Mathematical model of the interaction of two robots at synchronous execution of simultaneous operation

2020 ◽  
pp. 11-15
Author(s):  
V.I. Chizhikov ◽  
E.V. Kurnasov
Keyword(s):  
Inverse Kinematics ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Simultaneous Operation ◽  
Generalized Coordinates ◽  
Group Control ◽  
Inverse Kinematics Problem ◽  
Robot Group ◽  
Manipulation Robot ◽  
Complex Movement

The problem of a kinematic model of the interaction of two robots in joint synchronous work on the complex movement of an object is being solved. A solution to the inverse kinematics problem is proposed for two manipulators connected by the object of manipulation. Expressions are obtained for controlled generalized coordinates in group control with superimposed constraints with parallel manipulators. Keywords manipulation robot, group control, controlled generalized coordinates, continuity of connections, collaboration. [email protected]

Stiffness Analysis of a Spatial Parallel Mechanism With Flexible Moving Platform

2010 ◽  
Author(s):  
Amir Rezaei ◽  
Alireza Akbarzadeh ◽  
Javad Enferadi
Keyword(s):  
Inverse Kinematics ◽  
Strain Energy ◽  
Parallel Manipulators ◽  
Physical Structure ◽  
Fem Model ◽  
Lumped Model ◽  
Stiffness Analysis ◽  
Spatial Parallel Mechanism ◽  
Inverse Kinematics Problem ◽  
Moving Platform

In this paper, stiffness analysis of a 3-DOF spatial, 3-PSP type, parallel manipulator is investigated. Most previous stiffness analysis studies of parallel manipulators are performed using lumped model as well as assuming a rigid moving platform. In this paper, unlike traditional stiffness analysis, the moving platform is assumed to be flexible. Additionally, a continuous method is used for obtaining mathematical model of the manipulator stiffness matrix. This method is based on strain energy and Castigliano’s theorem [1]. For this purpose, first we solve inverse kinematics problem then We must find relationship between the applied external torques on the moving platform and the resultant joints forces. Next, strain energy moving platform is calculated. Strain energy of this element is calculated using force analysis and inverse kinematics problem. Finally, a FEM model is generated and used to simulate the physical structure. Simulation results are compared with the analytical model.

scholarly journals DETERMINATION OF THE DEPENDENCE OF GENERALIZED COORDINATES OF THE MECHANISM OF THE BASIC DEVICE WITH EXCESSIVE MOBILITY

2019 ◽  
Vol 46 (1) ◽  
pp. 79-89
Author(s):  
V. O. Antonov ◽  
V. I. Petrenko ◽  
V. B. Sychkov ◽  
F. B. Tebueva
Keyword(s):  
Inverse Kinematics ◽  
Wrist Joint ◽  
Local Coordinate System ◽  
Generalized Coordinates ◽  
Type Device ◽  
Inverse Kinematics Problem ◽  
The Absolute ◽  
End Node ◽  
Master Device

Objectives. The article considers the problem of accuracy in determining the generalized coordinates of the lever mechanisms of the copy-type setting devices with the condition of excessive mobility. The purpose of the article is to determine the analytical dependence of the generalized coordinates of the mechanism of the copy-type setting device with excess mobility.Method. The article describes the principle of forming generic coordinates of a copy-type setting device for controlling a three-link anthropomorphic manipulator with 7 degrees of mobility, which allows determining the position of any desired points of a copy-type device for controlling a three-link anthropomorphic manipulator with 7 degrees of mobility by solving the inverse kinematics problem.Result. Matrices for finding the position of the nodes of the manipulator in space are constructed. Matrices of rotation transformations around generatrix axes and the corresponding formulas for finding the coordinates of the end node are given. The formulas for the transition to the local coordinate system of the corresponding links and the formation of the absolute values of the coordinates are described.Conclusion. A complex relationship has been revealed that allows one to calculate the absolute values of the coordinates of the wrist joint at known angles between the links and the angles of rotation of the joints. The presented method of determining the coordinates of the system allows to simplify the calculated part and increase the accuracy of determining the end points, which entails a comprehensive increase in the performance of the system “master device - robot”.

Group interaction of robots with an arbitrary kinematic diagram of manipulators during synchronous execution of technological operations

2021 ◽  
pp. 3-10
Author(s):  
Keyword(s):  
Optimal Control ◽  
Dynamic Balance ◽  
Mathieu Equation ◽  
Static Equilibrium ◽  
Generalized Coordinates ◽  
Manipulation System ◽  
Group Control ◽  
Executive System ◽  
Kinematic Diagram ◽  
Robot Group

The stabilization of the manipulated object near the position of static equilibrium under kinematic and force disturbances during cooperative transportation by two robots of arbitrary structure is considered. The dynamic balance of an object in grippers is described by the Mathieu equation. The controlled executive system of the coupled robot provides adjustment of the manipulation system with minimal potential energy in the grippers. A variant of the optimal control in terms of speed is considered when transferring the system to a position close to static equilibrium. Keywords: robot, group control, controlled generalized coordinates, continuity of connections, cooperative work. [email protected]

scholarly journals Study on the Inverse Kinematics Problem of Robot (2nd Report)

1997 ◽  
Vol 63 (5) ◽  
pp. 699-703
Author(s):  
Xiaohai JIN ◽  
Sachio SHIMIZU ◽  
Nobuyuki FURUYA
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematics Problem

scholarly journals Cerebellum-inspired neural network solution of the inverse kinematics problem

2015 ◽  
Vol 109 (6) ◽  
pp. 561-574 ◽  
Author(s):  
Mitra Asadi-Eydivand ◽  
Mohammad Mehdi Ebadzadeh ◽  
Mehran Solati-Hashjin ◽  
Christian Darlot ◽  
Noor Azuan Abu Osman
Keyword(s):  
Neural Network ◽  
Inverse Kinematics ◽  
Network Solution ◽  
Inverse Kinematics Problem

Kinematics of a Fully-Decoupled Remote Center-of-Motion Parallel Manipulator for Minimally Invasive Surgery

2012 ◽  
Vol 6 (2) ◽  
Author(s):  
Chin-Hsing Kuo ◽  
Jian S. Dai
Keyword(s):  
Minimally Invasive Surgery ◽  
Minimally Invasive ◽  
Invasive Surgery ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Surgical Instruments ◽  
End Effector ◽  
Minimally Invasive Surgical ◽  
Inverse Kinematics Problem

A crucial design challenge in minimally invasive surgical (MIS) robots is the provision of a fully decoupled four degrees-of-freedom (4-DOF) remote center-of-motion (RCM) for surgical instruments. In this paper, we present a new parallel manipulator that can generate a 4-DOF RCM over its end-effector and these four DOFs are fully decoupled, i.e., each of them can be independently controlled by one corresponding actuated joint. First, we revisit the remote center-of-motion for MIS robots and introduce a projective displacement representation for coping with this special kinematics. Next, we present the proposed new parallel manipulator structure and study its geometry and motion decouplebility. Accordingly, we solve the inverse kinematics problem by taking the advantage of motion decouplebility. Then, via the screw system approach, we carry out the Jacobian analysis for the manipulator, by which the singular configurations are identified. Finally, we analyze the reachable and collision-free workspaces of the proposed manipulator and conclude the feasibility of this manipulator for the application in minimally invasive surgery.

Development and analysis of a bio-inspired wire-driven variable stiffness double spring based tapered multi-section flexible robot

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Alok Ranjan Sahoo ◽  
Pavan Chakraborty
Keyword(s):  
Inverse Kinematics ◽  
Kinematic Model ◽  
Variable Stiffness ◽  
Radius Of Curvature ◽  
Flexible Robot ◽  
Content Type ◽  
Cluttered Environments ◽  
Collapsed Buildings ◽  
Practical Implications ◽  
Robot Body

Purpose The purpose of this paper is to develop a tendon actuated variable stiffness double spring based continuously tapered multi-section flexible robot and study its capability to achieve the desired bending and compression for inspection in cluttered environments. Design/methodology/approach Spring-based continuum manipulators get compressed while actuated for bending. This property can be used for the advantage in cluttered environments if one is able to control both bending and compression. Here, this paper uses a mechanics based model to achieve the desired bending and compression. Moreover, this study tries to incorporate the tapered design to help in independent actuation of the distal sections with minimal effects on proximal sections. This study is also trying to incorporate the double spring based design to minimize the number of spacers in the robot body. Findings The model was able to produce desired curvature at the tip section with less than 4.62% error. The positioning error of the manipulator is nearly 3.5% which is at par with the state-of-the-art manipulators for search and rescue operations. It was also found that the use of double spring can effectively reduce the number of spacers required. It can be helpful in smooth robot to outer world interaction without any kink. From the experiments, it has been found that the error of the kinematic model decreases as one moves from high radius of curvature to low radius of curvature. Error is maximum when the radius of curvature is infinity. Practical implications The proposed manipulator can be used for search operations in cluttered environments such as collapsed buildings and maintenance of heavy machineries in industries. Originality/value The novelty of this paper lies in the design and the proposed kinematics inverse kinematics for a spring-based continuously tapered multi-section manipulator.

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