Journal articles: 'Planar Parallel Manipulator'

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Atia, Khaled R., and M. P. Cartmell. "A general dynamic model for a large-scale 2-DOF planar parallel manipulator." Robotica 17, no. 6 (November 1999): 675–83. http://dx.doi.org/10.1017/s0263574799001794.

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In this work a new concept of designing two degree of freedom (2-DOF) planar parallel manipulators (PPMs) is presented. With this design the manipulator's workspace can be increased by increasing the number of cells in the manipulator. A general dynamic model is formulated for the manipulator with any number of cells. The model is adapted for SCARA and ADEPT configurations, and a new approach for balancing these type of manipulators is proposed.

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Karnam, Murali K., Aravind Baskar, Rangaprasad A. Srivatsan, and Sandipan Bandyopadhyay. "Computation of the safe working zones of Planar and Spatial Parallel Manipulators." Robotica 38, no. 5 (July 25, 2019): 861–85. http://dx.doi.org/10.1017/s0263574719001139.

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SUMMARYThis paper presents the computation of the safe working zone (SWZ) of a parallel manipulator having three degrees of freedom. The SWZ is defined as a continuous subset of the workspace, wherein the manipulator does not suffer any singularity, and is also free from the issues of link interference and physical limits on its joints. The proposed theory is illustrated via application to two parallel manipulators: a planar 3-R̲RR manipulator and a spatial manipulator, namely, MaPaMan-I. It is also shown how the analyses can be applied to any parallel manipulator having three degrees of freedom, planar or spatial.

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Parsa, S. S., J. A. Carretero, and R. Boudreau. "Internal redundancy: an approach to improve the dynamic parameters around sharp corners." Mechanical Sciences 4, no. 1 (May 28, 2013): 233–42. http://dx.doi.org/10.5194/ms-4-233-2013.

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Abstract. In recent years, redundancy in parallel manipulators has been studied broadly due to its capability of overcoming some of the drawbacks of parallel manipulators including small workspaces and singular configurations. Internal redundancy, first introduced for serial manipulators, refers to the concept of adding movable masses to some links so as to allow to control the location of the centre of mass and other dynamic properties of some links. This concept has also been referred to as variable geometry. This paper investigates the effects of internal redundancy on the dynamic properties of a planar parallel manipulator while performing a family of trajectories. More specifically, the 3-RRR planar manipulator, where a movable mass has been added to the distal link, is allowed to trace trajectories with rounded corners and different radii. The proposed method uses the manipulator's dynamic model to actively optimise the location of the redundant masses at every point along the trajectory to improve the dynamic performance of the manipulator. Numerical examples are shown to support the idea.

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Arrouk, Khaled Assad, Belhassen Chedli Bouzgarrou, Sergiu Dan Stan, and Grigore Gogu. "CAD Based Design Optimization of Planar Parallel Manipulators." Solid State Phenomena 166-167 (September 2010): 33–38. http://dx.doi.org/10.4028/www.scientific.net/ssp.166-167.33.

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In this paper a new method for determination and optimization of the workspace of parallel manipulators is presented. The proposed method is based on a geometrical approach, and offers the possibility to generate automatically the workspace in a CAD environment. Thus, the relationship between the geometrical design parameters of the parallel manipulator and its workspace can be analyzed without difficulty. Optimization problem considered in this paper consists in determining the dimensions of a parallel manipulator having the closest workspace to a prescribed task region. Finally, numerical applications of two types of planar parallel manipulators are presented in order to illustrate the proposed approach.

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Alıcı, Gürsel, and Bijan Shirinzadeh. "Optimum synthesis of planar parallel manipulators based on kinematic isotropy and force balancing." Robotica 22, no. 1 (January 2004): 97–108. http://dx.doi.org/10.1017/s0263574703005216.

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This paper deals with an optimum synthesis of planar parallel manipulators using two constrained optimisation procedures based on the minimization of: (i) the overall deviation of the condition number of manipulator Jacobian matrix from the ideal/isotropic condition number, and (ii) bearing forces throughout the manipulator workspace for force balancing. A revolute jointed planar parallel manipulator is used as an example to demonstrate the methodology. The parameters describing the manipulator geometry are obtained from the first optimisation procedure, and subsequently, the mass distribution parameters of the manipulator are determined from the second optimisation procedure based on force balancing. Optimisation results indicate that the proposed optimisation approach is systematic, versatile and easy to implement for the optimum synthesis of the parallel manipulator and other kinematic chains. This work contributes to previously published work from the point of view of being a systematic approach to the optimum synthesis of parallel manipulators, which is currently lacking in the literature.

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Dash, Anjan Kumar, Sai Krishnamurthy, Shyam Prasadh, and Vishanth Sundar. "Position Control of a 3-RRR Planar Parallel Manipulator with Non-Planar Links Using External Encoders." Advanced Materials Research 971-973 (June 2014): 1280–83. http://dx.doi.org/10.4028/www.scientific.net/amr.971-973.1280.

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A Planar Parallel Manipulator (PPM) with non-planar links overcomes most of the shortcomings in conventional manipulators. Due to cantilever action, the links of a PPM develop bending stress. When the links are non-planar (having inclination with the horizontal plane), this cantilever action reduces and the same manipulator can have higher payload capacity. In this project, a planar 3-RRR manipulator with non-planar links is investigated for rectifying singularity at home configuration, and a novel method of position feedback of the motor is designed, fabricated and tested with rest of the motion control components.

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Ebrahimi, Iman, Juan A. Carretero, and Roger Boudreau. "Kinematic analysis and path planning of a new kinematically redundant planar parallel manipulator." Robotica 26, no. 3 (May 2008): 405–13. http://dx.doi.org/10.1017/s0263574708004256.

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SUMMARYIn this work, the 3-RPRR, a new kinematically redundant planar parallel manipulator with six-degrees-of-freedom, is presented. First, the manipulator is introduced and its inverse displacement problem discussed. Then, all types of singularities of the 3-RPRR manipulator are analysed and demonstrated. Thereafter, the dexterous workspace is geometrically obtained and compared with the non-redundant 3-PRR planar parallel manipulator. Finally, based on a geometrical measure of proximity to singular configurations and the condition number of the manipulators' Jacobian matrices, actuation schemes for the manipulators are obtained. Different actuation schemes for a given path are obtained and the quality of their actuation schemes are compared. It is shown that the proposed manipulator is capable of following a path while avoiding the singularities.

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Wang, Jinsong, Jun Wu, Tiemin Li, and Xinjun Liu. "Workspace and singularity analysis of a 3-DOF planar parallel manipulator with actuation redundancy." Robotica 27, no. 1 (January 2009): 51–57. http://dx.doi.org/10.1017/s0263574708004517.

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SUMMARYThis paper deals with the position workspace, orientation workspace, and singularity of a 3-degree-of-freedom (DOF) planar parallel manipulator with actuation redundancy, which is created by introducing a redundant link with active actuator to a 3-DOF nonredundant parallel manipulator. Based on the kinematic analysis, the position workspace and orientation workspace of the redundantly actuated parallel manipulator and its corresponding nonredundant parallel manipulator are analyzed, respectively. In the singularity analysis phase, the relationship between the generalized input velocity and the generalized output velocity is researched on the basis of the theory of singular value decomposition. Then a method to investigate the singularity of parallel manipulators is presented, which is used to determine the singularity of the redundantly actuated parallel manipulator. In contrast to the corresponding nonredundant parallel manipulator, the redundant one has larger orientation workspace and less singular configurations. The redundantly actuated parallel manipulator is incorporated into a 4-DOF hybrid machine tool which also includes a feed worktable to demonstrate its applicability.

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Narayanan, Sathya, and Anjan Kumar Dash. "Workspace Analysis and Optimization of 3-RRR Planar Parallel Manipulator." Applied Mechanics and Materials 813-814 (November 2015): 1047–51. http://dx.doi.org/10.4028/www.scientific.net/amm.813-814.1047.

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Predicting shape and finding out exact area of the workspace of 3-DOF planar parallel manipulator having three rotary joints has been a research topic for long time. Optimal design based on such calculations provides a conclusive design methodology. In this work, geometrical method is used o get the exact shape of the workspace and expression of area for the shape obtained. The 3-DOF parallel manipulator is treated as a combination of three independent serial manipulators and its workspace as the common intersection area of these three serial manipulators. The three workspaces are then translated by length equal to radius of the end effecter and the common intersection area is obtained as the workspace of the parallel manipulator under study. The area is determined using the mathematical expression for the shape obtained. Based on direct search algorithm, a methodology is developed to optimize the area. Thus, following, this methodology, an user with specification of area of the workspace can be provided with an optimized parallel manipulator taking into account the inventory of link lengths and the cost of the links.

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Wang, Bing, and Wei Na Han. "Performance Atlases of Global Conditioning Index of Planar 3-DOF Parallel Manipulator with Actuation Redundancy." Advanced Materials Research 479-481 (February 2012): 2316–20. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.2316.

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This paper takes a new kind of planar 3-DOF parallel manipulator with actuation redundancy as the object of study. We utilize a design space to obtain the relationship between the link lengths of planar 3-DOF paralel manipulator with actuation redundancy and performance criteria based on the global conditioning index. The corresponding performance atlases has been plotted, the atlases are an important base of reference for the mechanism design of this parallel manipulator.

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Gosselin, C. M. "Parallel Computational Algorithms for the Kinematics and Dynamics of Planar and Spatial Parallel Manipulators." Journal of Dynamic Systems, Measurement, and Control 118, no. 1 (March 1, 1996): 22–28. http://dx.doi.org/10.1115/1.2801147.

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This paper introduces a novel approach for the computation of the inverse dynamics of parallel manipulators. It is shown that, for this type of manipulator, the inverse kinematics and the inverse dynamics procedures can be easily parallelized. The result is a closed-form efficient algorithm using n processors, where n is the number of kinematic chains connecting the base to the end-effector. The dynamics computations are based on the Newton-Euler formalism. The parallel algorithm arises from a judicious choice of the coordinate frames attached to each of the legs, which allows the exploitation of the parallel nature of the mechanism itself. Examples of the application of the algorithm to a planar three-degree-of-freedom parallel manipulator and to a spatial six-degree-of-freedom parallel manipulator are presented.

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Kong, Xianwen, and Cle´ment M. Gosselin. "Generation and Forward Displacement Analysis of RP_R-PR-RP_R Analytic Planar Parallel Manipulators." Journal of Mechanical Design 124, no. 2 (May 16, 2002): 294–300. http://dx.doi.org/10.1115/1.1468224.

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Analytic manipulators are manipulators for which a characteristic polynomial of fourth degree or lower can be obtained symbolically. Six types of RP_R-PR-RP_R analytic planar parallel manipulators (APPMs) are first generated using the component approach and the method based on the structure of the univariate equation. Of the six types, four are composed of Assur II kinematic chains while the other two are composed of Assur III kinematic chains. The forward displacement analysis (FDA) of two types of RP_R-PR-RP_R APPMs composed of Assur III kinematic chains is then performed. The FDA of each of the two types of APPMs composed of Assur III kinematic chains is reduced to the solution of a univariate cubic equation and a quadratic equation in sequence. It is also proven that the maximum number of real solutions to the FDA is 4 for the RP_R-PR-RP_R planar parallel manipulator with one aligned platform and one orthogonal platform. Examples with 4 real solutions for the RP_R-PR-RP_R planar parallel manipulator with one aligned platform and one orthogonal platform or 6 real solutions for the RP_R-PR-RP_R planar parallel manipulator with two aligned platforms are given at the end of this paper.

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Boudreau, Roger, Scott Nokleby, and Marise Gallant. "Wrench Capabilities of a Kinematically Redundant Planar Parallel Manipulator." Robotica 39, no. 9 (January 26, 2021): 1601–16. http://dx.doi.org/10.1017/s0263574720001381.

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SUMMARYThis paper presents a methodology to obtain the wrench capabilities of a kinematically redundant planar parallel manipulator using a wrench polytope approach. A methodology proposed by others for non-redundant and actuation-redundant manipulators is adapted to a kinematically redundant manipulator. Four wrench capabilities are examined: a pure force analysis, the maximum force for a prescribed moment, the maximum reachable force, and the maximum moment with a prescribed force. The proposed methodology, which finds the exact explicit solution for three of the four wrench capabilities, does not use optimization and is very efficient.

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Daniali, H. R. Mohammadi. "Instantaneous Center of Rotation and Singularities of Planar Parallel Manipulators." International Journal of Mechanical Engineering Education 33, no. 3 (July 2005): 251–59. http://dx.doi.org/10.7227/ijmee.33.3.7.

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With regard to planar parallel manipulators, a general classification of singularities into three groups is given. The classification scheme relies on the properties of instantaneous centers of rotation. This method is very fast and can easily be applied to the manipulators under study. The method is applied to a planar three-degrees-of-freedom parallel manipulator and all its singular configurations are found.

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Ganesh, M., Banke Bihari, Vijay Singh Rathore, Dhiraj Kumar, Chandan Kumar, Apelagunta Ramya Sree, Karanam Naga Sowmya, and Anjan Kumar Dash. "Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators." Robotica 35, no. 10 (October 5, 2016): 2056–75. http://dx.doi.org/10.1017/s0263574716000710.

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SUMMARYOptimization is an important step in the design and development of a planar parallel manipulator. For optimization processes, workspace analysis is a crucial and preliminary objective. Generally, the workspace analysis for such manipulators is carried out using a non-dimensional approach. For planar parallel manipulators of two degrees of freedom (2-DOF), a non-dimensional workspace analysis is very advantageous. However, it becomes very difficult in the case of 3-DOF and higher DOF manipulators because of the complex shape of the workspace. In this study, the workspace shape is classified as a function of the geometric parameters, and the closed-form area expressions are derived for a constant orientation workspace of a three revolute–revolute–revolute (3-RRR) planar manipulator. The approach is also shown to be feasible for different orientations of a mobile platform. An optimization procedure for the design of planar 3-RRR manipulators is proposed for a prescribed workspace area. It is observed that the closed-form area expression for all the possible shapes of the workspace provides a larger solution space, which is further optimized considering singularity, mass of the manipulator, and a force transmission index.

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Wu, Xiaoyong. "Performance Analysis and Optimum Design of a Redundant Planar Parallel Manipulator." Symmetry 11, no. 7 (July 12, 2019): 908. http://dx.doi.org/10.3390/sym11070908.

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This work presents a comprehensive performance evaluation and optimum design of a novel symmetrical 4-PPR (P indicates the prismatic joint, R denotes the revolute joint, and the letter with underline represents an active joint) redundant planar parallel manipulator. The kinematic model is established, upon which the inverse position and singularity are analyzed. Based on the evaluation of dexterity, velocity, and stiffness performance, the optimum region is achieved. With the optical design parameters, a case study for the analysis of dynamic behavior is conducted. Performance comparison between the redundant manipulator and another two non-redundant 3-PPR planar parallel manipulators, one with a Δ-shape symmetrical structure and the other with U-shape symmetrical structure, is presented. Simulation results reveal that the U-shape manipulator has the greatest velocity performance. Moreover, the redundant manipulator possesses the best dexterity, stiffness, and dynamic performance.

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Varalakshmi, K. V., and J. Srinivas. "Optimum Design of Kinematically Redundant Planar Parallel Manipulator Following a Trajectory." International Journal of Materials, Mechanics and Manufacturing 3, no. 2 (2015): 74–79. http://dx.doi.org/10.7763/ijmmm.2015.v3.170.

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Ricard, Re´mi, and Cle´ment M. Gosselin. "On the Determination of the Workspace of Complex Planar Robotic Manipulators." Journal of Mechanical Design 120, no. 2 (June 1, 1998): 269–78. http://dx.doi.org/10.1115/1.2826968.

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A new method for the determination of the workspace of complex planar robotic manipulators is described in this paper. The method is based on the use of joint limits to obtain equations describing limiting curves. These limiting curves are then segmented at their mutual intersections and validated. The resulting sets of portions of curves form the envelope of the workspace. The algorithm is completely general and can be applied to any three-degree-of-freedom planar manipulator—serial, parallel or hybrid—with or without joint limits. Examples of the application of the method to a serial three-degree-of-freedom manipulator, to a hybrid three-degree-of-freedom manipulator and to a parallel three-degree-of-freedom manipulator are given.

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Alıcı, Gürsel. "Determination of singularity contours for five-bar planar parallel manipulators." Robotica 18, no. 5 (September 2000): 569–75. http://dx.doi.org/10.1017/s0263574700002733.

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From a design point of view, it is crucial to predict singular configurations of a manipulator in terms of inputs in order to improve the dexterity and workspace of a manipulator. In this paper, we present a simple, yet a systematic appoach to obtain singularity contours for a class of five-bar planar parallel manipulators which are based on five rigid links and five single degree of freedom joints – revolute and prismatic joints. The determinants of the manipulator Jacobian matrices are evaluated in terms of joint inputs for a specified set of geometric parameters, and the contours of the determinants at 0.0 plane which are the singularity contours in joint space are generated for the three types of singularities reported in the literature. The proposed approach/algorithm is simple and systematic, and the resulting equations are easy to solve on a computer. The singularity contours for all the class are presented in order to demonstrate the method. It is concluded that the proposed method is useful in trajectory planning and design of five-bar planar parallel manipulators in order to improve their dexterity and workspace.

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Sundar, Syam, Vijay S. Rathore, Manoj K. Sahi, V. Upendran, and Anjan Kumar Dash. "Workspace Analysis and Going through Singularities of 5-Bar Symmetric Planar Parallel Manipulator by Automated Selective Actuation Mechanism." Advanced Materials Research 588-589 (November 2012): 1664–68. http://dx.doi.org/10.4028/www.scientific.net/amr.588-589.1664.

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In this article‚ a new approach is presented to determine the various shapes of workspaces of 5 bar symmetric planar parallel manipulators. Here the shape of the workspace is determined by the number of ways the workspaces of the two serial manipulators intersect with each other. Geometric conditions are established in each case and area of each shape of workspace is determined in closed form. Singularity is another important consideration in the design of parallel manipulators. In this paper, an approach is presented to go through the singularity points using an automatic selective actuation mechanism. A prototype 5-bar planar manipulator is fabricated along with an automatic selective actuation mechanism demonstrating the manipulator going through the singularity points.

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Wang, L.-P., J.-S. Wang, Y.-W. Li, and Y. Lu. "Kinematic and dynamic equations of a planar parallel manipulator." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 217, no. 5 (May 1, 2003): 525–31. http://dx.doi.org/10.1243/095440603765226812.

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This paper presents an inverse dynamic formulation using the Newton-Euler approach for a planar parallel manipulator, which is used in a new five-axis hybrid machine tool. The inverse kinematics of the manipulator is given and the velocity and the acceleration formulae are derived. The driving forces acting on the legs are determined according to the dynamic formulation. The formulation has been implemented in a program and has been used for some typical trajectories planned for a numerical simulation experiment. The simulation results reveal the nature of the variation of the driving forces in the hybrid machine tool and justify the dynamic control model. The dynamic modelling approach presented in this paper can also be applied to other parallel manipulators with less than six degrees of freedom.

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Zarkandi, Soheil. "Acceleration Analysis of 3-DOF Planar Parallel Manipulators by Means of Screw Theory." Journal of Mechanical Engineering 45, no. 2 (July 28, 2016): 89–95. http://dx.doi.org/10.3329/jme.v45i2.28207.

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This paper deals with the second order kinematics of three degree-of-freedom (DOF) planar parallel manipulators. The simple and compact expressions are derived for both the inverse and forward acceleration analyses using screw theory. Moreover, as an example, a 3-DOF planar parallel manipulator is introduced and its kinematics is analyzed using the proposed method.

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McColl, Derek, and Leila Notash. "Workspace formulation of planar wire-actuated parallel manipulators." Robotica 29, no. 4 (August 19, 2010): 607–17. http://dx.doi.org/10.1017/s0263574710000469.

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SUMMARYIn this paper, a generalized form of the antipodal method from multi-finger grasping is presented and implemented for investigating the workspace of a wide range of planar wire-actuated parallel manipulators. Manipulators with distinct wire attachment points on the base and mobile platform are considered, in the absence and presence of external force. The examined workspaces are verified with the corresponding workspaces developed using static force analysis. By applying an external force, modeled as a wire for the antipodal method, the characteristics of the manipulator could be altered by enlarging its workspace in the direction of the applied force.

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Wu, Jun, Tiemin Li, and Boqiang Xu. "Force optimization of planar 2-DOF parallel manipulators with actuation redundancy considering deformation." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 6 (September 12, 2012): 1371–77. http://dx.doi.org/10.1177/0954406212458055.

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Internal force distribution is one of the most important issues for redundantly actuated parallel manipulators. This article presents a novel method for optimizing internal force to minimize the deformation of key components in a parallel manipulator. The dynamic model is first derived, and then an objective function is proposed by giving different weights on internal forces of different components based on its flexibility. The deformation of the component with big flexibility is minimized. A planar 2-DOF parallel manipulator with actuation redundancy is taken as an example to validate the force optimization method. The simulation results show that the deformation of the manipulator with the force optimization method proposed in this article is smaller than that with the traditional method to minimize the norm of driving forces. Thus, the manipulator precision can be improved.

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Fisher, R., R. P. Podhorodeski, and S. B. Nokleby. "Design of a reconfigurable planar parallel manipulator." Journal of Robotic Systems 21, no. 12 (2004): 665–75. http://dx.doi.org/10.1002/rob.20043.

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Kevin Jui, C. K., and Qiao Sun. "Path Tracking of Parallel Manipulators in the Presence of Force Singularity." Journal of Dynamic Systems, Measurement, and Control 127, no. 4 (January 17, 2005): 550–63. http://dx.doi.org/10.1115/1.2098893.

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Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

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Sun, Hui Hui, Bin Zi, and Sen Qian. "Modeling and Control of Winding Hybrid-Driven Based Cable-Parallel Manipulator." Applied Mechanics and Materials 373-375 (August 2013): 111–15. http://dx.doi.org/10.4028/www.scientific.net/amm.373-375.111.

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This paper deals with modeling and adaptive fuzzy control of winding hybrid-driven cable parallel manipulator (WHDCPM). The WHDCPM has the advantages of both the traditional cable-parallel manipulator (CPM) and hybrid-driven based cable-parallel manipulator (HDCPM) since the hybrid-driven planar five-bar mechanism in HDCPM is replaced by winding hybrid-driven five-bar manipulator in WHDCPM. The physical architecture of WHDCPM is determined, and kinematics and dynamics of the cable parallel manipulators have been studied based on Lagrange method. The numerical simulation is demonstrated as an example with adaptive fuzzy control theory, and the diagrams of trajectory tracking, cable tension, friction compensation and motor torque are shown, respectively. The results demonstrate the feasibility and superiority of the WHDCPM.

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Kang, Bongsoo, and James K. Mills. "Dynamic modeling of structurally-flexible planar parallel manipulator." Robotica 20, no. 3 (May 2002): 329–39. http://dx.doi.org/10.1017/s0263574701004039.

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This paper presents a dynamic model of a planar parallel manipulator including structural flexibility of several linkages. The equations of motion are formulated using the Lagrangian equations of the first type and Lagrangian multipliers are introduced to represent the geometry of multiple closed loop chains. Then, an active damping approach using a PZT actuator is described to attenuate structural vibration of the linkages. Overall dynamic behavior of the manipulator, induced from structural flexibility of the linkage, is well illustrated through simulations. This analysis will be used to develop a prototype parallel manipulator.

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Zhu, Xiao Rong, and Hui Ping Shen. "Performance Evaluation of a 2-DOF Planar Parallel Manipulator." Applied Mechanics and Materials 121-126 (October 2011): 2829–33. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.2829.

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In this paper, a 2-DOF planar parallel manipulator actuated horizontally by linear actuators is proposed. The inverse and forward kinematics can be described in closed form. The velocity equation, singularity of the manipulator and the conditioning index is investigated. In addition, the inverse dynamics problem of the device is investigated employing the Lagrange approach. The dynamic simulation is carried out. The results show that the kinematics performance and the force transmissibility are worse when the end-effecter moves near the singularity. The proposed manipulator can be applied to the field of machine tools or used as the mobile base for a spatial manipulator. The results of the paper are very useful for the design and application of the new manipulator.

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Zhang, Xinglei, Binghui Fan, Chuanjiang Wang, and Xiaolin Cheng. "Analysis of Singular Configuration of Robotic Manipulators." Electronics 10, no. 18 (September 7, 2021): 2189. http://dx.doi.org/10.3390/electronics10182189.

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Robotic manipulators inevitably encounter singular configurations in the process of movement, which seriously affects their performance. Therefore, the identification of singular configurations is extremely important. However, serial manipulators that do not meet the Pieper criterion cannot obtain singular configurations through analytical methods. A joint angle parameterization method, used to obtain singular configurations, is here creatively proposed. First, an analytical method based on the Jacobian determinant and the proposed method were utilized to obtain their respective singular configurations of the Stanford manipulator. The singular configurations obtained through the two methods were consistent, which suggests that the proposed method can obtain singular configurations correctly. Then, the proposed method was applied to a seven-degree-of-freedom (7-DOF) serial manipulator and a planar 5R parallel manipulator. Finally, the correctness of the singular configurations of the 7-DOF serial manipulator was verified through the shape of the end-effector velocity ellipsoid, the value of the determinant, the value of the condition number, and the value of the manipulability measure. The correctness of singular configurations of the planar 5R parallel manipulator was verified through the value of the determinant, the value of the condition number, and the value of the manipulability measure.

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Firmani, Flavio, and Ron P. Podhorodeski. "FORCE-UNCONSTRAINED POSES FOR PARALLEL MANIPULATORS WITH REDUNDANT ACTUATED BRANCHES." Transactions of the Canadian Society for Mechanical Engineering 29, no. 3 (September 2005): 343–56. http://dx.doi.org/10.1139/tcsme-2005-0021.

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A study of the effect of including a redundant actuated branch on the existence of force-unconstrained configurations for a planar parallel layout of joints is presented1. Two methodologies for finding the force-unconstrained poses are described and discussed. The first method involves the differentiation of the nonlinear kinematic constraints of the input and output variables with respect to time. The second method makes use of the reciprocal screws associated with the actuated joints. The force-unconstrained poses of non-redundantly actuated planar parallel manipulators can be mathematically expressed by means of a polynomial in terms of the three variables that define the dimensional space of the planar manipulator, i.e., the location and orientation of the end-effector. The inclusion of redundant actuated branches leads to a system of polynomials, i.e., one additional polynomial for each redundant branch added. Elimination methods are employed to reduce the number of variables by one for every additional polynomial. This leads to a higher order polynomial with fewer variables. The roots of the resulting polynomial describe the force-unconstrained poses of the manipulator. For planar manipulators it is shown that one order of infinity of force-unconstrained configurations is eliminated for every actuated branch, beyond three, added. As an example, the four-branch revolute-prismatic-revolute mechanism (4-RPR), where the prismatic joints are actuated, is presented.

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McCloy, D. "Some comparisons of serial-driven and parallel-driven manipulators." Robotica 8, no. 4 (October 1990): 355–62. http://dx.doi.org/10.1017/s0263574700000485.

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SUMMARYA two-dimensional serial-driven manipulator is compared with two different parallel-driven manipulators, using workspace, power requirements and stiffness as criteria. The parallel-driven devices are based on the planar five-bar linkage; one has four revolute joints and one prismatic joint; the other has five revolute joints. Parallel operation is shown to offer advantages.

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Behzadipour, Saeed, and Amir Khajepour. "Stiffness of Cable-based Parallel Manipulators With Application to Stability Analysis." Journal of Mechanical Design 128, no. 1 (April 28, 2005): 303–10. http://dx.doi.org/10.1115/1.2114890.

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The stiffness of cable-based robots is studied in this paper. Since antagonistic forces are essential for the operation of cable-based manipulators, their effects on the stiffness should be considered in the design, control, and trajectory planning of these manipulators. This paper studies this issue and derives the conditions under which a cable-based manipulator may become unstable because of the antagonistic forces. For this purpose, a new approach is introduced to calculate the total stiffness matrix. This approach shows that, for a cable-based manipulator with all cables in tension, the root of instability is a rotational stiffness caused by the internal cable forces. A set of sufficient conditions are derived to ensure the manipulator is stabilizable meaning that it never becomes unstable upon increasing the antagonistic forces. Stabilizability of a planar cable-based manipulator is studied as an example to illustrate this approach.

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Murray, Andrew P., François Pierrot, Pierre Dauchez, and J. Michael McCarthy. "A planar quaternion approach to the kinematic synthesis of a parallel manipulator." Robotica 15, no. 4 (July 1997): 361–65. http://dx.doi.org/10.1017/s0263574797000441.

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In this paper we present a technique for designing planar parallel manipulators with platforms capable of reaching any number of desired poses. The manipulator consists of a platform connected to ground by RPR chains. The set of positions and orientations available to the end-effector of a general RPR chain is mapped into the space of planar quaternions to obtain a quadratic manifold. The coefficients of this constraint manifold are functions of the locations of the base and platform R joints and the distance between them. Evaluating the constraint manifold at each desired pose and defining the limits on the extension of the P joint yields a set of equations. Solutions of these equations determine chains that contain the desired poses as part of their workspaces. Parallel manipulators that can reach the prescribed workspace are assembled from these chains. An example shows the determination of three RPR chains that form a manipulator able to reach a prescribed workspace.

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Alici, G., and B. Shirinzadeh. "Optimum force balancing of a planar parallel manipulator." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 217, no. 5 (May 1, 2003): 515–24. http://dx.doi.org/10.1243/095440603765226803.

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This paper focuses on optimum force balancing of a planar parallel manipulator, articulated with revolute joints, with a combination of a proper distribution of link masses and two springs connected to the driving links. After conducting the static force analysis of the mechanism, the force balancing is formulated as an optimization problem such that a mean-square root of the sum-squared values of bearing and spring forces is minimized throughout an operation range of the manipulator, provided that a set of balancing constraints consisting of balancing conditions and the sizes of some inertial and geometric parameters are satisfied. The minimization of bearing forces and spring forces adds to the life of bearings and springs, transmits less shaking force and moment to the ground, decreases wear in the mechanism components and consequently reduces the actuation burden on the actuators when the manipulator is in motion. Optimization results indicate that the proposed optimization approach is systematic, versatile and easy to implement for the optimal balancing of the parallel manipulator and other kinematic chains.

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Si, Guoning, Mengqiu Chu, Zhuo Zhang, Haijie Li, and Xuping Zhang. "Integrating Dynamics into Design and Motion Optimization of a 3-PRR Planar Parallel Manipulator with Discrete Time Transfer Matrix Method." Mathematical Problems in Engineering 2020 (May 12, 2020): 1–23. http://dx.doi.org/10.1155/2020/2761508.

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This paper presents a novel method of dynamic modeling and design optimization integrated with dynamics for parallel robot manipulators. Firstly, a computationally efficient modeling method, the discrete time transfer matrix method (DT-TMM), is proposed to establish the dynamic model of a 3-PRR planar parallel manipulator (PPM) for the first time. The numerical simulations are performed with both the proposed DT-TMM dynamic modeling and the ADAMS modeling. The applicability and effectiveness of DT-TMM in parallel manipulators are verified by comparing the numerical results. Secondly, the design parameters of the 3-PRR parallel manipulator are optimized using the kinematic performance indices, such as global workspace conditioning index (GWCI), global condition index (GCI), and global gradient index (GGI). Finally, a dynamic performance index, namely, driving force index (DFI), is proposed based on the established dynamic model. The described motion trajectory of the moving platform is placed into the optimized workspace and the initial position is determined to finalize the end-effector trajectory of the parallel manipulator by the further optimization with the integrated kinematic and dynamic performance indices. The novelty of this work includes (1) developing a new dynamic model method with high computation efficiency for parallel robot manipulators using DT-TMM and (2) proposing a new dynamic performance index and integrating the dynamic index into the motion and design optimization of parallel robot manipulators.

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Ganesh, M., Anjan Kumar Dash, P. Venkitachalam, and S. Shrinithi. "Static Characteristic Analysis of Spatial (Non-Planar) Links in Planar Parallel Manipulator." Robotica 39, no. 1 (May 6, 2020): 88–106. http://dx.doi.org/10.1017/s026357472000020x.

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SUMMARYConventional planar manipulators have their links in a single plane. Increasing payload at the end effector/mobile platform can induce high stress in the links due to the cantilever nature of links. Thus, it limits the total vertical load that can be applied on the mobile platform. In contrast to the links in conventional planar parallel mechanisms, non-planar links are proposed in this paper, that is, links are made inclined to the horizontal plane and non-planar legs are constructed. Though the links are made non-planar, the end effectors’ planar motion is retained. For studying the application of such non-planar links in planar manipulators, new models of inertia, stiffness and leg dynamics have to be developed. In this article, these models are developed by the static analysis of the planar manipulators with non-planar links, and the performance is compared with the corresponding conventional planar manipulators.

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Chen, Genliang, Lingyu Kong, Qinchuan Li, and Hao Wang. "A Simple Two-step Geometric Approach for the Kinematic Calibration of the 3-PRS Parallel Manipulator." Robotica 37, no. 5 (January 14, 2019): 837–50. http://dx.doi.org/10.1017/s0263574718001352.

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SummaryKinematic calibration plays an important role in the improvement of positioning accuracy for parallel manipulators. Based on the specific geometric constraints of limbs, this paper presents a new kinematic parameter identification method for the widely studied 3-PRS parallel manipulator. In the proposed calibration method, the planes where the PRS limbs exactly located are identified firstly as the geometric characteristics of the studied parallel manipulator. Then, the limbs can be considered as planar PR mechanisms whose kinematic parameters can be determined conveniently according to the limb planes identified in the first step. The main merit of the proposed calibration method is that the system error model which relates the manipulator’s kinematic errors to the output ones is not required for kinematic parameter identification. Instead, only two simple geometric problems need to be established for identification, which can be solved readily using gradient-based searching algorithms. Hence, another advantage of the proposed method is that parameter identification of the manipulator’s limbs can be accomplished individually without interactive impact on each other. In order to validate the effectiveness and efficiency of the proposed method, calibration experiments are conducted on an apparatus of the studied 3-PRS parallel manipulator. The results show that using the proposed two-step calibration method, the kinematic parameters can be identified quickly by means of gradient searching algorithm (converge within five iterations for both steps). The positioning accuracy of the studied 3-PRS parallel manipulator has been significantly improved by compensation according to the identified parameters. The mean position and orientation errors at the validation configurations have been reduced to 1.56 × 10−4 m and 1.13 × 10−3 rad, respectively. Further, the proposed two-step kinematic calibration method can be extended to other limited-degree-of-freedom parallel manipulators, if proper geometric constraints can be characterized for their kinematic limbs.

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Wang, Bing, and Zhi Hui Wei. "Analysis on Velocity Performance of Planar 3-DOF Parallel Manipulator with Actuation Redundancy." Advanced Materials Research 479-481 (February 2012): 2327–32. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.2327.

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In this paper, the design space is utilized to obtain the analytical relationship between the link lengths of planar 3-DOF paralel manipulator with actuation redundancy and performance criteria based on the global velocity index. The corresponding performance atlases has been plotted, the atlases are an important base of reference for the mechanism design of this parallel manipulator.

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Zarkandi, Soheil. "Kinematics of a star-triangle planar parallel manipulator." Journal of Mechanical Science and Technology 25, S1 (December 2011): 3223–30. http://dx.doi.org/10.1007/s12206-011-0931-9.

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Sánchez-Alonso, Róger E., José-Joel González-Barbosa, Eduardo Castillo-Castaneda, and Jaime Gallardo-Alvarado. "Kinematic analysis of a novel 2(3-RUS) parallel manipulator." Robotica 34, no. 10 (January 20, 2015): 2241–56. http://dx.doi.org/10.1017/s0263574714002860.

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SUMMARYThis paper introduces a novel 6-DOF parallel manipulator, which is composed of two 3-RUS parallel manipulators that share a common three-dimensional moving platform. Semi-analytical form solutions are easily obtained to solve the forward displacement analysis of the robot using the non-planar geometry of the moving platform, whereas the velocity, acceleration, and singularity analyses are performed using screw theory. A case study is included to show the application of the kinematic model, which is verified with the aid of a commercially available software. Simple kinematic analysis and reduced singular regions are the main benefits of the proposed parallel manipulator.

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Firmani, Flavio, Alp Zibil, Scott B. Nokleby, and Ron P. Podhorodeski. "FORCE-MOMENT CAPABILITIES OF REVOLUTE-JOINTED PLANAR PARALLEL MANIPULATORS WITH ADDITIONAL ACTUATED BRANCHES." Transactions of the Canadian Society for Mechanical Engineering 31, no. 4 (December 2007): 469–81. http://dx.doi.org/10.1139/tcsme-2007-0034.

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The force-moment capabilities of revolute-jointed planar parallel manipulators (PPMs) are presented. A previously developed analysis that determines explicitly the force-moment capabilities of parallel manipulators is considered and the formulation is improved. This analysis is based upon properly adjusting the actuator outputs to their maximum capabilities. The force-moment capabilities of two actuation layouts are investigated: the non-redundant 3-RRR PPM and the redundantly actuated 4-RRR PPM, where the underline indicates the actuated joint. Four studies of force-moment capabilities are presented: maximum force with a prescribed moment, maximum applicable force, maximum moment with a prescribed force, and maximum applicable moment. These studies are performed for constant payload orientation of the mobile platform throughout the manipulator’s workspace. It is concluded that the manipulator with the additional actuated branch shows an improvement of the force-moment capabilities at the expense of reducing its workspace.

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Saafi, Houssem, and Houssein Lamine. "Comparative Kinematic Analysis and Design Optimization of Redundant and Nonredundant Planar Parallel Manipulators Intended for Haptic Use." Robotica 38, no. 8 (November 5, 2019): 1463–77. http://dx.doi.org/10.1017/s0263574719001577.

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SUMMARYThis paper investigates a comparative kinematic analysis between nonredundant and redundant 2-Degree Of Freedom parallel manipulators. The nonredundant manipulator is based on the Five-Bar mechanism, and the redundant one is a 3-RRR planar parallel manipulator. This study is aimed to select the best structure for a haptic application. This latter requires a mechanism with a desired workspace of 10 cm × 10 cm and an admissible force of 5 N in all directions. The analysis criteria are the accuracy of the forward kinematic model and the required actuator torques. Thereby, the geometric parameters of the two structures are optimized in order to satisfy the required workspace such that parallel singularities are overcome. The analysis showed that the nonredundant optimally designed manipulator is more suitable for the haptic application.

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Khan, Waseem A., Venkat N. Krovi, Subir K. Saha, and Jorge Angeles. "Recursive Kinematics and Inverse Dynamics for a Planar 3R Parallel Manipulator." Journal of Dynamic Systems, Measurement, and Control 127, no. 4 (November 30, 2004): 529–36. http://dx.doi.org/10.1115/1.2098890.

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We focus on the development of modular and recursive formulations for the inverse dynamics of parallel architecture manipulators in this paper. The modular formulation of mathematical models is attractive especially when existing sub-models may be assembled to create different topologies, e.g., cooperative robotic systems. Recursive algorithms are desirable from the viewpoint of simplicity and uniformity of computation. However, the prominent features of parallel architecture manipulators-the multiple closed kinematic loops, varying locations of actuation together with mixtures of active and passive joints-have traditionally hindered the formulation of modular and recursive algorithms. In this paper, the concept of the decoupled natural orthogonal complement (DeNOC) is combined with the spatial parallelism of the robots of interest to develop an inverse dynamics algorithm which is both recursive and modular. The various formulation stages in this process are highlighted using the illustrative example of a 3R Planar Parallel Manipulator.

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Ganesh, M., R. Karthikeyan, Anjan Kumar Dash, M. Vikramadityan, and R. Gopalachary. "Kineto Static Design and Stiffness Analysis of a New Kind of 3-RRR Planar Parallel Manipulator." Applied Mechanics and Materials 592-594 (July 2014): 2303–7. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.2303.

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This paper presents a new design of a 3-RRR planar manipulator with non-planar legs. In contrast to the conventional 3-RRR planar parallel mechanism, the links are not planar. They are elevated above the X-Y plane and non planar legs are constructed. The kinematics of this model is realized on a common projected plane and traced back to its elevated position. The moment of inertia for the inclined links is computed. A stiffness model is established for the proposed design of 3-RRR manipulator and compared with a conventional 3-RRR planar manipulator. The analysis shows how the proposed design has better stiffness along all the three directions of motion.

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Assal, Samy F. M. "A novel planar parallel manipulator with high orientation capability for a hybrid machine tool: kinematics, dimensional synthesis and performance evaluation." Robotica 35, no. 5 (November 20, 2015): 1031–53. http://dx.doi.org/10.1017/s0263574715000958.

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SUMMARYIn order to potentially realize the advantages of planar parallel manipulators to be used for hybrid machine tools, the inherently abundant singularities which diminish the usable workspace must be eliminated. Proper structure synthesis and dimensional synthesis can provide a good solution. So, a non-conventional architecture of a three-PPR planar parallel manipulator is proposed in this paper for a hybrid machine tool. The proposed architecture permits a large dexterous workspace with unlimited orientation capability and no singularities. It also provides partially decoupled motion which permits independent actuators control. The kinematic, singularity, orientation capability and workspace analyses of the proposed manipulator are studied to verify those advantages. Based on a non-dimensional design parameter space, the highly important indices for this application namely the workspace index (WI), the motion/force transmission index, the kinematic and dynamic dexterity indices and the stiffness index are selected to be maximized yielding proper dimensions of the design parameters. Those performance indices are proven to be uniform over all the workspace achieving highly important characteristics of uniform accuracy, acceleration characteristics, rigidity and force transmissibility. Performance evaluation is finally presented to verify the high performance of the proposed non-singular planar parallel manipulator with high orientation capability.

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Gallant, Marise, and Clément Gosselin. "Singularities of a planar 3-RPR parallel manipulator with joint clearance." Robotica 36, no. 7 (April 2, 2018): 1098–109. http://dx.doi.org/10.1017/s0263574718000279.

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SUMMARYIf the joint clearances of the joints of a manipulator are considered, an unconstrained motion of the end-effector can be computed. This is true for all poses of the manipulator, even with all actuators locked.This paper presents how this unconstrained motion can be determined for a planar 3-RPR manipulator. The singularities are then studied. It is shown that when clearances are considered, the singularity curves normally found in the workspace of such a manipulator become singular zones. These zones can be significant and greatly reduce the usable workspace of a manipulator. Since a prescribed configuration that would not, in theory, corresponds to a singular pose can become singular due to the unconstrained motion, the results of this paper are relevant to manipulator design and trajectory planning.

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Wen, Kefei, TaeWon Seo, and Jeh Won Lee. "A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra." Robotica 35, no. 3 (August 17, 2015): 511–20. http://dx.doi.org/10.1017/s0263574715000661.

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SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

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Zhu, Xiao Rong, Yi Lu, and Hui Ping Shen. "Optimal Design of a Planar Five-Bar Parallel Manipulator Driven by Two Orthogonal Layout Actuators." Advanced Materials Research 490-495 (March 2012): 2681–85. http://dx.doi.org/10.4028/www.scientific.net/amr.490-495.2681.

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This paper addresses geometry design of a new kind of 2-DOF five-bar parallel manipulator actuated by two orthogonal layout linear actuators. Although the manipulator has only one geometric parameter, i.e., the link length, the distribution of performance index is more complex. Here, we propose a design approach utilizing a performance chart and local condition index. The key problem in the design of the manipulator is the determination of not the link length but the workspace satisfying the design index. This paper gives an effective method to obtain the basic good-condition workspace without dimension. Then, based on the optimum non-dimensional result, the optimum dimensional parameters are achieved which is suitable for the desired workspace. The optimum methodology of this paper is convenient and can be extended to other parallel manipulators

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Gallardo-Alvarado, Jaime, and Jesus H. Tinajero-Campos. "A Parallel Manipulator with Planar Configurable Platform and Three End-Effectors." Mathematical Problems in Engineering 2019 (September 25, 2019): 1–12. http://dx.doi.org/10.1155/2019/7972837.

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This work reports on the kinematic analysis of a planar parallel manipulator endowed with a configurable platform assembled with six terminal links serially connected by means of revolute joints. This topology allows the robot manipulator to dispose of three relative degrees of freedom owing to the mobility of an internal closed-loop chain. Therefore, the proposed robot manipulator can admit three end-effectors. The forward displacement analysis of the configurable planar parallel manipulator is easily achieved based on unknown coordinates denoting the pose of each terminal link. Thereafter, the analysis leads to twelve quadratic equations which are numerically solved by means of the Newton homotopy method. Furthermore, a closed-form solution is available for the inverse position analysis. On the contrary, the instantaneous kinematics of the robot manipulator is investigated by means of the theory of screws. Numerical examples are included with the purpose to illustrate the method of kinematic analysis.

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Journal articles on the topic 'Planar Parallel Manipulator'

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