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Considering frictional, inertial and machining forces, the authors have presented an enhanced analysis of a hexapod table as used in milling machines. The Newton-Euler analysis of hexapod’s components has been implemented by a simulation program developed by the authors in MATLAB environment and the results have been verified by those of others. The impact of various loads involved in machining operation carried out on a milling machine equipped with hexapod table has been presented in the paper. This provides a potential machine tool designer with guidelines on the importance of these loads and helps him give appropriate weights to them.

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In this paper, the forward kinematic of the special cases of 4- R" R' R' R" R", 4- R" R" R" R' R' and 4- R" R" R' R' R" parallel mechanisms that respectively lead to two 4- R R U R with different geometric structures and one 4- R U U spatial 4-DOF parallel robots has been studied. They are originated from the type synthesis of 4-DOF parallel mechanisms with motion patterns of 3 T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute joints. The directions of revolute joints have been different with each others that create three different geometrical structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 462 and 8 is indicated the forward kinematic problem of each parallel robot. Also, the results are compared with simulations.

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This paper involves the investigation of the forward kinematic problem of three 4-DOF parallel robots, named as 4-PRUR1, 4-PRUR2, 4-PUU, performing 3 translations and one rotation, namely Schönflies motion. The foregoing parallel robots are special cases of 3 parallel robots, named as 4-PR′R′R″R″, 4-PR″R″R′R′ and 4-PR″R′R′R″, respectively, arisen from the type synthesis performed for 4-DOF parallel mechanisms with identical kinematic limb structures. Each robot has 4 identical kinematic chains and each chain consists of one prismatic active joint and 4 revolute passive joints. Due to different direction of revolute joints in each limb, 3 different architectures are considered in this paper. The forward kinematic problem is explored in seven-dimensional kinematic space using the so-called Study's parameters and LIA algorithm and eventually, it has been shown that an algebraic expression of degree 4 indicates the forward kinematic of each kinematic chains of parallel robots under study in this paper. Moreover, using homotopy continuation and comparison with resultant method, it reveals that the forward kinematic problem of this robots have up to 236,236 and 2 real solutions, respectively.

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A modified measure for the parallel cable driven robots is presented in this paper. These robots have additional advantages compared to other robots and even the parallel structures, but they are readily exposed to disturbances. The presence of external wrench (Force-Moment) may be the cause of violation against the motion constraint. The stability measure proposes a number between zero and one that could be the criterion for the evaluation of the robot's ability while returning to its original equilibrium which was influenced by external disturbances. To offer a stability measure, Gibbs-Appell equations and acceleration energy are used. Robot kinematic and dynamic modeling based on Newton-Euler’s method calculates the measure. To illustrate the capabilities of the proposed measure, a 6 DOF cable robot with six cables is simulated. The results of the two simulations are presented and analyzed. The stability measure is depended to kinematic parameters and also to kinetics parameters as cables tension at the beginning of motion. Therefore using the proposed measure one can better evaluate the stability within the wider range of parallel cable robots.

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Parallel mechanisms are widely being used in industrial applications such as machine tool, metrology, earthquake simulator, fly simulator, medical equipment and etc. These mechanisms have some limitations like having erratic workspace, singular points in the workspace and complexity of control systems. These limitations should be studied for suitable usage of parallel mechanisms. In this article, a four degree of freedom parallel mechanism (three linear and one rotation degrees of freedoms) is proposed as machine tool and being studied and its workspace and singularity analysis are done by solving the kinematic relations and using Matlab software. So, at first the inverse and direct kinematic equations of mechanism were solved and then an algorithm is used to determine the workspace and singular points of proposed parallel mechanism. Finally, to investigate the results of workspace analysis the structure has been modeled in Solidworks software and the inverse kinematic relation and the obtained workspace have been validated using the simulation. At the last, to investigate the quality of robot performance and its dexterity in workspace, global condition index of mechanism using Jacobean matrix is calculated for different orientations of moving platform.

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In this paper, a multivariate statistical method called Principal Components Analysis, PCA, is utilized for detection faults in a 3-PSP parallel manipulator. This statistical method transfers original correlated variables into a new set of uncorrelated variables. PCA method can be used to determine the thresholds of statistics and calculate square prediction errors of new observations for checking the system when a fault occurs in the robot. To investigate on the ability of the PCA method for faults detection of the robot, a nonlinear model-based controller called Computed Torque Control, CTC, is designed. In this control scheme, rigid-body inverse dynamics model of the robot is utilized to linearize and to cancel the nonlinearity in the controlled system. Also, instead of using the robot prototype model, direct dynamics of the robot is used in the robot-control system. In this paper, two faults are artificially applied to the robot-control system. These two faults consist of faults in servo drive or servo motors and faults in joints clearances or position sensors. Finally, these faults are applied on the robot throughout a desired end-effector trajectory and the resultant outputs are obtained for both with and without faults in the manipulator. Consequently, the desired and faulty outputs are compared and faults detection using PCA method for the robot is performed.

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Regarding the progress in technology and increase in the capabilities of the robots, one of the main challenges in the field of robotics is the problem of real-time and collision-free path planning of robots. This paper focuses on the problem of path planning of a 3-DOF decoupled parallel robot called Tripteron in the presence of obstacles. The proposed algorithm is a synergy-based algorithm of convex optimization, disjunctive programming and model predictive control. This algorithm has many advantages compared to previous methods reported in the literature including not getting stuck in the local optimums and finding the global optimum and high computational speeds. Finally, the algorithm will be implemented on a model of the real robot. It should be mentioned that this algorithm has been implemented using Gurobi optimization package with C++ programming language in Qt Creator environment and the simulation of the parallel mechanism is performed by the CAD2MAT package for MATLAB. Obtained results reveal that the maximum computational time at each step is less that one second which, for this particular application, could be regarded as a real-time algorithm.

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This paper presents implementation of position control for planar cable-driven parallel robots using Visual servoing. The main contribution of this paper contains three objectives. First, a method is used toward kinematic modeling of the robot using four-bar linkage kinematic concept, which could be used in online control approaches for real-time purposes due to decreasing of the unknown parameters and computation time. In order to track the position of End-Effector, an online image processing procedure is developed and implemented. Finally, as the third contribution, two different controllers in classic and modern approaches are applied in order to validate the model with plant and obtain the most promising controller. As classic controller, pole placement approach is suggested and results demonstrate weaknesses in modeling the uncertainties although they represent acceptable performance. Due to the latter incapability, sliding mode controller is utilized and experimental tests represent effectiveness of this method. Result of the latter procedure is an inimitable operation on the desired task however, it suffers from chattering effect. Moreover, results of these controllers confirm accommodation between the model and robot. The whole procedure imposed, could be applied for any kind of cable-driven parallel robot.

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This paper deals with the collision-free path planning of planar parallel robot by avoiding mechanical interferences and obstacle within the workspace. For this purpose, an Artificial Potential Field approach is developed. As the main contribution of this paper, In order to circumvent the local minima problem of the potential fields, a novel approach is proposed which is a combination of Potential Field approach, Fuzzy Logic and also a novel algorithm consisting of Following Obstacle as well as Virtual Obstacle methods, as a hybrid method. Moreover, the inverse kinematic problem of the 3-RRR planar parallel robot is analyzed and then the aforementioned hybrid method is applied to this mechanism in singular-free case. It is worth mentioning that, in this paper, all the probable collisions, i.e., the collision between the mechanism and the obstacles and also among the links, are taken into accounts. Two general cases have been considered in collision-free path planning simulation; the first case considered a mobile robot in several workspaces and the second one was assigned to the 3-RRR planar parallel robot path planning. Results of the simulations, which are implemented in C programming language for the sake of real-time purposes. reveal that for the both cases, the newly proposed hybrid path planning method is efficient enough for the mobile robot, or the end-effector of the planar parallel robot to reach the goal without colliding with the obstacles.

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Cable-Driven Parallel Robot has many advantages. However, the problems of cable collision between each other and environment, the lacks proper structure and non-positive cable tension prevent the spread of them. Therefore, connecting a serial manipulator to mobile platform improve the ability to object manipulation. This paper investigates the multi-objective optimization structure design and comparative study of spatial constrained and suspended cable-driven parallel robot. By install serial manipulators possess a full hybrid robot’s features. The workspace volume, kinematic stiffness and sensitivity are three sets of optimization criteria. The workspace volume calculated by a novel approach of combination constraints as prevent cables collisions with each other, cable collision with moving platform, uncontrollability and singularity of the robot. First, examine range of the forces and torque reaction of the serial manipulator to moving platform. Then, the evolutionary optimization genetic algorithm use for the multi-objective optimization of constrained and suspended spatial cable-driven parallel robot structure to achieve proper Pareto front confrontation. The Pareto front reconciliation of these three criteria will be discussed. The constrained and suspended optimize by same criteria will compare in the same conditions. It is verified that the constrained structure significantly reduced actuation energy for manipulate a serial robot, supply greater workspace and manipulability. The result of this study used for manufacturing and development of a prototype spatial cable-driven parallel robot (RoboCab).

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In this paper, kinematic and dynamic model of planar cable-driven parallel robots are introduced in general form which are verified for a constrained cable-driven parallel robot in Sim-mechanics. Path planning based on artificial potential field approach is considered to prevent collision between dynamic obstacle, end-effector and cables in order to achieve collision-free path. As well as to reduce energy consumption, cable tension constraints have been involved in optimization of path planning. This method is proposed to control a cable robot. Therefore, obstacles are distributed randomly in order to have a complex environment. By this way, cable tension constraint is studied as one of the most crucial challenges for cable driven robots. Moreover, Fmincon function of Matlab is applied in order to take into account the required constraints and maintain the limits for cables tension. The latter leads to solve the redundancy resolution which is a definite asset in controlling a cable-driven parallel robot. Finally, a four-cables driven parallel robot is controlled by using the so-called computed torque method for tracking the desired and optimized path. The method is explained and obtained results indicate the efficiency of the proposed approach.

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This paper focuses on the problem of finding object orientation around Yaw & Pitch & Roll angels. The object orientation is computed in a real time manner using a mono-camera and three points on a solid object in a machine vision software. Three points should be selected from environment at the beginning. In order to reduce wreckful effects of environmental lights on detecting colorful objects and also to reduce the number of used software filters, IR LEDs with 850nm invisible wavelength are used. Artificial Neural Network (ANN) is used for solving this problem since orientation's equations are nonlinear and real-time solving for them is impossible. For solving the problem a feed forward artificial neural network with one hidden layer and 21 nodes in that is used, which has 3 nodes for output layer and 6 nodes for input layer. For having high accuracy in ANN, output data is also obtained from a MPU-9150 installed on a 2-DOF orientional parallel robot and compared to ANN outputs. 7243 data from Roll and Yaw angles and 751 data from Pitch angle is obtained from MPU-9150 sensor and the later 2-DOF orientional parallel robot and 467 data remains nonuse for learning ANN. After learning the neural network, results compared to nonuse data for ANN learning and desire results obtained with 0.038 maximum error

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Simulation of the four degree of freedom parallel robot (Quattrotaar) is subjective of this paper. The mathematical model of the parallel robot is obtained too. The workspace is optimized for Non-singular kinematic type-2. Artificial Bees Colony algorithm and Particle Swarm Optimization algorithm as overall exploring algorithms are implemented and the results are compared to each other. Neglect of any intrinsic complexity of the optimization problem the results show the capability of both methods for this robot parameters design. Comparison of the results indicates the Particle Swarm Optimization algorithm runs faster than Artificial Bees Colony algorithm. The exploring volume consists of a plan with 500 mm x 500 mm dimension which moves in a vertical direction from 500 mm to 1000 mm. One of the important hints of the paper is a 90-degree rotation of end effector around vertical axis Z. This rotation is caused more flexibility and dexterity for the robot. A 3-D model of Quattrotaar parallel robot is created by Computer Aided Design software and finally, Quattrotaar is fabricated in Human and Robot Interaction Laboratory (Taarlab)

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In this study, the effects of geometrical parameters of 6-DOF Hexa parallel robot on kinematic, and dynamic performance indices are investigated and its structure is optimized using the intelligent multi-objective Bees Algorithm. In this way, after describing the structure and specifying the geometrical parameters of the robot, inverse kinematic relations of the robot are obtained. Jacobian matrix that maps velocity from joint space to Cartesian space is developed. Mass matrix is obtained from calculating the total kinetic energy of the manipulator in terms of the actuated joints vector. Inverse of the homogen jacobian based condition number is considered as a index to evaluate the kinematic dexterity. based on mass matrix as relation between acceleration vector of the end effecter and torque vector of actuated joints, dynamic dexterity index is presented. Using the multi-objective Bees Algorithm and considering dynamic and kinematic performance indices in a pre-determined workspace as the objective functions, structure of Hexa parallel robot is optimized. In this way, the proper geometrical constraints such as limitation of universal and spherical joins, and the constraints to singularity avoidance are considered. Pareto front of the multi objective optimization of the robot is drawn. Diagrams of the kinematic and dynamic performance indices variation in the workspace and the effects of geometrical parameters variation on them are presented.

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In spite of several advantages of parallel robots, they generally have limited workspace. Therefore, it is of paramount importance to obtain the workspace by considering the mechanical interference. In this paper, the mechanical interference in planar parallel mechanisms, including interference between links and, collision between links and obstacles and between end-effector and obstacles, are investigated using geometrical reasoning. For this purpose, a new geometric method is proposed for collision detection in the workspace of planar parallel mechanisms based on the lines segment intersection. In this method, the configurations of the planar parallel robot are obtained in the entire workspace. Then, the interference of links with each other and obstacles, which are respectively modeled by line segment and polygon, are determined. Finally, the collision-free workspace of the parallel robot is obtained for a specified orientation of the moving platform. Moreover, in this paper, an index is presented which can be used for examining the workspace by considering mechanical interference. The foregoing index provides some insight into obtaining a well-conditioned workspace.  For the sake of validation, this method is implemented on two planar parallel robots, namely as 3-RRR and 3-PRR, for different working modes. The obtained results reveal that the ratio of the practical workspace to the theoretical workspace is decreased upon increasing the orientation of the end-effector for both clockwise and counterclockwise directions. Furthermore, due to differences in the number of the moving links, the mechanical interference-free workspace of 3-RRR parallel robot is usually more limited than 3-PRR parallel robot.

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In this study, a modified method has been introduced for forward dynamic analysis of fast parallel robots. For this purpose, inspired by the Lagrange-Virtual Spring (LVS) method, the Decoupled Natural Orthogonal Complement (DeNOC) method is modified which is a Newtonian based method. So far, virtual springs have been already used in energy based methods. However using the virtual springs in DeNOC method is a novel approach which is proposed in current study. In order to clarify the advantages of Modified Decoupled Natural Orthogonal Complement (MDeNOC) method, a planar 3RRR mechanism is chosen as case study. According to the results, the process of deriving the equations of motion is much less costly while the accuracy of MDeNOC is similar to the LVS and unlike the energy methods, the modified method is also able to calculate the constraint reactions, as well. On the other hand, the calculation time of MDeNOC is much more than the DeNOC and hence, is not suitable for real time calculations. Also, in closed loop systems, constraints must be defined in such a way that express the virtual springs’ longitudinal changes; otherwise, MDeNOC will not give proper results.

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In this paper, position control is addressed for a pneumatically actuated 6-DoF Gough-Stewart parallel robot. At first, dynamic model of the pneumatic system of each link of the robot which comprises a pneumatic actuator and a proportional electrical control valve is extracted. Unknown parameters of the obtained dynamic model consisting friction force, viscous coefficient and the parameters of the valve are identified by employing an evolutionary algorithm. Then, position control of the robot’s pneumatic actuator is performed based on designing Backstepping-Sliding Mode controller according to the nonlinear dynamic model of the pneumatic system. Moreover, kinematic equations of the 6-DoF parallel robot are achieved and a novel method is proposed, the so-called Geometry-based Quasi-Forward Kinematic, to the end of calculating the position of the end-effector of the robot without using expensive position sensors. Accordingly, kinematic closed-loop control of the parallel robot, which is based on simultaneous joint space and task space control, is investigated for trajectory tracking using potentiometers, a rotation sensor, and based on the computed position of the end-effector by the proposed method. Desired sinusoidal trajectories with pure motions and also complicated trajectories are tracked in which error of positions and rotations are lower than 2 (cm) and 3 (deg), respectively. The results reveal that the trajectory tracking control of the pneumatic 6-DoF Gough-Stewart parallel robot is performed properly based on the proposed control strategies and the novel method for calculating the position of the end-effector.

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