6340(Print), ISSN (Online) Volume 4, Issue 3, May - June (2013) IAEME AND TECHNOLOGY (IJMET) MODELLING OF ROBOTIC MANIPULATOR ARM

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1 INTERNATIONAL International Journal of JOURNAL Mechanical Engineering OF MECHANICAL and Technology (IJMET), ENGINEERING ISSN 0976 AND TECHNOLOGY (IJMET) ISSN (Print) ISSN (Online) Volume 4, Issue 3, May - June (2013), pp IAEME: Journal Impact Factor (2013): (Calculated by GISI) IJMET I A E M E MODELLING OF ROBOTIC MANIPULATOR ARM Srushti H. Bhatt 1, N. Ravi Prakash 2, S. B. Jadeja 3 1 Mechanical Engineering Department, B. H. Gardi, College of Engineering & Technology, Rajkot, Gujarat, India 2 RHRTD Group, Institute for Plasma Research, Gandhinagar, Gujarat, India 3 Mechanical Engineering Department, B. H. Gardi, College of Engineering & Technology, Rajkot, Gujarat, India ABSTRACT Kinematic modelling is an important section of robotic technology.the method was used for three link arm manipulator. The kinematic modelling of the three link arm manipulator with end effector was carried out. In this paper D-H matrix is used to solve kinematic equations of robot. The dynamic forces are calculated for the maximum stretch condition using multi body dynamics analysis. The results validated using the software analysis andthe mathematical formulation. Keywords Forward kinematics, Denavit-Hartenberg (D-H) model, Multi body dynamics 1. INTRODUCTION Kinematics & dynamics are important section of engineering, related to development of special application of robots. Kinematicsconcentrates on motion of robots independent of forces acting on it whereas Dynamics deals with the relationship between motion and the associated forces and torques.the aim of kinematics is to define position relative to reference frame & its origin. It is divided into two parts inverse kinematics and forward kinematics. Forward kinematics deal with finding position and orientation of robot end effector as function of its joint angle. Inverse kinematics deals with finding appropriate joint angles to get a certain desired position and orientation of the end effector. 125

2 International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 Simulation work was carried out for a robotic manipulatorarm withtwo two arm each having 3 degree of freedom.high High torque dc motors were used as actuation system. The joint angle was given using the potentiometer and final position obtained. Denavi Denavit Hartenberg representation of forward kinematic was used. In Multibody dynamics analysis, dynamics of mutually-interconnected interconnected multiple rigid bodies is studied. The work involved mathematical formulation &software analysis tofind find how bodies move as a system and what forces are generated in the process with static analysis analysis. The forward dynamic problem yields the motion of a Multibody system over a given time interval, as a consequence of the applied forces and given initial conditions. 2. MODEL OF ROBOT The dual arm robotic manipulator as a whole possesses possesses nine degree of freedom. The manipulator system was created using 3d cad Catia software as shown in the figure below. The manipulator arm carries payload 1.2 kg. Analytical forces were calculated at each joint for manipulator pulator arm shown in Figure II. Figure II: 3d Cad Model Of Manipulator Figure II: Manipulator Arm 126

3 3. METHODOLOGY 3.1 D-H Parameters The D-H model of representation is very simple way of modelling robot link and joints that can be used for any robot configuration, regardless of sequence and complexity. The D-H representation of rigid link is classified into four parameters, two link parameters (a i, αi) and two joint parameters (d i, θ i ). Link Length (ai) Link Twist (αi) Joint Distance (di) Joint Angle (θi) The arms are symmetric to each other&the results are described using appropriate data. TABLE I: D-H PARAMETER FOR MANIPULATOR ROBOT Joint i θ i d i (mm) a i (mm) α i 0 θ θ θ θ Forward Kinematic Relationship Between Adjacent Link & Its Solution On establishing D-H parameters on link homogeneous transformation matrix calculation were done. Four basic parameters for the matrix are rotation about z i-1 by an angle θ i, translation about z i-1 axis by distance d i, translation along x i axis by distance a i, and rotation about x i axis by an angle α i. A i = Rot(z, θ i )Trans(z, d i )Trans(x, a i )Rot(x, α i ) So the resultant T matrix is, T = T n = A 1 *A 2 *A 3 *A 4 : T=

4 Now calculating the static force acting at each joint of arm. The mathematical basic equations are formulated for finding force acting at each joint. The solution of the force value at each joint is as formulated below in table. TABLE II: MATHEMATICAL FORMULATION FOR FORCE Link Weight (kg) Length (mm) Force, mg (N) Mathematical solutions were compared with hyper work. The Motion View module was taken for multi body dynamic analysis. The software is validated for the robustness, speed, and quality.the analysis was carried out by importing the 3d cad model to the motion view and MBD static analysiss was carried for the maximum stretch condition of the manipulator arm.the results are displayed here. Figure III: MBD Analysis Using Software 128

5 4. RESULTS SN 5. CONCLUSION TABLE III: FORCE RESULT COMPARISON EXPERIMENTAL JOINTS RESULTS FOR FORCE SOFTWARE RESULTS OF FORCE 1 Joint Joint Joint This paper solves and formulates the kinematic problem of the link with base for the manipulator using D-H notation. Payload characteristic has been analysed using static force equation & also simulation studies carried out using hyper works software as a proof of concept. Both results are in good agreement. This result helps to choose proper actuators in the application of pick and place robot. 6. ACKNOWLEDGMENT The author acknowledges Institute for Plasma research, NFPfor giving financial support, infrastructure & necessary guideline which enabled to set up my experimental work. These supports are gratefully acknowledged. REFERENCES [1] Saeed B. Niku, "Introduction to Robotics", Pearson Prentice Hall, 2008, pg [2] R K Mittal, J Nagrath, "Robotics and Control", Tata McGraw-Hill, 2005, pp [3] Dr. Anurag Verma and Vivek A. Deshpande. End-effector Position Analysis of SCORBOT-ER Vplus Robot, International Journal of Smart Home Vol. 5, No. 1, January, [4] Mahmoud Gouasmi, Mohammed Ouali, Brahim Fernini and M hamed Meghatria. Kinematic Modelling and Simulation of a 2-R Robot Using SolidWorks and Verification by MATLAB/Simulink, International Journal of Advanced Robotic Systems 26 May [5] Peng Song Modelling, Analysis and Simulation of Multibody systems with contact and friction