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    Hybrid force/position control for a 3-DOF 1T2R parallel robot: Implementation, simulations and experiments

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    "This is an Author's Accepted Manuscript of an article published in Cazalilla, José, Marina Vallés, Ángel Valera, Vicente Mata, and Miguel Díaz-Rodríguez. 2016. Hybrid Force/Position Control for a 3-DOF 1T2R Parallel Robot: Implementation, Simulations and Experiments. Mechanics Based Design of Structures and Machines 44 (1 2). Informa UK Limited: 16 31. doi:10.1080/15397734.2015.1030679, available online at: https://www.tandfonline.com/doi/full/10.1080/15397734.2015.1030679."[EN] A robot interacting with the environment requires that the end effector \hboxposition is tracked and that the forces of contact are kept below certain reference values. For instance, in a rehabilitation session using a robotic device, the contact forces are limited by the allowed strength of the human limbs and their complex-joints. In these cases, a control scheme which considers both position and force control is essential to avoid damage to either the end effector or the object interacting with the robot. This paper therefore develops a real-time force/position control scheme for a three-DOF parallel robot whose end effector holds a DOF one translation (1T) and two rotations (2R). The implemented hybrid force/position control considers, as a reference, the normal force on the mobile platform, which is measured by means of a load cell installed on the platform. The position control is designed to track the orientations of the robot either in joint or task space using a model-based control scheme with identified parameters. Moreover, the force control is based on a PD action. The control scheme is developed through simulations, before being applied to an actual parallel robot. The findings show that with the implemented controller, the actual robot accomplishes the reference values for the normal force on the mobile platform, while at the same time the platform accurately follows the required angular orientation.The authors wish to thank the Plan Nacional de I+D, Comision Interministerial de Ciencia y Tecnologia (FEDER-CICYT) for the partial funding of this study under the projects DPI2011-28507-C02-01 and DPI2013-44227-R. This work was also partially supported by the Fondo Nacional de Ciencia, Tecnologia e Innovacion (FONACIT-Venezuela).Cazalilla, J.; Vallés Miquel, M.; Valera Fernández, Á.; Mata Amela, V.; Díaz-Rodríguez, M. (2016). Hybrid force/position control for a 3-DOF 1T2R parallel robot: Implementation, simulations and experiments. Mechanics Based Design of Structures and Machines. 44(1-2):16-31. https://doi.org/10.1080/15397734.2015.1030679S1631441-2Åström, K. J., & Murray, R. M. (2008). 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A methodology for dynamic parameters identification of 3-DOF parallel robots in terms of relevant parameters. Mechanism and Machine Theory, 45(9), 1337-1356. doi:10.1016/j.mechmachtheory.2010.04.007Diaz-Rodriguez, M., Valera, A., Mata, V., & Valles, M. (2013). Model-Based Control of a 3-DOF Parallel Robot Based on Identified Relevant Parameters. IEEE/ASME Transactions on Mechatronics, 18(6), 1737-1744. doi:10.1109/tmech.2012.2212716Farhat, N., Mata, V., Page, Á., & Valero, F. (2008). Identification of dynamic parameters of a 3-DOF RPS parallel manipulator. Mechanism and Machine Theory, 43(1), 1-17. doi:10.1016/j.mechmachtheory.2006.12.011Garg, A., Vikram, C. S., Gupta, S., Sutar, M. K., Pathak, P. M., Mehta, N. K., … Gupta, V. K. (2014). Design and Development of In Vivo Robot for Biopsy. Mechanics Based Design of Structures and Machines, 42(3), 278-295. doi:10.1080/15397734.2014.898587Gough, V. E., Whitehall, S. G. (1962). Universal tire test machine.Proceedings of 9th International Technical Congress FISITA, pp. 117–135.García de Jalón, J., & Bayo, E. (1994). Kinematic and Dynamic Simulation of Multibody Systems. Mechanical Engineering Series. doi:10.1007/978-1-4612-2600-0Lee, K.-M., & Arjunan, S. (1991). A three-degrees-of-freedom micromotion in-parallel actuated manipulator. IEEE Transactions on Robotics and Automation, 7(5), 634-641. doi:10.1109/70.97875Li, Y., & Xu, Q. (2007). Design and Development of a Medical Parallel Robot for Cardiopulmonary Resuscitation. IEEE/ASME Transactions on Mechatronics, 12(3), 265-273. doi:10.1109/tmech.2007.897257Merlet, J.-P. (2000). Parallel Robots. Solid Mechanics and Its Applications. doi:10.1007/978-94-010-9587-7Pierrot, F., Nabat, V., Company, O., Krut, S., & Poignet, P. (2009). Optimal Design of a 4-DOF Parallel Manipulator: From Academia to Industry. 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    Workspace and Singularity analysis of a Delta like family robot

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    Workspace and joint space analysis are essential steps in describing the task and designing the control loop of the robot, respectively. This paper presents the descriptive analysis of a family of delta-like parallel robots by using algebraic tools to induce an estimation about the complexity in representing the singularities in the workspace and the joint space. A Gr{\"o}bner based elimination is used to compute the singularities of the manipulator and a Cylindrical Algebraic Decomposition algorithm is used to study the workspace and the joint space. From these algebraic objects, we propose some certified three dimensional plotting describing the the shape of workspace and of the joint space which will help the engineers or researchers to decide the most suited configuration of the manipulator they should use for a given task. Also, the different parameters associated with the complexity of the serial and parallel singularities are tabulated, which further enhance the selection of the different configuration of the manipulator by comparing the complexity of the singularity equations.Comment: 4th IFTOMM International Symposium on Robotics and Mechatronics, Jun 2015, Poitiers, France. 201

    Kinematics and workspace analysis of a 3ppps parallel robot with u-shaped base

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    This paper presents the kinematic analysis of the 3-PPPS parallel robot with an equilateral mobile platform and a U-shape base. The proposed design and appropriate selection of parameters allow to formulate simpler direct and inverse kinematics for the manipulator under study. The parallel singularities associated with the manipulator depend only on the orientation of the end-effector, and thus depend only on the orientation of the end effector. The quaternion parameters are used to represent the aspects, i.e. the singularity free regions of the workspace. A cylindrical algebraic decomposition is used to characterize the workspace and joint space with a low number of cells. The dis-criminant variety is obtained to describe the boundaries of each cell. With these simplifications, the 3-PPPS parallel robot with proposed design can be claimed as the simplest 6 DOF robot, which further makes it useful for the industrial applications

    Miniaturized modular manipulator design for high precision assembly and manipulation tasks

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    In this paper, design and control issues for the development of miniaturized manipulators which are aimed to be used in high precision assembly and manipulation tasks are presented. The developed manipulators are size adapted devices, miniaturized versions of conventional robots based on well-known kinematic structures. 3 degrees of freedom (DOF) delta robot and a 2 DOF pantograph mechanism enhanced with a rotational axis at the tip and a Z axis actuating the whole mechanism are given as examples of study. These parallel mechanisms are designed and developed to be used in modular assembly systems for the realization of high precision assembly and manipulation tasks. In that sense, modularity is addressed as an important design consideration. The design procedures are given in details in order to provide solutions for miniaturization and experimental results are given to show the achieved performances

    Dynamics of the Orthoglide parallel robot

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    Recursive matrix relations for kinematics and dynamics of the Orthoglide parallel robot having three concurrent prismatic actuators are established in this paper. These are arranged according to the Cartesian coordinate system with fixed orientation, which means that the actuating directions are normal to each other. Three identical legs connecting to the moving platform are located on three planes being perpendicular to each other too. Knowing the position and the translation motion of the platform, we develop the inverse kinematics problem and determine the position, velocity and acceleration of each element of the robot. Further, the principle of virtual work is used in the inverse dynamic problem. Some matrix equations offer iterative expressions and graphs for the input forces and the powers of the three actuators

    Kinematic and Dynamic Analysis of the 2-DOF Spherical Wrist of Orthoglide 5-axis

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    This paper deals with the kinematics and dynamics of a two degree of freedom spherical manipulator, the wrist of Orthoglide 5-axis. The latter is a parallel kinematics machine composed of two manipulators: i) the Orthoglide 3-axis; a three-dof translational parallel manipulator that belongs to the family of Delta robots, and ii) the Agile eye; a two-dof parallel spherical wrist. The geometric and inertial parameters used in the model are determined by means of a CAD software. The performance of the spherical wrist is emphasized by means of several test trajectories. The effects of machining and/or cutting forces and the length of the cutting tool on the dynamic performance of the wrist are also analyzed. Finally, a preliminary selection of the motors is proposed from the velocities and torques required by the actuators to carry out the test trajectories

    Kinematic Analysis and Trajectory Planning of the Orthoglide 5-axis

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    The subject of this paper is about the kinematic analysis and the trajectory planning of the Orthoglide 5-axis. The Orthoglide 5-axis a five degrees of freedom parallel kinematic machine developed at IRCCyN and is made up of a hybrid architecture, namely, a three degrees of freedom translational parallel manip-ulator mounted in series with a two degrees of freedom parallel spherical wrist. The simpler the kinematic modeling of the Or-thoglide 5-axis, the higher the maximum frequency of its control loop. Indeed, the control loop of a parallel kinematic machine should be computed with a high frequency, i.e., higher than 1.5 MHz, in order the manipulator to be able to reach high speed motions with a good accuracy. Accordingly, the direct and inverse kinematic models of the Orthoglide 5-axis, its inverse kine-matic Jacobian matrix and the first derivative of the latter with respect to time are expressed in this paper. It appears that the kinematic model of the manipulator under study can be written in a quadratic form due to the hybrid architecture of the Orthoglide 5-axis. As illustrative examples, the profiles of the actuated joint angles (lengths), velocities and accelerations that are used in the control loop of the robot are traced for two test trajectories.Comment: Appears in International Design Engineering Technical Conferences \& Computers and Information in Engineering Conference, Aug 2015, Boston, United States. 201

    Kinematics, workspace and singularity analysis of a multi-mode parallel robot

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    A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity analysis of a 3-PRPiR parallel robot involving lockable Pi and R (revolute) joints. Here a Pi joint may act as a 1-DOF planar parallelogram if its lock-able P (prismatic) joint is locked or a 2-DOF RR serial chain if its lockable P joint is released. The operation modes of the robot include a 3T operation modes to three 2T1R operation modes with two different directions of the rotation axis of the moving platform. The inverse kinematics and forward kinematics of the robot in each operation modes are dealt with in detail. The workspace analysis of the robot allow us to know the regions of the workspace that the robot can reach in each operation mode. A prototype built at Heriot-Watt University is used to illustrate the results of this work.Comment: International Design Engineering Technical Conferences \& Computers and Information in Engineering Conference, Aug 2017, Cleveland, United States. 201
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