This work presents a **kinematic** study of 3 RRR **parallel** **robot**. Indeed, **Parallel** **robot** is fundamentally a closed-loop **kinematic** chain mechanism in which the end-effector is connected to the base by several independent **kinematic** chains. Due to the potential advantages of **parallel** robots such as high rigidity, high accuracy and great carrying payload capability, they have fascinated signiﬁcant attention and interest amongst the researchers in the past decade.

Abstrat : The manipulator provides a gain in terms of production rate compared to conventional serial manipulators. The trajectory planning made it possible to optimize the performance of the **parallel** **3RRR** manipulator in its workspace. This planning was done on the octave software, based on the **modeling** of the manipulator using the **inverse** geometry method. Which allowed to determine the workspace of the **robot**. The working space of a **parallel** **robot** therefore depends on the different independent **kinematic** chains that connect the base to the effector (mobile platform).

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want to work. But the controlling of **robot** manipulator has been challenges with higher DOF. Position and orientation analysis of robotic manipulator is an essential step to design and control. In this paper a basic introduction of the position and orientation analysis of a serial manipulator is given. A **robot** manipulator consist set of links connected together this either serial or **parallel** manner. The FK analysis is simple to analysis of model and calculate the position using the joint angle. But the challenge in to analyze the IK solution using the position. Complexity of the IK increases with increase the DOF.so to analyze IK in this Paper use the DH convention and transformation type solution.

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David [6] has provided a configuration-space description of the kinematics of the fingers plus-object system for multi fingered manipulation. Emily [7] has derived kinematics and dynamics equations in the design of an anthropomorphic robotic hand for space operation. Parasuraman and Shiau [8] have derived kinematics and dynamics equations for bio- mechanical analysis of human joints . Parasuraman [9] has improved kinematics derivation for humanoid **robot** manipulators to be used in the simulation MFRH using virtual reality toolbox. Valentin et al. [10] have given derivation for trajectory planning of a **robot** manipulator. Kevin and Thurston [11] have derived kinematics analysis of novel 6 DOF **parallel** manipulator. This **kinematic** analysis is used for three elbow angles before computing the position and orientation of the top plate. Mina et al. [12] have used **inverse** kinematics to find the joint of the **robot** finger. In dynamical model, Yavin [13] has derived the **kinematic** and dynamic for three-link manipulator. Jonker and Aarts [14] have improved dynamic simulation for the planar flexible link manipulator. Panagiotis and Kostas [15] have improved the kinematics and dynamic to find the position and force of the **robot** arm in application to teleoperation and orthosis. Ronen et al. [16] have used kinematics and dynamic equations for the planary flexible actuated **parallel** **robot**. Aaron [17] has derived forward and **inverse** **kinematic** for biologically inspired dexterous **robot** hand. Ramasamy and Arshad [18] also have derived the equation of **kinematic** and dynamic to the **robot** hand simulation using 30 Studio Max and Maya 30. The preliminary results of the study were presented in the ICORAFFS conference proceedings [19].

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Although a number of efforts have been made towards various aspects in error **modeling**, tolerance design and **kinematic** calibration of the Delta-type **parallel** robots [3, 7-9,11-14], a comprehensive methodology is still required to merge all threads into a framework. Therefore, addressing Fig.1 and taking such a 4-DOF **parallel** **robot** as an example, this paper proposes a systematic approach to improve the geometrical pose accuracy of the **robot** by integrating tolerance design with **kinematic** calibration. The remainder of this paper is organized as follows. In Section 2, a linearized error model containing all possible geometric source errors is formulated using the first order approximation, allowing the source errors affecting the compensatable and uncompensatable pose accuracy to be separated in an explicit manner. In Section 3, a statistical error model of the **robot** is formulated, leading to an optimal tolerance allocation by a very simple algorithm built upon sensitivity analysis. In Section 4, parameter identification is carried out using a simplified error model and distance measurements. The criterion to minimize the measurements is discussed and a linear compensator is designed for the real-time error compensation. In Section 5, experiments on a prototype machine are carried out to verify the effectiveness of the entire processes proposed before conclusions are drawn in Section 6.

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Kinematics model for **robot** is consisting of research the motion without concern the forces or torques that cause it. Kinematics model can divide into two types of the analysis problem; direct kinematics and **inverse** kinematics. **Inverse** kinematics model is an analysis to find the actuator joint variable with given the desired position and orientations of the end effector. Then, the direct kinematics model is the reverse process of the **inverse** kinematics model. In **robot** **parallel**, the **inverse** kinematics model is easy to analysis rather than the direct kinematics model. In order to derive the kinematics model of the **robot**, the various formulating (Siciliano, 1999 ; Yahya, Mohamed, & Moghavvemi, 2009; Parasuraman, Chan, and Liang, 2010; Zhang and Zhang, 2013 etc) are used. Determine the appropriate formulating of the kinematics model remain a challenging issues and research activities focusing on derivation mathematical model of kinematics since it is an important aspect for develops a new **robot** application (Province, 2012).

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In this paper a calibration method was designed in order to improve accuracy of a **parallel** **robot** that is inspired in the Delta **robot**. The method was tested by means of a visual controller, and errors in the controller and the velocity of an object were used to obtain an index. Thus, both collections (nominal and corrected) of **kinematic** parameters were compared. Difference between parameters calibrated and non calibrated have strong influence in the performance of the error in the visual controller. Therefore performance of a tracking visual controller is improved although correction of the parameters is extremely small (errors in the controller are reduced more than 3% when the **robot** is calibrated). Improvements in the controller performance can be explained as follows: Image visual controller makes use of the **robot** Jacobian and **robot** **kinematic** models (**inverse** and direct), when the controller corrects the **robot** trajectory, errors in the model have direct influence in the direction in which the controller tries to correct. On the other hand if the position of the object remains fixed, error in the visual controller converges to zero but the evolution of the error is different for two set of parameters. In this paper three main topics were discussed: 1.-Obtaining of a **kinematic** model based on incremental and measurements. 2.-Obtaining of a 3D measurement method from one camera in hand. 3.- Obtaining of the influence of small kinematical errors in a classical visual controller.

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Abstract: Industrial manipulators and **parallel** robots are often used for tasks like drilling or milling, that require three translational, but only two rotational degrees of freedom (“3T2R”). While **kinematic** models for specific m echanisms f or t hese t asks e xist, a g eneral k inematic m odel for **parallel** robots is still missing. This paper presents the definition of the rotational component of **kinematic** constraints equations for **parallel** robots based on two reciprocal sets of Euler angles for the end-effector orientation and the orientation residual. The method allows to completely remove the redundant coordinate in 3T2R tasks and to solve the **inverse** kinematics for general serial and **parallel** robots with the gradient-descent algorithm. The functional redundancy of robots with full mobility is exploited using nullspace projection.

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The connection giving the incited joint coordinates for a given posture of the end-effector is known as the **inverse** kinematics, which is straightforward for **parallel** robots. The **inverse** kinematics comprises in building up the estimation of the joint coordinates relating to the end-effector arrangement. Setting up the **inverse** kinematics is fundamental for the position control of **parallel** robots. There are different approaches to speak to the posture of an unbending body through a lot of parameters X. The most old-style route is to utilize the coordinates in a reference edge of a given point C of the body, and three edges to speak to its direction. In any case, there are different ways, for example, **kinematic** mapping which maps the dislodging to a 6-dimensional hyperquadric, the Study quadric, in a seventh-dimensional projective space. The **kinematic** mapping may have an enthusiasm as conditions including dislodging are arithmetical (and the structure of mathematical assortments is preferable comprehended over other non-direct structures) and may have intriguing properties, for instance, expressing that a point submitted to a removal needs to lie on a given circle is effectively composed as a quadric condition utilizing Study coordinates (Merlet, 2006).

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Dynamics of the walking machine can be divided into two basic categories: forward and **inverse** dynamics. The forward dynamics deals with finding the response of a given rigid body in- fluenced by force and torques applied on it, which was simulated by providing link length and rotat- ing angle to determine the position [14]. On the other hand, the opposite procedure is implement- ed to find the force and torques where motion is created in the system through **inverse** dynamic analysis. The link length and position is given to determine the angle of rotation of the links. This method is widely used in the control sys- tem of a motion [17]. In general, for the analysis and **modeling** of dynamic equations of complex mechanisms in **robot** design subjected to holo- nomic constraints, the Newton-Euler and Euler- Lagrange formulations are most common ones. The Lagrangian equation formulation involves the kinetic and potential energy of the system.

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A variable-geometry truss mechanism (VGTM) is a statically determinate truss that has been modi® ed to contain some number of variable length links. VGTMs have very good stiVness± weight ratios and are theoreti- cally composed of two force links. No bending moments or torques can be transmitted at the joints. Moreover, they can be designed to be collapsible. These char- acteristics give VGTMs potential applications, discussed by Arun et al. [1], such as beams to position equipment in space, supports for space antenna, berthing devices and manipulator arms. As a **robot** manipulator, VGTMs have higher stiVness than serial link manip- ulators and a large workspace compared with **parallel** ones. Therefore, they are considered as a new type of **robot** manipulator.

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[5] Trujillo J. L. A., Serrezuela R. R., Zarta J. R. & Ramos A. M. N. 2018. Direct and **Inverse** Kinematics of a Manipulator **Robot** of Five Degrees of Freedom Implemented in Embedded System-Compact RIO. Advanced Engineering Research and Applications, B. S. Ajaykumar and D. Sarkar Eds., Nueva Deli, India, Research India Publication. 405-419.

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The classic implicit calibration method proposed in the study by Wampler et al. 18 utilizes the closure relation of the **kinematic** chains to form implicit constraint equations instead of pursuing the analytical solutions of the closure equations such as the **inverse** **kinematic** model. The impli- cit calibration method emphasizes that the errors are involved in the **kinematic** loop equations implicitly, rather than being explicit outputs of a conventional input–output formulation. 18 By removing the requirement to express errors explicitly, the formulation allows the analyst to con- centrate on all sources of error. 18 And the implicit calibra- tion method has been effectively applied to H4 mechanism10 and 6-UPS **robot**. 18 In implicit calibration method, the absolute posture of the end-effector with respect to the base frame should be obtained with the employment of the contactless sensor. In most applications, the **kinematic** calibration is known as an optimization prob- lem with redundant nonlinear constraint equations. The methods such as classical nonlinear algorithms, 9,19 bundle adjustment approach, 20 and interval approach 21 are applied to solve it. The pose vector of end-effector with respect to the base frame is normally used to construct the objective function of the optimization problem based on 2-norm of vector. 10,18,22 Several **robot** posture configurations should be determined to collect enough information. The princi- ples for the configuration selection of **parallel** **robot** cali- bration have been given in some literature, 23,24 in which the error parameter Jacobian matrix is utilized to minimize the influence of measurement noise in all candidate configura- tions. For the 6-RSS **parallel** **robot**, the effect of the posture selection should be analyzed for relative posture-based algorithm (RPBA).

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In this research, Artificial Neural Networks (ANNs) have been used as a powerful tool to solve the **inverse** **kinematic** equations of a **parallel** **robot**. For this purpose, we have developed the **kinematic** equations of a Tricept **parallel** **kinematic** mechanism with two rotational and one translational degrees of freedom (DoF). Using the analytical method, the **inverse** **kinematic** equations are solved for specific trajectory, and used as inputs for the applied ANNs. The results of both applied networks (Multi-Layer Perceptron and Redial Basis Function) satisfied the required performance in solving complex **inverse** kinematics with proper accuracy and speed.

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and control. A **robot** manipulator consist a set of links connected together either in serial or **parallel** manner. The FK analysis is simple to do analysis of model and calculate the position using the joint angle. But the challenge is to analyze the IK solution using the position. So aim is to study complexity of the IK which increases with increase in the DOF. In this case we would be studying **robot** configurations i.e. 2R, 3R, 3R-1P, 5R, 6R where R and P stands for revolute and prismatic joints. The main motive of the study is to calculate the **robot** parameters i.e. study forward and **inverse** kinematics using algebraic method and then validate this calculations with the outputs from RoboAnalyser and MATLAB.

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In this paper a calibration method was designed in order to improve accuracy of a **parallel** **robot** that is inspired in the Delta **robot**. The method was tested by means of a visual controller, errors in the controller and the velocity of an object were used to obtain an index. Thus both sets (nominal and corrected) of **kinematic** parameters were compared. Calibrated parameters have strong influence in the performance of the error in the visual controller. Therefore performance of a tracking visual controller is improved although correction of the parameters is extremely small (errors in the controller are reduced more than 20% when the **robot** is calibrated). Improvements in the controller performance can be explained as follows: Image visual controller makes use of the **robot** Jacobian and **robot** **kinematic** models (**inverse** and direct), when the controller corrects the **robot** trajectory, errors in the model have direct influence in the direction in which the controller tries to correct. On the other hand if the position of the object remains fixed, error in the visual controller converges to cero but the evolution of the error is different for two set of parameters. In this paper three main topics were discussed: 1.-Obtaining of a **kinematic** model based on incremental and measurements. 2.-Obtaining of a 3D measurement method from one camera in hand. 3.-Obtaining of the influence of small kinematical errors in a classical visual controller.

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Kinematics analysis is the conversion from the Cartesian space to the joint space and vice versa. In this paper, an **inverse** kinematics **modeling** of 5 DOF stationary articulated **robot** arm which is used for educational tasks are presented, and shows an adopted **modeling** method to simulate and represent the simultaneous positional coordinates for each joint of the **robot** while it moving from one target to another. The standard Denavit-Hartenberg (DH) model is applied to build the mathematical **modeling** to determine and simulate the position and orientation of the end effector of (5 DOF) Lab-Volt R5150 **robot** manipulator. The simulation of the **inverse** **kinematic** of the **robot** arm is done through MATLAB software and compare the results with the data from RoboCIM software to know that the model is suitable for simulate and represent.

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well known Closed-loop **inverse** kinematics (CLIK) algorithm was proposed by Siciliano [37], to overcome the joint drift for open- chain **robot** manipulators, by including the feedback for the end-effector’s position and orientation. Wampler [38] proposed a least square method to generate the feasible output around singularities, by utilising a generalised **inverse** matrix of jacobian, known as singularity robust pseudoinverse. Due to the adapting and learning nature, ANN is an efficient method to solve non- linear problems. So it has a wide range of application in manufacturing industry, precisely for Electro discharge machining (EDM) process. Various authors had adopted ANN with different training algorithms namely Levenberg-Marquardt algorithm, scaled conjugate gradient algorithm, Orient descent algorithm, Gaussi Netwon algorithm and with different activation finction like logistic sigmoid, tangent sigmoid, pure lin to model the EDM process. Mandel et.al. [39] used ANN with back propagation as learning algorithm to model EDM process. They concluded that by considering different input parameters such as roughness, material removal rate (MRR), and Tool wear rate (TWR) are found to be efficient for predicting the response parameters. Panda and Bhoi [40], predicted MRR of D2 grads steel by

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Grid-computing environments are an emerging trend in **parallel** computing resources that typically consist of a collection of geographically distributed heterogeneous supercomputer resources (e.g., the NSF’s proposed new distributed terascale facilty 1 (DTF)). **Parallel** implementations for these environments are inherently multilevel and obtaining efficient mapping of work to processors can be extremely challenging. Extension of our previous implementation to the grid can be accomplished by using “grid-enabled” version of MPI libraries. Using the Globus toolkit and grid- enabled MPI (MPICH-G2 or VMI2-MPICH), required number of resources can be requested from multiple supercomputers. Grid-enabled MPI is a special version of MPI suitable for computational grids and is based on the “Globus” meta-computing toolkit (MPICH-G2) or the virtual machine interface 2 (VMI). MPICH-G2 is a Globus flavor of MPICH using services from the Globus toolkit (such as job startup, security etc.,). VMI2- MPICH uses middleware communication layer VMI with MPICH. MPI applications can be run on multiple machines potentially of different architectures using grid enabled MPI libraries. These libraries automatically convert data in messages sent between machines of different architectures and support multiple underlying communication protocols.

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