Journal articles: 'Linear manipulator'

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Kumar, Manoj. "A Non-Linear Stiffness Model for Serial and Parallel Manipulators." International Journal of Robotics Applications and Technologies 5, no. 1 (January 2017): 34–62. http://dx.doi.org/10.4018/ijrat.2017010103.

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The paper presents a methodology to enhance the stiffness analysis of serial and parallel manipulators with passive joints. It directly takes into account the loading influence on the manipulator configuration and, consequently, on its Jacobians and Hessians. The main contributions of this paper are the introduction of a non-linear stiffness model for the manipulators with passive joints, a relevant numerical technique for its linearization and computing of the Cartesian stiffness matrix which allows rank-deficiency. Within the developed technique, the manipulator elements are presented as pseudo-rigid bodies separated by multidimensional virtual springs and perfect passive joints. Simulation examples are presented that deal with parallel manipulators of the Ortholide family and demonstrate the ability of the developed methodology to describe non-linear behaviour of the manipulator structure such as a sudden change of the elastic instability properties (buckling).

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Wolf, A., and M. Shoham. "Investigation of Parallel Manipulators Using Linear Complex Approximation." Journal of Mechanical Design 125, no. 3 (September 1, 2003): 564–72. http://dx.doi.org/10.1115/1.1582876.

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This investigation deals with singularity analysis of parallel manipulators and their instantaneous behavior while in or close to a singular configuration. The method presented utilizes line geometry tools and screw theory to describe a manipulator in a given position. Then, this description is used to obtain the closest linear complex, presented by its screw coordinates, to the set of governing lines of the manipulator. The linear complex axis and pitch provide additional information and a better physical understanding of the type of singularity and the motion the manipulator tends to perform in a singular point and in its neighborhood. Examples of Hunt’s, Fichter’s and 3-UPU singularities, along with a few selected examples taken from Merlet’s work [1], are presented and analyzed using this method.

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Siqueira, A. A. G., and M. H. Terra. "Nonlinear controllers for underactuated cooperative manipulators." Robotica 25, no. 4 (January 15, 2007): 425–32. http://dx.doi.org/10.1017/s0263574706003201.

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SUMMARYIn this paper, two nonlinear $\mathcal{H}_{\infty}$ control techniques are used to solve the position control problem of underactuated cooperative manipulators. The first technique consists in representing the nonlinear system in a quasi-linear parameter varying form and the solution is given in terms of linear matrix inequalities. The second technique gives an explicit solution to the cooperative manipulators $\mathcal{H}_{\infty}$ control problem. The control of the squeeze force between the manipulator end-effectors and the object is also evaluated. Results obtained from an actual cooperative manipulator, which is able to work as a fully actuated and an underactuated manipulator, are presented.

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Kyatkin, A. B., and G. S. Chirikjian. "Synthesis of Binary Manipulators Using the Fourier Transform on the Euclidean Group." Journal of Mechanical Design 121, no. 1 (March 1, 1999): 9–14. http://dx.doi.org/10.1115/1.2829438.

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In this paper we apply the Fourier transform on the Euclidean motion group to solve problems in kinematic design of binary manipulators. In recent papers it has been shown that the workspace of a binary manipulator can be viewed as a function on the motion group, and it can be generated as a generalized convolution product. The new contribution of this paper is the numerical solution of mathematical inverse problems associated with the design of binary manipulators. We suggest an anzatz function which approximates the manipulator’s density in analytical form and has few free fitting parameters. Using the anzatz functions and Fourier methods on the motion group, linear and non-linear inverse problems (i.e., problems of finding the manipulator’s parameters which produce the total desired workspace density) are solved.

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Ashchepkova, Natalya Sergeevna. "STABILITY ANALYSIS OF SOFTWARE MANIPULATOR MOVEMENTS USING MATHCAD." Journal of Rocket-Space Technology 27, no. 4 (December 30, 2019): 52–57. http://dx.doi.org/10.15421/451908.

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Abstract. The method of the stability analysis of the manipulator program movements with use of Mathcad applied programs package is offered. On the basis of the manipulator’s kinematic scheme, the matrices of homogeneous transformations of Denavit Hartenberg are formed and a mathematical model of the extended control object is drawn up. An outline of an extended object control system consisting of a manipulator and an actuator is presented. For example, the linear equations of the manipulator, actuators, meter and controller are considered. The task of synthesizing the manipulator control algorithm is to determine the coefficients of the matrix transfer function of the controller that satisfy the conditions of stability and quality of transients. Mathematical modeling of manipulator programmatic movements was performed using the Matchad application package. The analysis of simulation results allows us to evaluate: manipulator workspace, control system performance, grip positioning accuracy, dependence of grip positioning error on the nature of load and the law of motion. A change in the dynamic characteristics of an extended control object causes a change in the controllability of systems, for the considered example rang Q = 2, i.e. the system is fully controllable. This method can be used to analyze the manipulation of the manipulator at the design stage; allows to determine the influence of design, kinematic and dynamic parameters on the manipulation of the manipulator and perform mathematical modeling of the manipulator motion. Calculation examples are given that confirm the expediency and effectiveness of using the Mathcad application software package to solve this type of problem.

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Saito, Takashi Kei, Kento Onodera, Riku Seino, Takashi Okawa, and Yasushi Saito. "300-N Class Convex-Based Telescopic Manipulator and Trial for 3-DOF Parallel Mechanism Robot." Journal of Robotics and Mechatronics 33, no. 1 (February 20, 2021): 141–50. http://dx.doi.org/10.20965/jrm.2021.p0141.

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We designed a new telescopic manipulator that uses a clustered elastic convex tape. The manipulator has an ultra-wide expansion range and toughness against mechanical stress. Compared to conventional linear actuators, our convex-type manipulators have high extension range and are very lightweight. Moreover, they are compact when rolled up. The telescopic manipulators designed in the previous study had insufficient output due to structural problems and were unstable. In this study, we report a Type-K telescopic manipulator mechanism (Makijaku-Ude Type-K), which is a redesigned manipulator that can be easily used with a 300-N class power, and applied the mechanism to a three degrees-of-freedom spatial parallel-mechanism robot.

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Gallardo-Alvarado, Jaime, Horacio Orozco-Mendoza, Alvaro Sánchez-Rodríguez, and Gursel Alici. "Kinematic analyses of novel translational parallel manipulators." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 228, no. 2 (April 4, 2013): 330–41. http://dx.doi.org/10.1177/0954406213484225.

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This study reports on the kinematic analyses of four translational parallel manipulators (3RPC, SPS + 2RPC, RPPR + 2RPC and RPPR + 2PPP) articulated with linear actuators. They are based on serially connected chains which are connected with cylindrical (C), prismatic (P), revolute (R), spherical (S) and universal (U) joints. Of these manipulators, the one which is a fully decoupled, fully isotropic and singularity-free translational parallel manipulator (RPPR+2PPP) offers a one-to-one correspondence between its input and output displacement. This makes its forward and inverse position analyses simpler with a set of linear equations to be solved. Although the other manipulators have coupled kinematics, they still have simpler forward kinematic equations over other well-known translational parallel manipulators reported in the literature. We also employ screw theory to undertake the velocity and acceleration analyses. The primary contribution of this manuscript is to show how the 3-RPC translational parallel manipulator can be gradually modified in order to obtain a fully isotropic, fully decoupled and singularity-free translational parallel manipulator.

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Tso, S. K., M. L. Lai, and P. L. Law. "Variable-Structure Linear-Model-Following Control of Manipulators." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 207, no. 1 (February 1993): 35–45. http://dx.doi.org/10.1243/pime_proc_1993_207_313_02.

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The paper describes the interaction between modelling, control and adaptation of a variable-structure model-following method applied to highly non-linear plants. The method is particularly appealing in the control of high-performance robot manipulators. The problems concerned with its application are discussed with reference to the use of a controller in a commercial manipulator as a case study.

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Kohli, D., Soo-Hun Lee, Kao-Yueh Tsai, and G. N. Sandor. "Manipulator Configurations Based on Rotary-Linear (R-L) Actuators and Their Direct and Inverse Kinematics." Journal of Mechanisms, Transmissions, and Automation in Design 110, no. 4 (December 1, 1988): 397–404. http://dx.doi.org/10.1115/1.3258936.

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In this paper, a new type of two-degree-of-freedom actuator called the rotary-linear (R-L) actuator is described. The R-L actuator permits a rotation and a translation along the axis of rotation, thus simulating a cylinder pair. The R-L actuators are then used in type synthesis of mechanical manipulator chains. Closed-loop three-, four, five, and six-degree-of-freedom chains containing four to nine links, R-L actuators, revolute pairs (R), prismatic pairs (P), cylindrical pairs (C), and spheric pairs (S) are then obtained. A class of manipulator configurations where the hand is connected to the ground via six-degree-of-freedom dyads or triads and containing three grounded R-L actuators is treated for inverse kinematics. Since all the actuators are on the ground in this configuration, higher payload capacities and smaller actuator sizes can be expected from these configurations. In addition, generally, the computations required for inverse kinematics are also significantly less than those required for serial link open-loop manipulators. The direct kinematics, however, is much more involved and computationally intensive for these manipulators than for serial-link manipulators. The direct kinematics of an example manipulator is derived and requires solution of a 16th-order polynomial equation. Numerical examples are presented for illustration.

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Lu, Yi, Zhuohong Dai, and Yang Lu. "Precise Stiffness and Elastic Deformations of Serial–Parallel Manipulators by Considering Inertial Wrench of Moving Links." Robotica 38, no. 12 (January 31, 2020): 2204–20. http://dx.doi.org/10.1017/s0263574720000041.

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SUMMARYA general serial–parallel manipulator connected in series by two different parallel manipulators with linear active legs is constructed. Its precise stiffness and elastic deformations are studied systematically. Its unified precise stiffness and precise elastic deformation models are established by considering both the moving links inertial wrench and the dynamic active/constrained wrench. A 3SPR+3RPS-type serial–parallel manipulator is illustrated for solving its precise stiffness and precise elastic deformation. The derived formulae of the precise stiffness and the precise elastic deformations of the general serial–parallel manipulator are verified by the theoretical solutions of the 3SPR+3RPS serial–parallel manipulator.

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Hu, Hongjun, Shungen Xiao, and Haikuo Shen. "Modified Linear Active Disturbance Rejection Control for Uncertain Robot Manipulator Trajectory Tracking." Mathematical Problems in Engineering 2021 (June 4, 2021): 1–13. http://dx.doi.org/10.1155/2021/8892032.

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To solve the problems of model uncertainties, dynamic coupling, and external disturbances, a modified linear active disturbance rejection controller (MLADRC) is proposed for the trajectory tracking control of robot manipulators. In the computer simulation, MLADRC is compared to the proportional-derivative (PD) controller and the regular linear active disturbance rejection controller (LADRC) for performance tests. Multiple uncertain factors such as friction, parameter perturbation, and external disturbance are sequentially added to the system to simulate an actual robot manipulator system. Besides, a two-degree-of-freedom (2-DOF) manipulator is constructed to verify the control performance of the MLADRC. Compared with the regular LADRC, MLADRC is significantly characterized by the addition of feedforward control of reference angular acceleration, which helps robot manipulators keep up with target trajectories more accurately. The simulation and experimental results demonstrate the superiority of the MLADRC over the regular LADRC for the trajectory tracking control.

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Jen, S. C., and D. Kohli. "Automated Formation of Closed Form Kinematic Displacement Polynomials for Open Loop Planar and Spatial Chains." Journal of Mechanical Design 117, no. 1 (March 1, 1995): 83–88. http://dx.doi.org/10.1115/1.2826121.

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A new numerical approach for determining inverse kinematic polynomials of manipulators is presented in this paper. Let the inverse kinematic polynomial of a manipulator in one revolute joint variable θi be represented by gnTn + gn-1Tn-1 + gn-2Tn-2 + • + g1T + go = 0. T = tanθi/2 and go, g1...gn are polynomial type functions of hand position variables. The coefficients g are expressed in terms of undetermined coefficients and hand position variables. Then the undetermined coefficients are evaluated by using direct kinematics and the solutions of sets of linear equations, thus determining coefficients g and the inverse kinematic polynomial. The method is general and may be applied for determining inverse kinematic polynomials of any manipulator. However, the number of linear equations required in determining coefficients g become significantly larger as the number of links and the degrees of the manipulator increase. Numerical examples of 2R planar and 3R spatial manipulator are presented for illustration.

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Lu, Yi, Cong Cong, Chen Liwei, and Peng Wang. "Solving elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 12 (February 19, 2013): 2810–24. http://dx.doi.org/10.1177/0954406213478374.

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It has been a significant and challenging issue to determine the elastic deformation of parallel manipulators for their precision analysis and control. A new method is proposed and studied for solving the elastic deformation of some parallel manipulators with linear active legs using computer-aided design variation geometry. First, an original simulation mechanism of a parallel manipulator is constructed; each of the vectors in the force transformation matrix of the parallel manipulators is constructed by this simulation mechanism. The active/constrained wrench and their pose are determined based on the Newton–Euler formulation. Second, the elastic deformed dimensions of the active legs are determined based on the elastic deformation equation and the active/constrained wrench. Third, a new simulation mechanism of this parallel manipulator is constructed by replacing the original dimensions of active legs with the deformed dimensions of active legs and the elastic deformations of parallel manipulators are solved using the pose difference between the original and new simulation mechanisms. Finally, two parallel manipulators are illustrated and their elastic deformations are solved and verified by both analytic approach and finite element method.

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Noh, Sun Young, Kyungmin Jeong, Yong-chil Seo, Chang-hoi Kim, Jongwon Park, Yoo Rark Choi, Sung Uk Lee, Yeong-Geol Bae, and Seungho Kim. "Development of a Prototype Robotic System for Radiosurgery with Upper Hemispherical Workspace." Journal of Healthcare Engineering 2017 (2017): 1–9. http://dx.doi.org/10.1155/2017/4264356.

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This paper introduces a specialized robotic system under development for radiosurgery using a small-sized linear accelerator. The robotic system is a 5-DOF manipulator that can be installed above a patient to make an upper hemispherical workspace centered in a target point. In order to determine the optimal lengths of the link, we consider the requirements for the workspace of a linear accelerator for radiosurgery. A more suitable kinematic structure than conventional industrial manipulators is proposed, and the kinematic analysis is also provided. A graphic simulator is implemented and used for dynamic analysis. Based on those results, a prototype manipulator and its control system are under development.

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Chen, Wen Jia, Yan Zhong He, and Jiang Zhang. "A Four Degrees of Freedom Parallel Manipulator for Machining." Advanced Materials Research 139-141 (October 2010): 2168–71. http://dx.doi.org/10.4028/www.scientific.net/amr.139-141.2168.

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In the past decades, a number of parallel manipulators have been extensively studied. However, most efforts are dedicated to six degrees of freedom (DOF) or three-DOF manipulators. There is a need for equipment providing more than three DOF's arranged in parallel and based on simpler arrangements than six-DOF arrangements in application. This paper presents a novel four-DOF parallel platform manipulator with base mounted prismatic actuators. The manipulator is driven by four linear actuators. The movable platform of the manipulator can translate along two directions and rotate around two axes respectively. The kinematics model is formulated, which describes the inverse and forward kinematics transformation. It is very easy to develop a five-axis NC machine-tool which is of large-workspace based on the four-DOF parallel mechanism presented in this paper.

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Gallardo-Alvarado, Jaime, Gürsel Alici, and Ramón Rodríguez-Castro. "A novel three degrees of freedom partially decoupled robot with linear actuators." Robotica 30, no. 3 (July 21, 2011): 467–75. http://dx.doi.org/10.1017/s026357471100083x.

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SUMMARYIn this work, a new translational robot formed with two different parallel manipulators with a common control point is introduced. An asymmetric parallel manipulator provides three translational degrees of freedom to the proposed robot while the orientation of the end-effector platform is kept constant by means of a Delta-like manipulator. An exact solution is easily derived to solve the forward displacement analysis while a semi-closed form solution is available for solving the inverse displacement analysis. The infinitesimal kinematics of the robot is approached by applying the theory of screws. Finally, a numerical example that consists of solving the inverse/forward displacement analysis as well as the forward acceleration analysis of the end-effector platform is presented. The example also includes the computation of the workspace and the direct/inverse singularities of the example.

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Wang, Shuai Jun, Bo Zhang, Xin Wang, and Xue Qian Wang. "Design and Research of a Novel Fast Connecting and Separating Modular Space Manipulator." Applied Mechanics and Materials 775 (July 2015): 357–62. http://dx.doi.org/10.4028/www.scientific.net/amm.775.357.

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With the increasing complexity of the space mission, the ability of fast reconstruction of manipulator is more and more important. To solve the problem of space manipulator’s fast reconstruction, this paper designs a novel manipulator that contains mechatronics modular joints and a connecting mechanism. Compared to the traditional manipulator, the manipulator in this paper have the advantage of great convenience of assembling and replacement of the modular joint. In this paper, we analyze the relationship between tolerance ability and structural parameters and computed the tolerance ability after optimization of the connecting mechanism; Using the perturbation method, we conducted the simulation of analysis error. Results show that relationship between the end position error and the error of the modular joints is approximate linear, which providing a theory instruction for the design of manipulator.

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Zhang, Jian Ye, Chen Zhao, and Da Wei Zhang. "Pose Accuracy Analysis of Robot Manipulators Based on Kinematics." Advanced Materials Research 201-203 (February 2011): 1867–72. http://dx.doi.org/10.4028/www.scientific.net/amr.201-203.1867.

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The pose accuracy of robot manipulators has long become a major issue to be considered in its advanced application. An efficient methodology to generate the end-effector position and orientation error model of robotic manipulator has been proposed based on the differential transformation matrix theory. According to this methodology, a linear error model that described the end-effector position and orientation errors due to robot kinematics parameters errors has been presented. A computer program to generate the error model and perform the accuracy analysis on any serial link manipulator has been developed in MATLAB. This methodology and software are applied to the accuracy analysis of a Phantom Desktop manipulator. The positioning error of the manipulator in its workspace cross section (XOZ) has been plotted as 3D surface graph and discussed.

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Salmasi, H., R. Fotouhi, and P. N. Nikiforuk. "A manoeuvre control strategy for flexible-joint manipulators with joint dry friction." Robotica 28, no. 4 (August 27, 2009): 621–35. http://dx.doi.org/10.1017/s0263574709990373.

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SUMMARYA new control strategy based on the singular perturbation method and integral manifold concept is introduced for flexible-joint manipulators with joint friction. In controllers so far developed based on the singular perturbation theory, the dynamics of actuators of flexible-joint manipulators are partially modelled, and the coupling between actuators and links is ignored. This assumption leads to inaccuracy in control performance and error in trajectory tracking which is crucial in high-precision manipulation tasks. In this paper, a comprehensive dynamic model which takes into account the coupling between actuators and links is developed and a composite controller is then designed based on the singular perturbation theorem and integral manifold concept. To overcome the joint friction, a novel method is introduced in which a linear feed-forward torque is designed using the principle of work and energy. Finally, the experimental set-up of a single rigid-link flexible-joint manipulator in the Robotics Laboratory at the University of Saskatchewan is used to verify the proposed controller. Experimental results employing the new controller show that the trajectory tracking error during and at the end of the motion of the robot manipulator is significantly reduced.

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Yang, Ze Guo, Ming Lei Shao, and Dong Ik Shin. "Kinematic Optimization of Parallel Manipulators with a Desired Workspace." Applied Mechanics and Materials 752-753 (April 2015): 973–79. http://dx.doi.org/10.4028/www.scientific.net/amm.752-753.973.

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A kinematic optimization method of parallel manipulators is presented in this paper. A desired workspace for a parallel manipulator is usually an essential requirement in a practical application. Additionally, a good kinematic performance and/or a relatively small physical size would be of great significance. A dexterity index is utilized to measure the kinematic performance of parallel manipulators. A method to define the physical size of a parallel manipulator is introduced. The cost function is then formulated as a linear combination of a dexterity index and a physical size measurement. The Optimization Tool Box of MATLAB is applied to solve the optimization problem. Finally, a general Stewart-Gough platform is taken as an example to specify the design methodology.

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AL_Zahed, Farah J. "Approximate Solution to Finite of Linear Control System Collection of Linear Control System and its Application to Robotic Manipulator Problem." Journal of Advanced Research in Dynamical and Control Systems 24, no. 4 (March 31, 2020): 273–90. http://dx.doi.org/10.5373/jardcs/v12i4/20201442.

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Lee, Hong-You, and Charles F. Reinholtz. "Inverse Kinematics of Serial-Chain Manipulators." Journal of Mechanical Design 118, no. 3 (September 1, 1996): 396–404. http://dx.doi.org/10.1115/1.2826899.

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This paper proposes a unified method for the complete solution of the inverse kinematics problem of serial-chain manipulators. This method reduces the inverse kinematics problem for any 6 degree-of-freedom serial-chain manipulator to a single univariate polynomial of minimum degree from the fewest possible closure equations. It is shown that the univariate polynomials of 16th degree for the 6R, 5R-P and 4R-C manipulators with general geometry can be derived from 14, 10 and 6 closure equations, respectively, while the 8th and 4th degree polynomials for all the 4R-2P, 3R-P-C, 2R-2C, 3R-E and 3R-S manipulators can be derived from only 2 closure equations. All the remaining joint variables follow from linear equations once the roots of the univariate polynomials are found. This method works equally well for manipulators with special geometry. The minimal properties may provide a basis for a deeper understanding of manipulator geometry, and at the same time, facilitate the determination of all possible configurations of a manipulator with respect to a given end-effector position, the determination of the workspace and its subspaces with the different number of configurations, and the identification of singularity positions of the end-effector. This paper also clarifies the relationship between the three known solutions of the general 6R manipulator as originating from a single set of 14 equations by the first author.

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Suarez, Alejandro, Manuel Perez, Guillermo Heredia, and Anibal Ollero. "Cartesian Aerial Manipulator with Compliant Arm." Applied Sciences 11, no. 3 (January 22, 2021): 1001. http://dx.doi.org/10.3390/app11031001.

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This paper presents an aerial manipulation robot consisting of a hexa-rotor equipped with a 2-DOF (degree of freedom) Cartesian base (XY–axes) that supports a 1-DOF compliant joint arm that integrates a gripper and an elastic linear force sensor. The proposed kinematic configuration improves the positioning accuracy of the end effector with respect to robotic arms with revolute joints, where each coordinate of the Cartesian position depends on all the joint angles. The Cartesian base reduces the inertia of the manipulator and the energy consumption since it does not need to lift its own weight. Consequently, the required torque is lower and, thus, the weight of the actuators. The linear and angular deflection sensors of the arm allow the estimation, monitoring and control of the interaction wrenches exerted in two axes (XZ) at the end effector. The kinematic and dynamic models are derived and compared with respect to a revolute-joint arm, proposing a force-position control scheme for the aerial robot. A battery counterweight mechanism is also incorporated in the X–axis linear guide to partially compensate for the motion of the manipulator. Experimental results indoors and outdoors show the performance of the robot, including object grasping and retrieval, contact force control, and force monitoring in grabbing situations.

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Yu, Xiao Yan, and Li Chen. "Singular perturbation adaptive control and vibration suppression of free-flying flexible space manipulators." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229, no. 11 (September 15, 2014): 1989–97. http://dx.doi.org/10.1177/0954406214551777.

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Singular perturbation adaptive control is designed for free-flying space manipulators with multiple flexible links and unknown physical parameters. The dynamical Lagrange equation was established based on assumed mode technique and linear momentum conservation theory. A singular perturbation model has been formulated and used for designing a reduced-order controller. This controller consisted of a slow control component and a fast control component. An adaptive control law was constructed for the slow counterpart of the flexible manipulator. The flexible-link fast subsystem controller would damp out the vibrations of flexible links by optimal linear quadratic regulator method. Numerical simulations by undertaking a computer simulation of a two-flexible-link space manipulator using the fourth-order Runge–Kutta integration method showed that the link vibrations had been stabilized effectively with good tracking performance.

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Li, Wen Guang, Guang Liang Liu, Dong Yang, Tie Chen, and Wei Chen. "The Calibration of Manipulator Based on Linear Precision." Applied Mechanics and Materials 182-183 (June 2012): 1545–48. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1545.

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In order to improve the absolute accuracy of the robot, one new simple and inexpensive, yet accurate robot calibration method is presented. The process assumes the robot can move along a line in the robot’s workspace. The actuators remember the angle information of each joint, when the robot moves along the line. The date that obtained by this method, simplify the process of deducing the kinematic parameters. The paper establishes the evaluation function, which demonstrates the fitness degree of the robot’s position and orientation to the line. In the end, simulation method has been adopted to testify the method, and the method is shown simple and feasible.

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Baressi Šegota, Sandi, Nikola Anđelić, Ivan Lorencin, Milan Saga, and Zlatan Car. "Path planning optimization of six-degree-of-freedom robotic manipulators using evolutionary algorithms." International Journal of Advanced Robotic Systems 17, no. 2 (March 1, 2020): 172988142090807. http://dx.doi.org/10.1177/1729881420908076.

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Lowering joint torques of a robotic manipulator enables lowering the energy it uses as well as increase in the longevity of the robotic manipulator. This article proposes the use of evolutionary computation algorithms for optimizing the paths of the robotic manipulator with the goal of lowering the joint torques. The robotic manipulator used for optimization is modelled after a realistic six-degree-of-freedom robotic manipulator. Two cases are observed and these are a single robotic manipulator carrying a weight in a point-to-point trajectory and two robotic manipulators cooperating and moving the same weight along a calculated point-to-point trajectory. The article describes the process used for determining the kinematic properties using Denavit–Hartenberg method and the dynamic equations of the robotic manipulator using Lagrange–Euler and Newton–Euler algorithms. Then, the description of used artificial intelligence optimization algorithms is given – genetic algorithm using random and average recombination, simulated annealing using linear and geometric cooling strategy and differential evolution. The methods are compared and the results show that the genetic algorithm provides best results in regard to torque minimization, with differential evolution also providing comparatively good results and simulated annealing giving the comparatively weakest results while providing smoother torque curves.

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Filaretov, Vladimir, Alexander Zuev, Alexander Procenko, and Sergey Melman. "Fault Detection of Actuators of Robot Manipulator by Vision System." Applied Mechanics and Materials 865 (June 2017): 457–62. http://dx.doi.org/10.4028/www.scientific.net/amm.865.457.

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This paper considers synthesis method of fault detection system for actuators of robot manipulators based on using of signals fusion from stereo camera, angles sensors of joints and desired values of joint variables. The vision system is used for determining the position of three markers rigidly connected with working tool in the coordinate system associated with the manipulator. The advantage of proposed fault detection system is the simplicity of implementation and precision of detection of typical faults without knowledge about non-linear dynamic of robot and actuators. The results of mathematical simulation on the example of the PUMA-type manipulator using its kinematic model, position and orientation data of markers placed on working tool of manipulator, obtained from vision system fully confirm the efficiency of the proposed fault detection system.

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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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Izumi, Kiyotaka, Keigo Watanabe, and Masatoshi Nakamura. "Simplified Adaptive Nonlinear Robust Controller for Linearized Pantagraph-Type Manipulator." Journal of Robotics and Mechatronics 7, no. 3 (June 20, 1995): 242–49. http://dx.doi.org/10.20965/jrm.1995.p0242.

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If physical parameters are adjusted suitably in the pantagraph-type manipulator, the mathematical model becomes linear so that we can apply a linear controller. However, when the manipulator has an additional mass as an end-effector, the linear controller does not work well because the resultant model becomes nonlinear. In this paper, we propose a simplified adaptive nonlinear robust controller which we can apply to the manipulator, irrespective of the system linearity or nonlinearity. The effectiveness of the controller is illustrated by some simulations.

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30

Özkan, Bülent. "Guidance and control of a planar robot manipulator used in an assembly line." Transactions of the Institute of Measurement and Control 40, no. 2 (July 20, 2016): 389–99. http://dx.doi.org/10.1177/0142331216657800.

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Robot manipulators have been successfully utilized in assembly lines within the last few decades. In order to increase productivity and diminish costs, they have been enrolled at several stages of automation, including transportation, welding, mounting and quality control processes of the components that are assembled to construct the entire system. In this study, an unusual method is proposed to make the robot manipulators and moving belts serve accordingly in an efficient manner. To this extent, the motion of a two-link robot manipulator is planned in a continuous fashion by the use of a proper guidance law compatible with the uninterrupted movement of the moving belt upon which the components are placed by means of the manipulator. For this purpose, a control system is built for the manipulator based on its dynamic modelling by regarding the PI (proportional plus integral) control law in accordance with the linear homing guidance law. Moreover, engagement geometry is constructed. Having performed computer simulations, it is observed that the tip point of the manipulator can catch the slot on the belt at speeds from 0.5 to 2.5 m/s for different initial positions and speeds of the tip point from 5.0×10−5 to 0.5 m/s.

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Wang, Songtao, Gang Cheng, Jianhua Yang, and Xihui Chen. "Bifurcation and stability analysis for 3SPS+1PS parallel hip joint manipulator based on unified theory." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 24 (November 14, 2016): 4603–16. http://dx.doi.org/10.1177/0954406216670681.

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For a parallel hip joint manipulator, the unified kinematics and stiffness model are established based on a novel unified theory, and then the bifurcation and stability are analyzed under the same unified theory framework. In bifurcation analysis, a chaos method is first applied to solve the non-linear bifurcation equations in order to get the full configuration of the parallel hip joint manipulator, which improves the convergence rate and accuracy. Based on the full-configuration solution, the single-parameter and double-parameter simulation for the bifurcation and stability of the parallel hip joint manipulator is performed. The bifurcation simulation results show that the configuration only changes along the corresponding path but cannot change to other paths when the configuration of the parallel hip joint manipulator is at a certain path. The stability simulation results show that when the parallel hip joint manipulator enters into an uncontrolled domain of a bifurcation posture along different paths, the posture component which changes dramatically will lose control first, and the other posture components will move along the changed configuration. In this paper, the kinematics, stiffness, bifurcation and stability of the parallel hip joint manipulator are solved under the same theory framework, which improves the solving efficiency and enriches the mechanical theory for the parallel manipulators.

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Altuzarra, O., B. Şandru, Ch Pinto, and V. Petuya. "A symmetric parallel Schönflies-motion manipulator for pick-and-place operations." Robotica 29, no. 6 (February 25, 2011): 853–62. http://dx.doi.org/10.1017/s0263574711000063.

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SUMMARYThis paper presents a new symmetric parallel Schönflies-motion generator. The design is an evolution of a previous robot with linear inputs. The complete kinematic analysis of the 4-degree-of-freedom (dof) parallel manipulator is presented. The degrees of freedom are obtained from the Group Theory, the direct and inverse position problems are solved obtaining the manipulator's workspace, and the Jacobian analysis is presented. Then the isotropic configurations of the manipulator are discussed and the local dexterity map within the workspace is produced. Finally, two alternatives of a rotational mechanical device, which will increase the angular end-effector range, are proposed.

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Antonov, V. O. "ANALYSIS OF THE COMPUTATIONAL COMPLEXITY OF THE METHOD OF ITERATIVE DIMENSIONAL-LINEAR GENERATION OF THE TRAJECTORY OF MOTION OF THE THREE-LINE ANTHROPOMORPHIC MANIPULATOR IN THE VOLUME SPACE WITH OBSTRUCTION." Proceedings of the Southwest State University 22, no. 3 (June 28, 2018): 13–28. http://dx.doi.org/10.21869/2223-1560-2018-22-3-13-28.

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Energy efficiency is an actual problem of the present, including in the field of robotics. Existing methods for planning the trajectory of motion of manipulators with excessive mobility face a number of problems, one of which is the impossibility of working in real time mode due to the high complexity of the scheduling algorithm. Moreover, the existing algorithms that work in real time are significantly inferior to the accuracy of the target operations. Therefore, earlier, in the author's articles, an iterative method of piecewise linear generation of the manipulator's trajectory was developed. In this paper, we analyze the computational complexity of the numerical method of iterative piecewise linear generation of the trajectory of a three-link anthropomorphic manipulator with 7 degrees of mobility in a volume space with an obstacle, an approximated hypersphere, in real time. A short description of the proposed method of planning the trajectory of motion is given. To move between the waypoints, the Denavite-Hartenberg representation used, with the formulation and solution of the problem of nonlinear optimization with the objective function of minimizing energy consumption when the manipulator moved to the target point. The initial generalized algorithm of the path planning method described. The number of operations that must performed in the process of execution of a recursive algorithm is considered. Parallelizing the branching recursive algorithm allows you to reduce the execution time to the time of executing a non-branching recursive algorithm with the same computational complexity and depth. A formula developed that allows you to select the values of variable parameters of the algorithm based on the available computational power and the allowable calculation time, and to determine the requirements for the manipulator computer system at the development stage.

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Youcef-Toumi, Kamal, and Haruhiko Asada. "The Design of Open-Loop Manipulator Arms With Decoupled and Configuration-Invariant Inertia Tensors." Journal of Dynamic Systems, Measurement, and Control 109, no. 3 (September 1, 1987): 268–75. http://dx.doi.org/10.1115/1.3143854.

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A manipulator design theory for reduced dynamic complexity is presented. The kinematic structure and mass distribution of a manipulator arm are designed so that the inertia matrix in the equation of motion becomes diagonal and/or invariant for an arbitrary arm configuration. For the decoupled and invariant inertia matrix, the system can be treated as a linear, single-input, single-output system with constant parameters. Consequently, control of the manipulator arm is simplified, and more importantly, the reduced dynamic complexity permits improved control performance. First, the problem of designing such an arm with a decoupled and/or configuration-invariant inertia matrix is defined. The inertia matrix is then analyzed in relation to the kinematic structure and mass properties of the arm links. Necessary conditions for a decoupled and/or configuration-invariant manipulator inertia matrix are then obtained. Using the necessary conditions, the kinematic structure and mass properties are found which reduce the inertia matrix to a constant diagonal form. Possible arm designs for decoupled and/or invariant inertia matrices are then determined for 2 and 3 degree-of-freedom manipulators.

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Sanger, D. J., J. Q. Chen, S. J. Zhang, and D. Howard. "A general method for the stiffness analysis of manipulator mechanisms." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 214, no. 5 (May 1, 2000): 673–85. http://dx.doi.org/10.1243/0954406001523687.

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This paper is concerned with the displacement of the end effector of a manipulator, when subjected to an externally applied force system, which arises because of the flexibility of the actuator drives. General results are developed for the end effector infinitesimal stiffnesses (and compliances) in terms of the actuator infinitesimal stiffnesses (and compliances) for serial and parallel manipulators. It is shown that these quantities are dependent upon the instantaneous force system applied to the end effector, so that the relationship between the applied force system and the resulting displacement is non-linear, even for a given manipulator configuration. These results are of interest for a number of reasons. For example, the accuracy of a manipulator is directly related to its stiffness, and knowledge of the stiffnesses (or compliances) can be used to develop means of simultaneously controlling the force and displacement for a partially constrained end effector. Examples are provided to demonstrate the application of the general results to specific manipulator mechanisms, including both serial and parallel types.

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Zhu, H. A., C. L. Teo, and G. S. Hong. "An Uncertainty-Attenuating Controller for Mechanical Manipulators with Electromechanical Dynamics." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 207, no. 3 (August 1993): 165–71. http://dx.doi.org/10.1243/pime_proc_1993_207_335_02.

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It is known that the cross-coupled non-linear electromechanical dynamics of motor-manipulator systems is more complex than when only the mechanical dynamics is considered. In this paper, control of manipulators with non-negligible motor dynamics is studied and a control strategy is developed for achieving ease of controller design and high control performance. By using the developed algorithm not only can the highly complicated electromechanical dynamics be effectively controlled, but also the motors are made ‘sensible’ to sense and compensate for the uncertain dynamics acting at the manipulator joints. What is more, as an encouraging by-result, the difficulty and complexity in modelling and controlling such systems can be reduced significantly.

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Chung, Seong Youb, Han Sol Kang, and Myun Joong Hwang. "Singularity Avoidance for Linear Motion of 6-DOF Manipulator." Journal of Institute of Control, Robotics and Systems 24, no. 11 (November 30, 2018): 1025–32. http://dx.doi.org/10.5302/j.icros.2018.18.0164.

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Gutleben, Hans, and John T. Yates. "A simple way to build a linear motion manipulator." Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films 9, no. 1 (January 1991): 170. http://dx.doi.org/10.1116/1.577122.

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Kazim, Issraa Jwad, Yuegang Tan, and Layth Qaseer. "Integration of DE Algorithm with PDC-APF for Enhancement of Contour Path Planning of a Universal Robot." Applied Sciences 11, no. 14 (July 16, 2021): 6532. http://dx.doi.org/10.3390/app11146532.

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In the robotic engineering field, the main target, especially in industry, manufacturing, and surgical operations, is reaching the optimal performance of manipulators. The purpose of this paper is to quantify the contour tracking performance of collaborative universal manipulator robot (UR5) by setting the gain of position domain controller. In order to improve and enhance the track of manipulator in experimental applications we utilize differential evolution (DE) optimization, using MATLAB toolbox with an applied robot operating system (ROS). The adopted current approach does not only optimize the gain of position domain controller but also prevent collisions by detecting a “border crossing” without turning off the manipulator and allowing the automation agent to be on the scene, coexisting in harmonic mode and avoiding collisions. This requires the implementation of an algorithm that detects an obstacle to avoid anticipated collisions. For this purpose, the adopted algorithm uses the DE algorithm to modify the artificial potential field (APF). The results of this paper present that on one hand, meta-heuristic optimization algorithm features give the best performance indices for linear and non-linear contours, and on the other hand, DE algorithm features give good modification to APF to generate collision free contour path planning.

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Yang, Bin, Yuqing He, Jianda Han, and Guangjun Liu. "Rotor-Flying Manipulator: Modeling, Analysis, and Control." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/492965.

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Equipping multijoint manipulators on a mobile robot is a typical redesign scheme to make the latter be able to actively influence the surroundings and has been extensively used for many ground robots, underwater robots, and space robotic systems. However, the rotor-flying robot (RFR) is difficult to be made such redesign. This is mainly because the motion of the manipulator will bring heavy coupling between itself and the RFR system, which makes the system model highly complicated and the controller design difficult. Thus, in this paper, the modeling, analysis, and control of the combined system, called rotor-flying multijoint manipulator (RF-MJM), are conducted. Firstly, the detailed dynamics model is constructed and analyzed. Subsequently, a full-state feedback linear quadratic regulator (LQR) controller is designed through obtaining linearized model near steady state. Finally, simulations are conducted and the results are analyzed to show the basic control performance.

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Izadbakhsh, Alireza, and Saeed Khorashadizadeh. "Robust task-space control of robot manipulators using differential equations for uncertainty estimation." Robotica 35, no. 9 (September 8, 2016): 1923–38. http://dx.doi.org/10.1017/s0263574716000588.

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SUMMARYMost control algorithms for rigid-link electrically driven robots are given in joint coordinates. However, since the task to be accomplished is expressed in Cartesian coordinates, inverse kinematics has to be computed in order to implement the control law. Alternatively, one can develop the necessary theory directly in workspace coordinates. This has the disadvantage of a more complex robot model. In this paper, a robust control scheme is given to achieve exact Cartesian tracking without the knowledge of the manipulator kinematics and dynamics, actuator dynamics and nor computing inverse kinematics. The control design procedure is based on a new form of universal approximation theory and using Stone–Weierstrass theorem, to mitigate structured and unstructured uncertainties associated with external disturbances and actuated manipulator dynamics. It has been assumed that the lumped uncertainty can be modeled by linear differential equations. As the method is Model-Free, a broad range of manipulators can be controlled. Numerical case studies are developed for an industrial robot manipulator.

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Rao Pundru, Srinivasa, and Mohan Rao Nallur. "Spatial Three Degree of Freedom Parallel Manipulator Forward Kinematic Position Analysis." International Journal of Engineering & Technology 7, no. 4.5 (September 22, 2018): 147. http://dx.doi.org/10.14419/ijet.v7i4.5.20032.

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This work presents forward kinematic position analysis of a spatial three degree of freedom parallel manipulator, which has three symmetric loops. The three loops consist of an actuated sliding links- rotational and spherical joints. The actuated sliding links are attached to inclined base platform via rotational joints. The limbs are connected from rotational joints to moving platform by spherical joints. The degree of freedom of a spatial parallel manipulator is analyzed via kutzbach criterion. The forward kinematic position analysis carried out by using 3-coupled trigonometric equations which are formulated with side and behaviour constraints of the manipulator. There are many difficulties in solving the system of non-linear equations in kinematics of manipulator therefore by using MATLAB the three non-linear coupled algebraic equations are solved. The forward position kinematic analysis part is used in the development procedure of spatial parallel manipulator to check, the required and obtained positions of the moving platform of the developed manipulator.

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Joshi, Sameer A., and Lung-Wen Tsai. "The Kinematics of a Class of 3-DOF, 4-Legged Parallel Manipulators." Journal of Mechanical Design 125, no. 1 (March 1, 2003): 52–60. http://dx.doi.org/10.1115/1.1540992.

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In this paper, a class of 3-DOF, 4-legged parallel manipulators are enumerated. The general architecture of such manipulators consists of a moving platform, a fixed base, and four supporting legs that meet the fixed base at four distinct points and the moving platform at four distinct points. One of the four legs is passive whereas each of the remaining three legs is driven by a linear actuator. To gain a better understanding of the mechanisms, a methodology for analyzing the kinematics of such manipulators is presented. The Tricept manipulator is used as an example to illustrate the methodology.

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Shoji, Yasumasa, Makoto Inaba, Toshio Fukuda, and Hidemi Hosokai. "Stable Control of Robotic Manipulator with Collision Phenomena : Positioning of Multi-Degrees-of-Freedom Linear Manipulator." JSME international journal. Ser. C, Dynamics, control, robotics, design and manufacturing 36, no. 2 (1993): 226–32. http://dx.doi.org/10.1299/jsmec1993.36.226.

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Sadegh, Nader, Roberto Horowitz, Wei-Wen Kao, and Masayoshi Tomizuka. "A Unified Approach to the Design of Adaptive and Repetitive Controllers for Robotic Manipulators." Journal of Dynamic Systems, Measurement, and Control 112, no. 4 (December 1, 1990): 618–29. http://dx.doi.org/10.1115/1.2896187.

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A unified approach, based on Lyapunov theory, for synthesis and stability analysis of adaptive and repetitive controllers for mechanical manipulators is presented. This approach utilizes the passivity properties of the manipulator dynamics to derive control laws which guarantee asymptotic trajectory following, without requiring exact knowledge of the manipulator dynamic parameters. The manipulator overall controller consists of a fixed PD action and an adaptive and/or repetitive action for feed-forward compensations. The nonlinear feedforward compensation is adjusted utilizing a linear combination of the tracking velocity and position errors. The repetitive compensator is recommended for tasks in which the desired trajectory is periodic. The repetitive control input is adjusted periodically without requiring knowledge of the explicit structure of the manipulator model. The adaptive compensator, on the other hand, may be used for more general trajectories. However, explicit information regarding the dynamic model structure is required in the parameter adaptation. For discrete time implementations, a hybrid version of the repetitive controller is derived and its global stability is proven. A simulation study is conducted to evaluate the performance of the repetitive controller, and its hybrid version. The hybrid repetitive controller is also implemented in the Berkeley/NSK SCARA type robot arm.

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Tadikonda, S., and H. Baruh. "Pointwise-Optimal Control of Robotic Manipulators." Journal of Dynamic Systems, Measurement, and Control 110, no. 2 (June 1, 1988): 210–13. http://dx.doi.org/10.1115/1.3152673.

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A method is presented for the pointwise-optimal control of robotic manipulators along a desired trajectory. An approximate expression for the manipulator response is used to minimize a quadratic performance index with a linear regulator and tracking criterion, during each sampling period. The delay associated with implementation of the control action is analyzed, and its adverse effects are eliminated by estimation of the joint angles and torques one time step ahead.

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Hao, Guangbo, and Xianwen Kong. "A structure design method for compliant parallel manipulators with actuation isolation." Mechanical Sciences 7, no. 2 (November 30, 2016): 247–53. http://dx.doi.org/10.5194/ms-7-247-2016.

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Abstract. Since precise linear actuators of a compliant parallel manipulator suffer from their inability to tolerate the transverse motion/load in the multi-axis motion, actuation isolation should be considered in the compliant manipulator design to eliminate the transverse motion at the point of actuation. This paper presents an effective design method for constructing compliant parallel manipulators with actuation isolation, by adding the same number of actuation legs as the number of the DOF (degree of freedom) of the original mechanism. The method is demonstrated by two design case studies, one of which is quantitatively studied by analytical modelling. The modelling results confirm possible inherent issues of the proposed structure design method such as increased primary stiffness, introduced extra parasitic motions and cross-axis coupling motions.

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Teo, C. L., H. A. Zhu, and G. S. Hong. "An Uncertainty-Attenuating Controller for Mechanical Manipulators with Electromechanical Dynamics: Part 2." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 208, no. 4 (November 1994): 215–19. http://dx.doi.org/10.1243/pime_proc_1994_208_334_02.

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Decoupling control of robotic manipulators, based on a dynamic model that includes both the mechanical dynamics of the links and the electrical dynamics of the joint motors, is studied in this paper. By using an algorithm of feedback linearization developed in this paper, the highly non-linear and strongly cross-coupled electromechanical system is decoupled and linearizd into a set of decoupled linear subsystems. Then, disturbance decoupling is further conducted for disturbance and uncertainty attenuation. It is shown that, by using the proposed control scheme, both modelling difficulty and control complexity of the manipulator system can be significantly reduced.

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Sun, Jingyu, Yanjun Liu, and Chen Ji. "Extended singular robust inverse solution of redundant serial manipulators." Advances in Mechanical Engineering 12, no. 2 (February 2020): 168781402090773. http://dx.doi.org/10.1177/1687814020907731.

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We propose the use of a damping matrix β to replace the unified damping coefficient λ in the singular robust inverse method, allowing for adjustment of the manipulator’s singularity for different joints separately. In addition, the correction coefficient matrix α is employed to eliminate the Jacobian matrix approximation error, which usually exists in the iterative control solving process; the extended singular robust inverse method is thereby proposed. This article contains analyses of the singularities caused by three methods and how they result in larger values of the manipulator terminal error and joint angular velocity; additionally, the semi-empirical selection principles of β and α are given. The stability of the proposed method is investigated with the Lyapunov stability criteria, and its effectiveness is verified for spatial linear and curve trajectories with 7-axis and 10-axis redundant serial manipulators. The simulation results show that the proposed method exhibits improved optimization performance and stability, and the terminal error is stable and within the allowable range. The least singular value is larger and the joint angular velocity is the lowest, which is the expected outcome. Furthermore, the simulation results for the 10-axis manipulator also indicate the generality of the proposed method.

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Mesa Montoya, Carlos Andrés, Hector Fabio Quintero Riaza, and Federico Gutiérrez Madrid. "Morphological Synthesis and workspace design for a parallel manipulator with linear actuators." DYNA 87, no. 213 (April 1, 2020): 129–39. http://dx.doi.org/10.15446/dyna.v87n213.80676.

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This paper addresses the kinematic structure and workspace analysis of a parallel manipulator with linear actuators considering two studies.The first one was based on a morphological synthesis in which a kinematic connections approach was implemented. The set of combinations of joints and links for the desired system and their linkage are illustrated. Finally, the development regarding the conceivable morphologyis detailed, providing three linear degrees of freedom between the mobile and fixed platforms. The second study presented the dimensional synthesis of the manipulator, considering a workspace required and an input transmission index. The geometrical design was based on the maximum inscribed workspace volume; the cylindrical shape radius inscribed on a workspace intersection is also exemplified. The geometric determination of the workspace for the manipulator was demonstrated using computer-aided design. A design result of the Delta as checked with the stiffness and condition indices.

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Journal articles on the topic 'Linear manipulator'

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