kinematics-based calibration method using Denavit-Hartenberg (DH) convention and used the Stewart platform "Tiger 66.1" developed in their lab for experimenting with the photogrammetry-based calibration strategies described in this paper. This system became operational upon completion of construction, marking its inaugural use. The authors used their calibration model for estimating the errors in the system and adopted three compensation options or strategies as per least-square method to improve the accuracy of the system. These strategies leveraged a high-resolution digital camera and off-the-shelf software to capture the poses of the moving platform's center. This process is non-invasive and does not need any additional equipment to be attached to the hexapod or any alteration of the hexapod hardware. This photogrammetry-based calibration process involves multiple high-resolution images from different angles to measure the position and orientation of the platform center in the three-dimensional space. The target poses and actual poses are then compared, and the error compensations are estimated using the least-square methods to calculate the predicted poses. Results from each of the three compensation approaches demonstrated noticeable enhancements in platform pose accuracies, suggesting room for further improvements. Given that "Tiger 66.1" is based on the general Stewart platform structure, the proposed calibration method holds promise for extension to machines operating on similar principles where non-invasive calibration is desirable. This study contributes to advancing the field of Stewart platform calibration, paving the way for more precise and efficient applications in various domains. [ABSTRACT FROM AUTHOR]

The lower hook mechanism is one of the key mechanisms in netting machine. The weft reel diameter of the new generation netting machine has doubled to the original one, resulting in a large route change of lower hook, thus the lower hook mechanism needs to be redesigned. By comparing the fitting results under different methods, the hook tip trajectory with smaller acceleration is determined. By using the closed vector method, the inverse and forward kinematic models of the mechanism is established and solved. By using NSGA-II genetic algorithm, the transmission performance parameters of the mechanism are effectively optimized. The kinematic simulation of the optimized mechanism is completed in Adams to verify the correctness of kinematic models and the effectiveness of optimization results. The comparison result of the simulated and initial fitted trajectory shows that the lower hook mechanism designed in this paper could meet the technical requirements of the position and posture of the lower hook. [ABSTRACT FROM AUTHOR]

In rigid lower-mobility parallel manipulators the motion of the end-effector is partially constrained due to a combination of passive kinematic pairs and rigid components. Translational mechanisms, such as the Delta manipulator, are the most common ones among this type of mechanisms. When flexible elements are introduced, as in Parallel Continuum Manipulators, the constraint is no longer rigid, and new challenges arise in performing certain motions depending on the degree of compliance. Mobility analysis shifts from being purely a geometric issue to one that heavily relies on force distribution within the mechanism. Simply converting classical lower-mobility rigid parallel mechanisms into Parallel Continuum Mechanisms may yield unexpected outcomes. This work, making use of a planar parallel continuum Delta manipulator, on the one hand, presents two different approaches to solve the Forward Kinematics of planar continuum manipulators, and, on the other hand, explores some challenges and issues in assessing the resultant workspace for different design alternatives of this kind of flexible manipulators.

This manuscript introduces a symmetrical gripping mechanism, a significant piece of robotic equipment, adept at adjusting to the variable dimensions of disparate objects within an extensive range. The innovative mechanism presented in this treatise has dual degrees of freedom (DOF), and its parameters can be customized to satisfy diverse requirements. Symbolic computation is employed to dissect both the forward and inverse kinematics of the mechanism. Furthermore, the requisite driving force of the mechanism, when paired with parameterized objects, is discussed. Ultimately, a methodology is suggested for discerning the mechanism's parameters in relation to variously grasped widths and forces. The article concludes with the introduction of a prototype construction process. Experimental results substantiate the effectiveness and functionality of the proposed mechanism. [ABSTRACT FROM AUTHOR]

We have proposed an open-source holonomic mobile manipulator composed of the KUKA youBot holonomic mobile platform with four Swedish wheels and a stationary aboard six-degrees-of-freedom Kinova Jaco Gen 2H manipulator, and we have developed corresponding kinematic problems. We have defined forward and inverse analytic Jacobians and designed Jacobian algorithms of forward and inverse mobile manipulator kinematics. An experimental test conducted with the designed laboratory prototype of the investigated mobile manipulator with the described kinematics was used to verify the obtained theoretical results. The goal of the test was to keep constant the position of the gripper in 3D space while the mobile platform is moving to some extend in the 2D workspace. [ABSTRACT FROM AUTHOR]

Electromechanical systems that interact with the user to offer power amplification, assistance, or replacement of motor function are known as exoskeletons for the upper limbs. The upper extremity rehabilitation exoskeletons have garnered increasing attention and impact in the healthcare sector over the past years due to the advancements in the field of robotic control devices and actuation elements. The necessity for assistive supporting and rehabilitation devices that either help improve human strengths or provide assistance in regaining lost motion of a specific limb joint arises as a result of changing trends and a growing population. Age-related bone loss often results in weaker, more fragile bones that make lifting and carrying huge loads more difficult. A stroke can impair mobility and is more likely occurs to the elderly people. Accidental paralysis as well as other health issues including spinal cord injuries, musculoskeletal disorders due to work environment are on the rise resulting in an increased urge for the assistive devices. The motive of this paper is to design a mathematical model of the human upper limb involving DH parameters and forward kinematics alongside with the human joint study to precisely design the model in order to design an upper extremity exo-skeleton for offering limb rehabilitation considering the human joint constraints with respect to the Sagittal, Coronal and Transverse planes. This study is aimed in providing a significant vision in developing the precise rehabilitation devices that can aim in offering the joint specific treatment to the user for human upper arm therapy. [ABSTRACT FROM AUTHOR]

This paper presents a algorithm of fast-solving forward kinematics for a class of three-degrees-of-freedom (3-DoF) of planar parallel mechanisms (PPMs) based on the kinematic mapping of constrained planar motions and planar quaternions. Firstly, a kinematic mapping is established based on planar quaternions, which formulates the forward kinematics equations of PPMs into the quadratic equations in the form of planar quaternion. The constrained trajectory equations for the RR-type limbs in the kinematic mapping image space are parameterized. Secondly, an efficient algorithm is proposed to obtain numerical solutions to the equation system. The convergence and singularity issues of the algorithm are discussed, revealing the inherent connection between algorithm singularity and PPMs motion characteristics. Finally, the application of the new algorithm is demonstrated through two examples: a 3-RPR PPM and a 3-PRR PMM. The computational results demonstrate that the proposed algorithm can achieve competitive convergence speed and computational efficiency compared with Newton's method and quasi-Newton methods. The proposed algorithm provides a possible solution for real-time control based on forward kinematics. [ABSTRACT FROM AUTHOR]

This paper proposes a new type of hybrid manipulator that can be of extensive use in industries where translational motion is required while maintaining an arbitrary end-effector orientation. It consists of two serially connected parallel mechanisms, each having three degrees of freedom, of which the upper platform performs a pure translational motion with respect to the mid-platform. Closed-form forward and inverse kinematic analysis of the proposed manipulator has been carried out. It is followed by the determination of all of its singular configurations. The theoretical results have been verified numerically, and the 3D modeling and simulation of the manipulator have also been performed. A simple optimal design is presented based on optimizing the kinematic manipulability, which further demonstrates the potential of the proposed hybrid manipulator. [ABSTRACT FROM AUTHOR]

Redundant degree-of-freedom (DOF) manipulators offer increased flexibility and are better suited for obstacle avoidance, yet precise control of these systems remains a significant challenge. This paper addresses the issues of slow training convergence and suboptimal stability that plague current deep reinforcement learning (DRL)-based control strategies for redundant DOF manipulators. We propose a novel DRL-based intelligent control strategy, FK-DRL, which integrates the manipulator’s forward kinematics (FK) model into the control framework. Initially, we conceptualize the control task as a Markov decision process (MDP) and construct the FK model for the manipulator. Subsequently, we expound on the integration principles and training procedures for amalgamating the FK model with existing DRL algorithms. Our experimental analysis, applied to 7-DOF and 4-DOF manipulators in simulated and real-world environments, evaluates the FK-DRL strategy’s performance. The results indicate that compared to classical DRL algorithms, the FK-DDPG, FK-TD3, and FK-SAC algorithms improved the success rates of intelligent control tasks for the 7-DOF manipulator by 21%, 87%, and 64%, respectively, and the training convergence speeds increased by 21%, 18%, and 68%, respectively. These outcomes validate the proposed algorithm’s effectiveness and advantages in redundant manipulator control using DRL and FK models.

With the rapid advancement of industrial automation and artificial intelligence technologies, particularly in the textile industry, robotic technology is increasingly challenged with intelligent path planning and executing high-precision tasks. This study focuses on the automatic path planning and yarn-spool-assembly tasks of textile robotic arms, proposing an end-to-end planning and control model that integrates deep reinforcement learning. The innovation of this paper lies in the introduction of a cascaded fuzzy reward system, which is integrated into the end-to-end model to enhance learning efficiency and reduce ineffective exploration, thereby accelerating the convergence of the model. A series of experiments conducted in a simulated environment demonstrate the model's exceptional performance in yarn-spool-assembly tasks. Compared to traditional reinforcement learning methods, our model shows potential advantages in improving task success rates and reducing collision rates. The cascaded fuzzy reward system, a core component of our end-to-end deep reinforcement learning model, offers a novel and more robust solution for the automated path planning of robotic arms. In summary, the method proposed in this study provides a new perspective and potential applications for industrial automation, especially in the operation of robotic arms in complex and uncertain environments. [ABSTRACT FROM AUTHOR]

In order to resolve redundancy and path planning of a high DOF mobile manipulator using conventional approaches like Jacobian and a pseudoinverse method, researchers face the limitation of computational load and delay in response. If such kind of mobile manipulator is traversing the rough terrain, then conventional methods become too costly to implement due to the handling of redundant joints, obstacles, and wheel-terrain interaction. A few optimization-based redundancy resolution approaches try incorporating wheel-terrain interaction but fail in real-time response. This paper describes a 14 DOF Rover Manipulator System's end-effector path-tracking approach using CG-Space framework to incorporate wheel-terrain interaction. CG-Space means the center of gravity (CG) locus of the Rover. The Rover's CG is calculated while traversing over 3D terrain using a multivariable optimization method and a 3D point cloud image of the actual terrain and stored as CG-Space over the given terrain. First of all, we decide which part of the system moves to track the path, that is, arm or Rover, depending upon the manipulator's work volume and manipulability measure restrictions. The next task is to obtain the Rover pose according to the end-effector path using a simple arm's inverse kinematic solution between the CG-Space and end-effector task space without resolving redundancy. Meanwhile, obstacles and non-traversable regions are avoided in CG-Space. On diverse 3D terrains, simulation and experimental results support the suggested CG-Space framework for end-effector tracking. [ABSTRACT FROM AUTHOR]

The design of the robotic arm's trajectory is based on inverse kinematics problem solving, with additional refinements of certain criteria. One common design issue is the trajectory optimization of the robotic arm. Due to the difficulty of the work in the past, many of the suggested ways only resulted in a marginal improvement. This paper introduces two approaches to solve the problem of achieving robotic arm trajectory control while maintaining the minimum reachability time. These two approaches are based on rule-based optimization and a genetic algorithm. The way we addressed the problem here is based on the robot’s forward and inverse kinematics and takes into account the minimization of operating time throughout the operation cycle. The proposed techniques were validated, and all recommended criteria were compared on the trajectory optimization of the KUKA KR 4 R600 six-degree-of-freedom robot. As a conclusion, the genetic based algorithm behaves better than the rule-based one in terms of achieving a minimal trip time. We found that solutions generated by the Genetic based algorithm are approximately 3 times faster than the other solutions generated by the rule-based algorithm to the same paths. We argue that as the rule-based algorithm produces its solutions after discovering all the problem’s searching space which is time consuming, and it is not the case as per the genetic based algorithm. [ABSTRACT FROM AUTHOR]

We introduce the notion of the Lie derivative in the context of dual quaternions that represent rigid motions and twists. First we define the wrench in terms of dual quaternions. Then we show how the Lie derivative helps understand how actuators affect an end effector in parallel robots, and make it explicit in the two cases case of Stewart Platforms, and cable-driven parallel robots. We also show how to use Lie derivatives with the Newton-Raphson Method to solve the forward kinematic problem for over constrained parallel actuators. Finally, we derive the equations of motion of the end effector in dual quaternion form, which include the effect of inertia from the actuators. [ABSTRACT FROM AUTHOR]

This paper introduces a novel dexterous 3-DOF parallel wrist-gripper assembly with a large singularity-free range of motion. It consists of a zero-torsion 2-DOF parallel wrist and a 1-DOF parallel gripper. The wrist produces a 2-DOF sphere-on-sphere pure rolling motion. This large singularity-free 2-DOF sphere-on-sphere pure rolling motion of the wrist allows for smooth and precise manipulation of objects in various orientations, making it suitable for applications such as assembly, pick-and-place, and inspection tasks. Using a geometrical approach, analytical solutions for the inverse and forward kinematics problems of the wrist and gripper are derived. From the inverse kinematic equations, the Jacobian matrices are derived and it is shown that the whole workspace is free of type I and type II singularities. It is shown that with a proper choice of design variables, a large singularity-free range of motion can be obtained. The absence of singularities in the whole workspace of the wrist-gripper assembly is an important feature that enhances its reliability. Finally, the correctness of the derived equations for the wrist inverse and forward kinematics are verified using MSC Adams. These results confirm the feasibility and effectiveness of the proposed parallel wrist-gripper assembly. Overall, the novel parallel wrist-gripper assembly presented in this paper demonstrates great potential for improving the efficiency and flexibility of robotic manipulators in a variety of industrial and research applications. [ABSTRACT FROM AUTHOR]

Forward kinematics is fundamental to robot design, control, and simulation. Different forward kinematics algorithms have been developed to deal with the complex geometry of a robot. This paper presents a robot forward kinematics algorithm in dual quaternion space. The presented method uses Denavit-Hartenberg (DH) convention for uniform definition of successive rotational and translational transformations in joints along the robot’s kinematic chain. This research aims to utilize the advantages of dual quaternions and DH convection for forward kinematics computation and make the algorithm, which is compact, intuitive, numerically robust, and computationally efficient as it uses the minimal number of parameters required for the computation, suitable for implementation in ROS and similar software. The algorithm is verified on the 6DoF industrial robot RL15, with the symbolic equations and numerical simulation presented.