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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.

This article introduces a novel modification of a Delta-type parallel robot. The robot has five degrees of freedom and provides its end-effector with a 3T2R motion pattern (three translational and two rotational degrees of freedom). The fifth degree of freedom (rotation) is kinematically decoupled from the other four motions, and it is controlled by two drives. Thus, the proposed robot has a redundant actuation. In this article, we present an algorithm to solve the inverse kinematics of this robot and apply it to a path modeling example of a spiral-like trajectory. Numerical simulations illustrate the algorithm and show how the actuated coordinates change along the considered trajectory. Forward kinematics follows next, and an approach is introduced to determine all end-effector configurations for the specified displacements in the actuated joints. A numerical example presents four assembly modes of the robot corresponding to four real solutions of the forward kinematic problem. Finally, this article demonstrates a computer-aided design and analysis of the proposed robot: we describe a procedure for analyzing inverse kinematics and calculating actuation torques. This study forms the basis for the future manufacturing and experimental analysis of a robot prototype.

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.

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.

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.

Virtual reality technology brings a series of changes to physical education. In this paper, Madgwick algorithm is chosen as the main algorithm of the human body attitude tracking system, which is widely used in the attitude solution of Jetlink inertial guidance system for its high accuracy and uncomplicated calculation. The use of forward kinematics is then utilized to capture and abstract the human body. To analyze its positive effects on students’ physical fitness, sports interest, sports technology mastery, and personalized development, the application of virtual reality technology is used in college sports teaching. The results show that in breaststroke exercise, there is a significant difference between the experimental group and the control group in physical fitness, lung capacity P=0.001

Inverse kinematics is a fundamental concept in robotics that plays a crucial role in a robot’s ability to perform tasks. In this contribution, we propose a novel geometric approach based on vector calculus to solve the inverse kinematics problem. The primary advantage of this approach originates from the solutions, which exhibit a linear form and uncoupled equations. To validate the effectiveness and correctness of our proposed method, we constructed a six-degrees-of-freedom robot. This robot is controlled by an Arduino Mega 2650 on which we have implemented the inverse kinematics algorithm. The validation process involved considering various desired trajectories of the end-effector, which were simulated in Matlab and then performed by the physical robot. Importantly, our findings confirm that the end-effector successfully tracks the predefined trajectories. Furthermore, we conducted a comparative analysis between Paul’s method and the results obtained from joint angles using our proposed approach. Interestingly, our study reveals a significant similarity between the two sets of results, reaffirming the accuracy and validity of the approach presented in this study.

The trajectory planning and control of the manipulator are based on forward kinematics analysis. At present, the analytical method mainly used is the D-H parameter method. This study proposes a screw theory method which is faster and simpler in terms of calculation than the D-H method. The kinematics modeling and forward kinematics equation of dual-arm operating system are established by product of exponentials formula. Simpack software is used to simulate and analyze the dual-arm operating system. The correctness of the forward kinematics model established by screw theory is verified by comparing the simulation results with the results obtained by the forward kinematics equation. Matlab software is used to analyze the workspace, and the workspace of the dual-arm operating system is obtained by comparing the workspace cloud map.

In this article, the solution to the inverse and forward kinematics of a novel three-legged, serial-parallel, compliant robot are presented. The design of the robot aims to combine properties from serial and parallel architectures, thereby targeting an agile, yet precisely controllable robot that possibly allows both for dynamic locomotion and accurate manipulation tasks. The robot embodies the series connection of two parallel architectures, a planar and a spherical mechanism, realized in a highly dense mechanical assembly, allowing for lightweight, functionally redundant and compliant 4-DOF legs. A hybrid compliance behaviour is achieved, serving as a threshold between a stiff and compliant systemic state of the robot. Based on the mechanism design, the study involves the derivation of an alternative, yet complete solution for the inverse and forward kinematics of the spherical parallel manipulator (SPM). The approach utilizes spherical trigonometry and spatial vector geometry and yields a unique solution, while being both easy to implement and numerically efficient, thereby being applicable to real time implementations. Conceptually, a reduction of the mechanism assembly and working modes was directly integrated into the solution terms, drastically simplifying the expressions as they only represents the mechanically meaningful configuration relevant for actual physical systems. In addition to the active joint coordinates, the solution yields a unique set of all passively driven joints. The derived robot kinematics are furthermore verified through a 3D simulation model, showing the robot performing several motions. Thereby, the simulations portray the characteristics of the motor units by means of their corresponding phase profiles, revealing a balanced utilisation.

Lower-limb exoskeletons enhance motor function in patients, benefiting both clinical rehab and daily activities. Nevertheless, pediatric exoskeletons remain largely underdeveloped. To address this gap, this study presents a new robotic lower-limb exoskeleton (LLE) design specifically tailored for children. Utilizing anthropometric data from the target demographic, the LLE has a size-adjustable design to accommodate children aged 8 to 12. The design incorporates six active joints at the hip and knee, actuated using Brushless DC motors in conjunction with Harmonic Drive gears. This study conducts a rigorous analysis of forward and inverse kinematics applied to the robotic LLE. While forward kinematics are essential for dynamic modeling and model-based control formulation, inverse kinematics play a crucial role in facilitating balance control. The study uses an algebraic-geometric method to solve the inverse kinematics of LLEs with four DOFs per leg, including one in the frontal plane and three in the sagittal plane. A unique model of validation and verification is then employed using the Simulink® and SimscapeTM computational environments. The accuracy of the forward kinematic analysis is confirmed by comparing separately modeled outcomes in both environments. The validity of the inverse kinematic model is verified by implementing sequential forward and inverse kinematic analyses, comparing the forward kinematic inputs with inverse kinematic outputs. Simulation results conclusively validate both the forward and inverse kinematic analyses, suggesting the exoskeleton’s potential in accommodating standard gait patterns.

This article is a new robotic arm for cleaning the floor in the toilet with an increased radius ofaction of the robotic arm type SCARA. The most common current trends in production includeshort production cycles, low volumes and a wide variety of orders that can be solved with the helpof the SCARA robot. With the advent of the COVID-19 virus in the world, the term "cleaningand disinfection" has become one of the most important tools for preventing the population frombecoming infected with the virus. The research focuses on the research and implementation ofSCARA-type robots and describes the possibilities of using a SCARA-type robot. This articledescribes the selection and deployment of a SCARA robot in industrial automation. This researchproject describes the simulation of a new SCARA-type robotic arm with a long reach and slidingmechanism, we have developed a new multi-joint robotic arm for working in confined spaces withan autonomous toilet floor cleaning system.

This paper presents a solution to the inverse kinematics problem for robotic manipulator based on the Adaptive Multi-Agent System (AMAS) approach. In this research, multi-agent system is in charge of controlling a robot arm with four degrees of freedom (DOF) and two motorized wheels, giving appropriate commands, such as rotation angles and velocities, to reach the desired position and orientation of the end effector. The calculation of commands is directly related to the solving of forward and inverse kinematics. Before the learning process of AMOEBA, the rotational angles, θ values, are encoded into a single number N, this parameter is the desired value that we are going to predict in the predicting stage. During the learning phase, the Agnostic MOdEl Builder by self-Adaptation (AMOEBA) builds context agents, which has local models and is able to self-adapt. After the getting the predicted value, Npred, it will be decoded back to get the set of rotational angles that is given to robot end effector. In addition, the robot with all its physical parameters is modeled and simulated in the Robot Operating System (ROS) environment

Robot modeling is essential before using control systems to verify that the desired task is completed with the lowest feasible error rate according to the inputs. When modeling a robot, the derivation of the forward movement of the robot axes is a fundamental step based on the method of Denavit–Hartenberg. This research aims to control the robot arm motion using two controllers. PID controller was used as a reference to compare the results with those of an FLC. First, an FLC was used to enhance the nonlinearity of the robot arm.FLC was designed based on Mamadani pro-Max inference. four different defuzzification methods were used and compared to obtain the control signal. These are BOA, MOM, SOM, and COG.The results of this controller were then compared to the PID results on a transient response scale. Finally, simulation was done using MATLAB Simulink software.Based on the simulation results, BOA, MOM, and SOM techniques yield almost identical results; however, the COG strategy yields a broad range of outcomes. Implementing a simple defuzzification approach resulted in system optimization due to the complexity of processes like fuzzification and defuzzification.Based on the simulation results, the FLC system yields better results than those obtained with a PID. The FLC has lower rise time, settling time, steady-state error, and less overshoot than the PID controller.

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.

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.

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.

For the parallel configuration of the robot manipulator, the solution of Forward Kinematics (FK) is tough as compared to Inverse Kinematics (IK). This work presents a novel hybrid method of optimizing an Artificial Neural Network (ANN) specifically Multilayer Perceptron (MLP) with Genetic Algorithm (GA) and Step-wise Linear Regression (SWLR) to solve the complex FK of Delta Parallel Manipulator (DPM). The joint space angular positional data has been iterated using IK to generate point cloud of Cartesian space positional data. This data set is highly random and broad which leads to higher-order nonlinearity. Hence, normalization of the dataset has been done to avoid outliers from the dataset and to achieve better performance. The developed ANN based MLP gave a mean square error of 0.0000762 and an overall R2 value of 0.99918. Finally, the proposed network has been simulated to solve FK of the parallel manipulator and to check its efficacy. For given joint angles, the proposed network predicted positional values which are in good approximation with known trajectory solved by standard analytical method.

Kinematic modelling of parallel manipulators poses significant challenges due to the absence of analytical solutions for the Forward Kinematics (FK) problem. This study centres on a specific parallel planar robot, specifically a 3RRR configuration, and addresses the FK problem through two distinct methodologies: Genetic Algorithms (GA) and Neural Networks (NN). Utilising the Inverse Kinematic (IK) model, which is readily obtainable, both GA and NN techniques are implemented without the need for closed-loop formulations or non-systematic mathematical tools, allowing for easy extension to other robot types. A comparative analysis against an existing numerical method demonstrates that the proposed methodologies yield comparable or superior performance in terms of accuracy and time, all while reducing development costs. Despite GA’s time consumption limitations, it excels in path planning, whereas NN delivers precise results unaffected by stochastic elements. These results underscore the feasibility of using neural networks and genetic algorithms as viable alternatives for real-time kinematic modelling of robots when closed-form solutions are unavailable.

This paper presents the development of vision-based robotic arm manipulator control by applying Proportional Derivative-Pseudoinverse Jacobian (PD-PIJ) kinematics and Denavit Hartenberg forward kinematics. The task of sorting objects based on color is carried out to observe error propagation in the implementation of manipulator on real system. The objects image captured by the digital camera were processed based on HSV-color model and the centroid coordinate of each object detected were calculated. These coordinates are end effector position target to pick each object and were placed to the right position based on its color. Based on the end effector position target, PD-PIJ inverse kinematics method was used to determine the right angle of each joint of manipulator links. The angles found by PD-PIJ is the input of DH forward kinematics. The process was repeated until the square end effector reached the target. The experiment of model and implementation to actual manipulator were analyzed using Probability Density Function (PDF) and Weibull Probability Distribution. The result shows that the manipulator navigation system had a good performance. The real implementation of color sorting task on manipulator shows the probability of success rate cm is 94.46% for euclidian distance error less than 1.2 cm.

Taking parallel mechanism as a research object， aiming at the problem that neural network algorithm is easy to fall into local optimization and the Newton-Raphson algorithm is sensitive to the initial value of iteration when solving forward kinematics， a general forward kinematics algorithm combining PSO-BPNN and Newton-Raphson algorithm is proposed. The inverse kinematics equation of parallel mechanism is established to obtain the value of the driving rod， which is used as the training sample， and the BPNN model is optimized by PSO to obtain the solution for forward kinematic， which is taken as the initial iterative value of the newton-raphson algorithm to solve the forward kinematics of parallel mechanism. To verify the effectiveness and universality of the algorithm， simulation examples of 3-PCR and 3-PPR parallel mechanisms are given. The simulation results show that Newton-Raphson algorithm does not converge due to the large difference between the initial iteration value and the target value. Compared with the PSO-BPNN algorithm， the absolute error obtained by combining PSO-BPNN and Newton-Raphson algorithm is reduced by at least 99.68% and 99.96%， and the number of iterations is less. PSO-BPNN and Newton-Raphson algorithm not only overcomes the shortcomings of poor local convergence of the neural network algorithm， but also avoids the influence of initial value selection on the accuracy of the Newton-Raphson algorithm， which has good versatility.

This paper analyses the problem of the kinematic singularity of 6 DOF serial robots by extending the use of Monte-Carlo numerical methods to visualize singularity configurations. To achieve this goal, first, forward kinematics and D-H parameters have been derived for the manipulator. Second, the derived equations are used to generate and visualize a workspace that gives a good intuition of the motion shape of the manipulator. Third, the Jacobian matrix is computed using graphical methods, aiming to locate positions that cause singularity. Finally, the data obtained are processed in order to visualize the singularity and to design a trajectory free of singularity. MATLAB robotics toolbox, Symbolic toolbox, and curve fitting toolbox are the MATLAB toolboxes used in the calculations. The results of the surface and contour plots of the determinate of the Jacobian matrix behavior lead to design a manipulator’s trajectory free of singularity and show the parameters that affect the manipulator’s singularity and its behavior in the workspace.

This paper proposes a methodology for creating simplified structural schemes and forward geometric models for industrial robots with serial architecture, with the goal of reducing thermal deformation errors that negatively impact positioning accuracy during operation. Unlike classical approaches, the proposed methodology introduces modifications to the order of matrix multiplication and incorporates new parameters to create a forward geometric model that better corresponds to the deformation characteristics of these robots. Details are presented on how to build and employ this extended model and integrate it into a thermal error compensation algorithm. The implementation of the algorithm in a software application is presented along with experimental results that demonstrate its effectiveness. This work addresses a real phenomenon that occurs in industrial robot operation and has implications for improving the performance of robots in manufacturing applications.

An 8-DOF manipulator with prismatic pair is proposed for space environment， which can complete equipment maintenance and object grabbing in space environment. The pose transformation matrix and forward kinematics equation of 8-DOF manipulator are derived by standard D-H parameter method. The simulation model of the manipulator is established by Matlab robotics toolbox， and the simulation model is compared with the kinematics equation of the manipulator. Monte Carlo method is used to solve the workspace of the manipulator， and the point cloud of the workspace of the end effector of the manipulator is drawn. The trajectory planning of the manipulator is simulated by Matlab， and the displacement， velocity and acceleration curves of each joint in the motion process are drawn. The rationality of the structure design of the manipulator is verified， it provides a reference for the follow-up research work.

A novel quantum-based kinematic model for computing the position and the orientation of the six-jointed IRB 140 ABB robotic arm is presented. Position is determined through successive elementary translations and rotations from the end effector down to the base frame, whereas orientation is derived from quaternion representation. The model is based on the equivalence between quaternions and Pauli matrices or gates. Based on comparison to experimental results, the quantum kinematic model is valid. Its main advantage is that it uses only one qubit to model both position and orientation, which represents a major saving in terms of computing resources and time. This model could guide development of other quantum models and simulation software to be used in future quantum computers and could also inform classical computing theory for robotic arm kinematics modeling.

This paper presents the forward, inverse, and velocity kinematics analysis of a 5 DOF robotic arm. The Denavit-Hartenberg (DH) parameters are used to determination of the forward kinematics while an algebraic solution is used in the inverse kinematics solution to determine the position and orientation of the end effector. Jacobian matrix is used to calculate the velocity kinematics of the robotic arm. The movement of the robotic arm is accomplished using the microcontroller (Arduino Mega2560), which controlling on five servomotors of the robotic arm joints and one servo of the gripper. The position and orientation of the end effector are calculated using MATLAB software depending on the DH parameters. The results indicated the shoulder joint is more effect on the velocity of the robotic arm from the other joints, and the maximum error in the position of the end-effector occurred with the z-axis and minimum error with the y-axis.

In this paper, a spatial parallel mechanism with five degrees of freedom is studied in order to provide a promising dynamic model for the control design. According to the inverse kinematics of the mechanism, the dynamic model is derived by using the Lagrangian method, and the co-simulation using MSC ADAMS and MATLAB/Simulink is adopted to verify the established dynamic model. Then the pre-trained deep neural network (DNN) is introduced to predict the real-time state of the end-effector of the mechanism. Compared to the traditional Newton’s method, the DNN method reduces the cost of the forward kinematics calculation while ensuring prediction accuracy, which enables the dynamic compensation based on feedback signals. Furthermore, the computed torque control with DNN-based feedback compensation is implemented for the trajectory tracking of the mechanism. The simulations show that, in the most complicated case that involves friction and external disturbance, the proposed controller has better tracking performance. The results indicate the necessity of dynamic modeling in the design of control with high precision.

The forward kinematics in parallel manipulators is a mathematically challenging issue, unlike serial manipulators. Kinematic constraint equations are non-linear transcendental equations that can be reduced to algebraic equations with appropriate transformations. For this reason, sophisticated and time-consuming methods such as the Bezout method, the Groebner bases method, and the like, are used. In this paper, we demonstrate that these equations can be solved by non-complicated mathematical methods for some special types of manipulators such as the 3-3 and 6-3 types of Stewart platforms, and the 3-RRR planar parallel manipulator. Our first method is an analytical approach that exploits the special structure of kinematic constraint equations and yields polynomials of 32nd and 16th order, as mentioned in the previous works. In the second method, an error function is defined. This error function is employed to find the most appropriate initial values for the non-linear equation solver which is used for solving kinematic constraint equations. Determining the initial values in this manner saves computation time and guarantees fast convergence to real solutions.

A continuum robot is a unique type of robots which move because of the elastic deformation of their bodies. The kinematics of such robots is typically described using constant curvature assumption. Such an assumption, however, does not completely describe the kinematics of a real-life continuum robot. As a result, variable curvature assumptions describe the kinematics of the continuum robot better, however, they are more complicated to formulate and work with. In particular, the existing methods of solving the inverse kinematics problem of multisection continuum robots with variable curvature suffer from a variety of deficiencies. Those deficiencies include complex matrix calculations, singularity problems, unscalability, and inability to find a numeric solution in some cases. In this work, we present FABRIKx: fast and reliable algorithm to solve the problem of inverse kinematics of the multisection continuum robot with variable curvature. In particular, to describe the variable curvature, we utilize a piecewise constant curvature assumption. The proposed algorithm combines both tangent and chord approaches to solve the inverse kinematics problem. The inverse kinematics of a single bending section of piecewise constant curvature is also described. To evaluate FABRIKx effectiveness, we compare it with the Jacobian-based and FABRIKc-based algorithms via simulation studies for different robots. The obtained results show that FABRIKx demonstrates a higher success rate and a lower solution time.

The purpose of this work is to compare, with the same digging diagrams, the velocity, accelerations and dynamic performances of two excavators with different arm configurations. In particular, constructive solutions involving the use of two and three mobile arms will be examined. For excavators the different construction geometry (2-3 arms) is mainly dictated by reasons of use, in fact the 3 arms solution is normally used in areas that allow poor mobility of vehicle and present obstacles during the excavation phase. The dynamic comparison between the two solutions is performed on real working conditions to which they can be subjected during the exercise. The elaborations are performed both analytically and numerically. Essentially the analysis shows that in the condition of leveling and lifting at minimum distance from the rotation axis the dynamic performances are similar, there are significant differences in the lifting condition at the maximum distance. The diversity also implies significant variations in the forces of the hydraulic cylinders used to move both the load and the arms, an aspect which finds greater emphasis even in the case in which the arms are made by adopting unconventional materials for their realization as aluminum and composites.

This paper presents a geometric approach for real-time forward kinematics of the general Stewart platform, which consists of two rigid bodies connected by six general serial manipulators. By describing the rigid-body motion as exponential of twist, and taking advantage of the product of exponentials formula, a step-by-step derivation of the proposed algorithm is presented. As the algorithm naturally solves all passive joint displacements, the correctness is then verified by comparing the forward-kinematic solutions from all chains. The convergence ability and robustness of the proposed algorithm are demonstrated with large amounts of numerical simulations. In all test cases, the proposed algorithm terminates within four iterations, converging with near-quadratic speed. Finally, the proposed algorithm is also implemented on a mainstream embedded motion controller. Compared with the incremental method, the proposed algorithm is more robust, with an average execution time of 0.48 ms, meeting the requirements of most applications, such as kinematic calibration, motion simulation, and real-time control.

Currently, the most prevalent surgical treatment method is laparoscopic surgery. Robotic surgery has many advantages over laparoscopic surgery. Therefore, robotic surgery technology is currently constantly evolving. The advantages of robotic surgery are that it can minimize incision, bleeding, and sequelae. Other advantages of robotic surgery are that it can reduce hospitalization, recovery period, and side effects. The appeal of robotic surgery is that it requires fewer surgical personnel compared to laparoscopic surgery. This paper proposes an ultra-compact 7-axis vertical multi-joint robot that employs the wire-driven method for minimally invasive surgery. The proposed robot analyzes the degree of freedom and motion coupling for control. The robot joint is composed of a total of seven joints, and among them, the 7-axis joint operates the forceps. At this time, the forceps joint (#7 axis) can only operate open and close functions, while the link is bent and rotatable, regardless of position change. This phenomenon can be analyzed by Forward Kinematics. Also, when the DOF rotates, the passing wires become twisted, and the wire is generated through length change and coupling phenomenon. The maximum rotation angle of DOF is 90° and the rotating passing wire is wound by the rotation of the wire pulley. If the DOF is rotated to the full range of 120°, the second DOF will be rotated to 90°, and at this time, the coupling phenomenon caused by the first DOF rotation can be eliminated. The length change and the robot joint angle change related to the motor drive, based on the surgical robot control using the wire-driven method, are correlated, and the values for the position and direction of the end effector of the robot can be obtained through a forward kinematic analysis. The coupling problem occurring in the wire connecting the robot driving part can be solved through a kinematic analysis. Therefore, it was possible to test the position of the slave robot and the performance of the surgical forceps movement using the master system.

Current treatment for patients suffering from cervical spine injuries is by static braces which causes discomfort and immobilization of the neck. This paper presents a novel comfortable wearable therapy device for treating patients suffering with head/neck posture problems using parallel mechanism concept. To achieve this, a conceptual design of a three-degrees-of-freedom Revolute-Prismatic-Spherical configuration parallel manipulator with 3 extensible links is proposed. However, precision and workspace are the general considerations for designing a parallel manipulator. In this research, workspace and position analysis is carried out for the device. By applying geometrical method and vector-loop approach, the inverse kinematics equations are derived. The parallel manipulator is modeled using SolidWorks and simulated using MATLAB. From the simulation results, stroke length of the actuators, angular tilt and position of the moving platform is obtained. To validate the simulation results a preliminary prototype is built and tests were carried. The obtained results found to be satisfying the cause of the research. Furthermore, the device needs to automated and safely operated under the therapist supervision.

Solving the forward kinematics of parallel robots efficiently is important for real-time applications. However, it remains a difficult problem due to its high nonlinearity. This paper combines artificial neural networks and the Global Newton-Raphson with Monotonic Descent (GNRMD) algorithm to decrease the training sets of neural networks while avoiding divergence problem. Furthermore, simplified Newton iteration is introduced to reduce the duration of solution time. The proposed method is demonstrated taking a Stewart platform as an example and the nonlinear equations are established with the geometrical method. Based on the continuous characteristic of real-time applications, the result of the previous solution cycle is used as the initial value of the current solution cycle. Moreover, a threshold adjusting the effective scope of GNRMD algorithm and simplified Newton iteration is set to balance the efficiency and number of iteration. The performance of the algorithm is verified in the environment of Microsoft Visual Studio 2013 based on the continuous feedback of the Stewart platform. Besides, it is compared with GNRMD algorithm and a higher-order numerical method. The results indicate that the proposed algorithm can improve the efficiency of solving the forward kinematics problem.

Robotics can play a significant role to increase efficiency and lighten the farmer’s load. Despite challenges in the agricultural robotic designs, robots are capable of performing various tasks and changing themselves accordingly, based on specific conditions. To address modern problems in the agricultural field, an agricultural robot is one of the key technologies. Although agricultural robotic is still in the development stage, robots have a bright future ahead. This paper proposes a new 5DOF articulated robotic arm design that would become a solution for heavy crop harvestings like pumpkin and cabbage. After the development stage, this robotic arm will be mounted on a robot tractor for real experimentation. The main design process of this robotic arm was conceived using 6 stages of Shigley design process. All components were designed, assembled and analyzed by using Solidworks 2014 in compliance with Japanese Industrial Standards (JIS) standards. The parts of the system that had dynamic nature were analyzed manually using standard mechanical formulas. Calculations of the workspace required joint torque, and coordination of mass center position was done by using standard machine design methods. Denavit-Hartenberg method was used to calculate forward and inverse kinematics. To resolve the torque reduction, components were designed using different materials and mass centers and comparing their performance. Results showed that total torque in Joints number 1, 2, 3, 4 and 5 were 6.15, 257.35, 103.4, 20.2 and 0.1 respectively with a rotational speed range of 15 ~ 60 rpm. Changes in the linkage material and servo motor location improved 29.7% ~ 47.7% and 29.7% ~ 68.9% of the total required torque for each joint. The maximum distance covered by the arm was 1421 mm from the and 2026 mm from the attachment point. According to the feedback received

Forward kinematics is one of the main research fields in robotics, where the goal is to obtain the position of a robot’s end-effector from its joint parameters. This work presents a method for achieving this using a recursive algorithm that builds a 3D computational model from the configuration of a robotic system. The orientation of the robot’s links is determined from the joint angles using Euler Angles and rotation matrices. Kinematic links are modeled sequentially, the properties of each link are defined by its geometry, the geometry of its predecessor in the kinematic chain, and the configuration of the joint between them. This makes this method ideal for tackling serial kinematic chains. The proposed method is advantageous due to its theoretical increase in computational efficiency, ease of implementation, and simple interpretation of the geometric operations. This method is tested and validated by modeling a human-inspired robotic mobile manipulator (CHARMIE) in Python.

The iterative search method（ Newton or Quasi-Newton） is an important numerical method for solving the forward kinematics（ FK） problem of parallel mechanisms. Due to the extremely displacement singularity in the limbs,the search space is easy to be out of the mechanism workspace,which causes failed in solving the FK problem of the class of 2 RUS/2 RRS mechanism. Taking the plane series branch as an example,the equivalent method of eliminating the extremely displacement singularity is given,and the 2 RUS/2 RRS mechanism is equivalent to a 2 UPS/2 RPS mechanism. Based on the relationship between the angular velocity and the Euler’s derivative,the 4 × 4 Jacobian matrix is gotten through the virtual mechanism method. The Jacobian matrix of the initial pose of the equivalent mechanism can be taken as the approximate initial value of the Quasi-Newton method,which can reduce the calculation and improve the computational efficiency. The FK problem of 2 RUS/2 RRS are numerically verified by inverse Broyden algorithm in Quasi-Newton method.

In this work, we began to take forward kinematics of the Gough–Stewart (G-S) platform as an unconstrained optimization problem on the Lie group-structured manifold SE(3) instead of simply relaxing its intrinsic orthogonal constraint when algorithms are updated on six-dimensional local flat Euclidean space or adding extra unit norm constraint when orientation parts are parametrized by a unit quaternion. With this thought in mind, we construct two kinds of iterative problem-solving algorithms (Gauss–Newton (G-N) and Levenberg–Marquardt (L-M)) with mathematical tools from the Lie group and Lie algebra. Finally, a case study for a general G-S platform was carried out to compare these two kinds of algorithms on SE(3) with corresponding algorithms that updated on six-dimensional flat Euclidean space or seven-dimensional quaternion-based parametrization Euclidean space. Experiment results demonstrate that those algorithms on SE(3) behave better than others in convergence performance especially when the initial guess selection is near to branch solutions.

For coordinating the body change and leg movement to promote jump and over-obstacle ability of a bionic robot,a new type of quadruped bionic robot configurations with spine is introduced. On this basis,the forward kinematics problem of this kind of the robot is studied. Firstly,according to the structure of the robot,the motion equations are established which contain the all driving angles. The motion equations contain many redundant drive angles,which is very difficult to solve the redundant drive angles,a dimensionality-reduction method is adopted. By using the dimensionality-reduction method,one of the formulas is translated to the constraint condition,the iteration procedure is used for the rest of equation sets to seek solutions of the redundant drive angles which satisfy the constraint condition. On this basis,the pose of mass center for the quadruped bionic robot with spine is solved and analyzed. An example is given to illustrate the process,this research is helpful to accelerate the use of this kind of robot.

The forward position solution (FPS) of any complex parallel mechanism (PM) can be solved through solving in sequence all of the independent loops contained in the PM. Therefore, when solving the positions of a PM, all independent loops, especially the first loop, must be correctly selected. The optimization selection criterion of the position analysis route (PAR) proposed for the FPS is presented in this paper, which can not only make kinematics modeling and solving efficient but also make it easy to get its symbolic position solutions. Two three-translation PMs are used as the examples to illustrate the optimization selection of their PARs and obtain their symbolic position solutions.

In this paper, a numerical method for forward kinematics of general Stewart manipulator using natural coordinates is presented. The kinematic equations are in quadratic forms and the corresponding Jacobian matrix is a linear function of coordinates because of using natural coordinates. According to the characteristics of the kinematic equations, the Newton-Raphson algorithm is simplified to decrease the renewal time of iterations between equations and Jacobian matrix, and used to solve the kinematic equations. The singularity and convergence problems of the algorithm are discussed. Furthermore, the method using natural coordinates is compared with the traditional method using rotation matrix through numerical examples. Comparison results show that the method using natural coordinates is very accurate, more efficient, and has a greater convergence domain.

Many assembly modes exist due to multi-solutions for forward kinematics of 6-UPS parallel robot. However, the existing theoretical research results have not been well applied to the real-time control, because of the complexity of the forward kinematics. This paper proposes an analytic algorithm to establish the forward kinematics model of a 6-UPS parallel robot with an extra displacement sensor mounted on the centers of upper and lower platform ((6+1)-UPS). Based on the unit quaternion method, the improved forward kinematics model of the proposed (6+1)-UPS system is theoretically derived to be four equations about four components of unit quaternion. The whole computation process is analytical. The method of measurement of the 7th link length and the utilization of unit quaternion reduces the complexity of computation process of forward kinematics, avoids the computer memory spillover and increases the computation efficiency to be suitable for the real-time control application. Then, the analytical solution of the position vector and orientation matrix of the (6+1)-UPS parallel robot are obtained. Finally, the correctness and effectiveness of the proposed approach are illustrated with a numerical example.

The 3- RRRS mechanism is adopted to connect motion platform with static platform,which can achieve the 6 dimensions change of pose for static platform relative to moving platform. Releasing S vice,the mechanism configuration can be used for the general structure of reptiles bionic robot. Because the mechanism configuration has redundant drive characteristics,it can improve motion performance and work space of motion platform. The forward kinematics problem is studied. Firstly,according to the structure relationship,the motion equations including redundant drive variables are established. Secondly,the redundancy drive variables are solved by Bezout equation and variable substitution. Finally,a calculation model of the motion trajectory and direction matrix for motion platform are obtained. An analysis example is described. A reference for solving the similar problem is provided.

This work proposes a close form solution algorithm to solve the inverse kinematics for a five degree of freedom (DOF) robot manipulator, close form solution is preferable to numerical solutions because analytical ones yield complete solutions and are computationally fast and reliable. The motion path of a robot arm is calculated using the geometric analysis. The proposed algorithm is verified using developed simulation modules. Computer simulation is conducted to demonstrate accuracy of the proposed algorithm to generate an appropriate joint angle for reaching desired Cartesian coordinate. The algorithm has been tested yield fair, which have also compared with the robot arm's actual reading.

Motion capture systems provide an efficient and interactive solution for extracting information related to a human skeleton, which is often exploited to animate virtual characters. When the character cannot be assimilated to an anthropometric shape, the task to map motion capture data onto the armature to be animated could be extremely challenging. This paper presents two methodologies for the automatic mapping of a human skeleton onto virtual character armatures. Kinematics chains of the human skeleton are analyzed in order to map joints, bones and end-effectors onto an arbitrary shaped armatures. Both forward and inverse kinematics are considered. A prototype implementation has been developed by using the Microsoft Kinect as body tracking device. Results show that the proposed solution can already be used to animate truly different characters ranging from a Pixar-like lamp to different kinds of animals.

In this paper, a new approach for the forward kinematics of nearly general Stewart platform (i.e., both the fixed base and moving platform are restricted to planar platforms) with an extra sensor is presented. Fifteen compatible algebra equations which express the coupling relationships between the position and orientation variables of the moving platform are obtained. Because the magnitude of the position vector is measured by the extra sensor, the fifteen compatible algebra equations can be transformed into a set of linear algebraic equations with two unknown variables with the help of elimination by substitution, from which a unique solution can be obtained. In the end, a numerical example is presented to verify the correctness of the proposed approach. The proposed approach is simple and does not need any iteration, is expected to be used in real time applications.

This paper presents for the first time a complete kinematic analysis of 5250 Lab-Volt 5-Dof robot which include both forward kinematics and inverse kinematics for this robot arm. The kinematics problem is defined as the transformation from the Cartesian space to the joint space and vice versa. The forward and inverse kinematics for any type of robots are very important in both trajectory planning and position control for the robot arm,the Denavit-Harbenterg (D-H) representation is used to model robot links and joints in this paper. The inverse kinematics have been solved using analytical solution and programmed using MATLAB to move the robot.

This paper suggests a mathematical solution to parallel manipulator with six degrees of freedom and follows the movement on a specific track to evaluate the singularity position. Mathematical equation was derived based on the fundamental principles of the coordinate and orientation vectors of the moving platform center. According to this equation, each leg length was calculated. It means that the independent coordinates (linkage length) was calculated with respect to the dependent coordinates (coordinate and orientation of the moving platform center) by using (MathCad 14) software. By solving the forward kinematics, the coordinate and orientation of the moving platform center were evaluated when this center was moving in a specific track. The center of moving platform moved between two points. When the robot moved using animated program turns the moving platform to imaginary at (position 4), when lose control of the robot and this is a big problem occurs in special cases when the movement of the robot is called singularity.

In this paper, a forward kinematics problem is concerned with the relationship between the individual joint of robot arm and the position and orientation of the tool or end-effector. The standard Denavit_Hartenberg(D-H) analytical scheme is applied to building mathematical modeling to predict, simulate and recovering the end-effector location (position and orientation) placement of 5DOF R5150 Robot manipulator for different joint variables, the basic challenge associated with the R5150 arm is the limited information available on its governing control model for position placement. Two ways by which control can be effected on R5150 arm, this robot can be programmed by using either a hand-held terminal (teach pendant) or a RoboCIM simulation software. The non-versatility of this control software is seen in the non-availability of a programmable environment by users. The user interface of RoboCIM allows for numeric keyboard inputs such that each input results in the orientation of a specific joint by a margin equivalent to the input. The relationship between the keyboard inputs and joint motion of the arm is not feasible to the users. The proposed D-H scheme as presented herein has successfully reproduced the end-effecter position of the Lab_volt R5150 Robot arm with marginal differences for different experimental trials. The simulation of robot arm forward kinematics is performed through MATLAB. The adopted modeling is validated in the physical behaviors in determine position of robot arm.

This paper demonstrates the use of multiple low-cost inertial/magnetic sensors as a pedestrian navigation system for indoor positioning. This research looks at the problem of pedestrian navigation in a practical manner by investigating dead-reckoning methods using low-cost sensors. This work uses the estimated sensor orientation angles to compute the step size from the kinematics of a skeletal model. The orientations of limbs are represented by the tilt angles estimated from the inertial measurements, especially the pitch angle. In addition, different step size estimation methods are compared. A sensor data logging system is developed in order to record all motion data from every limb segment using a single platform and similar types of sensors. A skeletal model of five segments is chosen to model the forward kinematics of the lower limbs. A treadmill walk experiment with an optical motion capture system is conducted for algorithm evaluation. The mean error of the estimated orientation angles of the limbs is less than 6 degrees. The results show that the step length mean error is 3.2 cm, the left stride length mean error is 12.5 cm, and the right stride length mean error is 9 cm. The expected positioning error is less than 5% of the total distance travelled.

A study on the issue that the forward kinematics and workspace of a manipulator with 8--DOF is carried out.Firstly,according to the structural characteristics of the manipulator,the link coordinate system of manipulator are established by using D-H method,and its forward kinematics is obtained.Secondly,the simulation model of manipulator is set up by using the MATLAB Robotics Toolbox,and the correctness of the kinematics forward solution is testified.Finally,according to the position vector of the end actuator,the Monte Carlo method is applied to analyze the manipulator workspace,and the workspace range of the manipulator end actuator is acquired,and it is consistent with the design parameters of the manipulator.