Inverse dynamics of a 3PRC parallel kinematic machine (original) (raw)
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Recursive modelling for the kinematics and dynamics of the known 3-PRR planar parallel robot is established in this paper. Three identical planar legs connecting to the moving platform are located in a vertical plane. Knowing the motion of the platform, we develop first the inverse kinematics and determine the positions, velocities and accelerations of the robot. Further, the principle of virtual work is used in the inverse dynamics problem. Several matrix equations offer iterative expressions and graphs for the power requirement comparison of each of three actuators in two different actuation schemes: prismatic actuators and revolute actuators. For the same evolution of the moving platform in the vertical plane, the power distribution upon the three actuators depends on the actuating configuration, but the total power absorbed by the set of three actuators is the same, at any instant, for both driving systems. The study of the dynamics of the parallel mechanisms is done mainly to solve successfully the control of the motion of such robotic systems.
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The performance of robotic systems with parallel kinematics can be evaluated by their kinematic, static, and dynamic properties. These properties are directly used in model-based controllers which potentially offer higher accuracy for robotic systems. Inverse dynamic solution is an essential part of these controllers. In the present work, the inverse dynamics model of a 3-PRR (prismatic—revolute—revolute) planar parallel manipulator based on the natural orthogonal complement (NOC) method is developed. To drive the NOC for the 3-PRR closed-loop systems, the explicit expressions of the loop constraints equations and the associated Jacobian matrices are first obtained. Next the NOC matrix, which is a velocity transformation matrix relating the Cartesian angular/translational velocities of various bodies to the motor joint rates, is calculated. Finally results of the NOC method are compared with simulation of a 3-PRR planar parallel manipulator using two commercial softwares: SimMechani...
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Proceedings of the Romanian Academy - Series A: Mathematics, Physics, Technical Sciences, Information Science
Matrix relations for kinematics and inverse dynamics of the 3-RRR planar parallel robot are established in this paper. Three identical planar legs connecting to the moving platform are located in the same plane. Knowing the general motion of the platform, we develop first the inverse kinematics problem and determine the positions, velocities and accelerations of the robot's elements. The inverse dynamics problem is solved using the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with multipliers. Recursive equations offer expressions and graphs for the input powers of three revolute actuators and the internal forces in the joints. A of joint k m k J – mass and symmetric matrix of tensor of inertia of k T about the link-frame k k k z y x 10 10 10 , , A B C p p p – powers of three fixed revolute actuators 1. INTRODUCTION Compared with serial manipulators, the followings are the potential advantages of parallel robots: high...
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In the world of robotics, the parallel kinematic manipulators have proved their unique potentials like rigid structural capacities, better dynamic behaviours, and excellent spatial positional accuracy for many applications. One of the prime focus areas of the paper is to test and to establish a simplified novel approach for the Inverse Kinematics problem solution for a 3-PSU Parallel Kinematic Manipulator platform. Additionally, the methodology for simulation of Inverse Kinematics has been checked and verified. The obtained solution is further used for positional simulation of virtual prototype of 3-PSU PKM using Pro/Mechanism module. Further, these derived data is used for simulation of the Rigid Dynamics Solution for PKM (considering inertial forces acting on actuator) is also simulated in case of circular contouring.
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Parallel mechanisms are widely used in various fields of engineering and industrial applications such as machine tools, flight simulators, earthquake simulators, medical equipment, etc. Parallel mechanisms are restricted to some limitations such as irregular workspace, existence of singular points and complexity of control systems which should be studied and analyzed for effective and efficient use. In this research, a new machine tool with parallel mechanism which has three translational degrees of freedom is studied and the workspace and singular points are determined by deriving analytical equations and then utilizing of Matlab software. To do so, forward and inverse kinematics of the mechanism are obtained and workspace and singular points are calculated using a search algorithm. Afterward, in order to validate the results, the proposed mechanism is simulated in automatic dynamics analysis of mechanical systems (ADAMS) software. Moreover, in order to investigate the quality of robot performance and dexterity of the mechanism in its workspace, global dexterity index (GDI) of the robot is calculated using Jacobean matrix at different positions of the mobile platform.
Inverse dynamics of a parallel manipulator
Journal of Robotic Systems, 1994
Presented is an analysis of the kinematics and the inverse dynamics of a proposed three degree of freedom {dof) parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity, and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangian technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline. 0 1994 john Wiley G. Sons, Inr.
Dynamic modelling of a 3-DOF parallel manipulator using recursive matrix relations
Robotica, 2006
In this paper, a simple and convenient method -Recursive Matrix method -is proposed for kinematic and dynamic analysis of all types of complex manipulators. After addressing the principle of the method, an example -a 3-DOF parallel manipulator with prismatic actuators -is demonstrated for the efficiency of the method in solving kinematic and dynamic problems of complex manipulators. With the inverse kinematic solutions, the inverse dynamic problem is solved with the virtual powers method. Matrix relations and graphs of the acting forces and powers for all actuators are analysis and determined. It is shown that the proposed method is an effective mean for kinematic and dynamic modelling of parallel mechanisms.
Kinematic Analysis of Planar Parallel Mechanism
The paper deals with kinematic model of parallel mechanism equipped with elastic members. The main aim is to determine the workspace of particular point of the mechanism in order to designing of whole mechanism for the future. Whole mechanisms should consist of several same segments which creates concept of serial mechanism. Since there is investigated parallel mechanism, at first has to be solved inverse kinematic model in order to obtain generalized variables, which are necessary for direct kinematic model. In the paper Jacobian matrix is derived for investigated mechanism. Then the algorithm for inverse kinematic model is described. The inverse kinematic model uses damped least squares method which appears as suitable method for our purposes. The results of inverse kinematic solution is consequently used for direct kinematic model, which is described by homogeneous transformation matrices. The planar parallel mechanism is simulated in software Matlab and the results are expressed in the graphs as well as our approach is discussed in the conclusion.