INTERNATIONAL JOURNAL OF MECHANICAL ENGINEERING AND TECHNOLOGY (IJMET) International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 6340(Print), ISSN 0976 6340 (Print) ISSN 0976 6359 (Online) Volume 5, Issue 3, March (2014), pp. 20-30 IAEME: www.iaeme.com/ijmet.asp Journal Impact Factor (2014): 7.5377 (Calculated by GISI) www.jifactor.com IJMET I A E M E ADVANCEMENT AND STIMULATION OF FIVE DEGREE OF FREEDOM ROBOT LEVER ARM Saifuldeen Abed Jebur 1, Prabhat Kumar Sinha 2, Ishan Om Bhargava 3 1 Automation & Systems Research Center /Industrial Development & Research Directorate / Ministry of Science and Technology of republic Iraq.+ Department of Mechanical Engineering (SSET), Sam Higginbottom Institute of Agriculture Technology and Sciences, Allahabad U.P (INDIA) 2 Department of Mechanical Engineering (SSET), Sam Higginbottom Institute of Agriculture Technology and Sciences, Allahabad U.P (INDIA) 3 Department of Mechanical Engineering (SSET), Sam Higginbottom Institute of Agriculture Technology and Sciences, Allahabad U.P (INDIA) ABSTRACT In this article the development of virtual software package, where a Robot Lever arm has been taken as a case study. MATLAB will be used for testing motional kinematics. It has adopted the design methodology as a tool for analyzing characteristics of the Robot lever arm. Moreover, the model analysis is carried in order to analyze through kinematics and testing the virtual arm by comparing between the approaches applied to the arm in terms of kinematics. The development of this robot lever arm is used as an guide tool in enhancing the applied experimental research opportunities and improving it s application. KEYWORDS: Modeling, MATLAB, Robot Lever Arm, Kinematics. INTRODUCTION Over the last two decades, artificial intelligence has been based on mobile robotics and promoted the development of lever arm. The goal of this research work is to design and develop a five degree of freedom robot lever arm for determining it s motional characteristics using MATLAB. The robot lever arm is chosen as a case study in this research. MATLAB will be used for testing motional characteristics of the arm. A complete study and mathematical analysis for the kinematics, is presented and implemented. This is implemented and applied to the robot lever arm and it s physical characteristics. A comparison between the kinematic solutions of the robot arm s physical motional behavior is discussed. Many industrial robot arms are built with simple 20
geometries such as intersecting or parallel joint axes to simplify the associated kinematics computations [MAN 01]. Papers that developed software for modeling 2D and 3D robots arm such as [MAN 01, KOY 02 and GUR 03], Kinematics is analyzed by [PAS 04] using V-Realm Builder 2.0 for virtual reality prototyping and testing the of designs before the implementation phase of the robot. Martin and Arya in [ROH 05, WIR 06], developed Robot Simulation Software for forward and inverse kinematic using VRML and MATLAB. [JAM 07] reported the development of the software for robot. [KOL 08] has presented on educational purposes in Education Conferences. The work has adopted the virtual reality interface design methodology utilizing MATLAB. It started from the kinematics of the robot arm taking into consideration the position and orientation of robot joint. This research is on the kinematical and mathematical analysis of the robot lever arm. The focus of this paper is on developing components related to MATLAB. KINEMATIC MODELLING For the robot lever arm analysis is done, its purpose is to carry the analysis of the movements of each part of the lever arm mechanism. The kinematics analysis is divided into forward and inverse kinematic analysis. The forward kinematics consists of finding the position of the arm in the space knowing the movements of its joints as F (θ1,θ2,,θn ) = [ x, y, z, R], and the inverse kinematics consists of determining the joint variables corresponding to a given position and orientation as F ( x, y, z, R)= θ1,θ2,,θn. Figure shown below shows a simplified block diagram of kinematic modeling. Forward Kinematic Joints Movements Geometric Parameters Position and Orientation of the end-effector Inverse Kinematics KINEMATIC MODELLING BLOCK DIAGRAM A commonly used convention for selecting frames of reference in robotic applications is the Denavit Hartenberg. In this convention each homogenous transformation Ti is represented as a product of four basic transformations. The kinematics analysis is divided into two solutions, the first one is the solution of Forward kinematics, and the second one is the inverse kinematics solution. Forward kinematics has been determining the position of robot lever arm if all joints are known. Where as the inverse kinematics is being used to calculate what each joint variable must be if the desired position and orientation of end point is determined. Hence, Forward kinematics is defined as transformation from joint space to Cartesian space where as Inverse kinematics is defined as transformation from Cartesian space to joint space. 21
A commonly used convention for selecting frames of reference in robotic applications is the Denavit Hartenberg frame. In this convention each homogenous transformation is represented as a product of four basic transformations. T i =,,,, COORDINATE FRAME Where the notation Rot (x, α ) stands for rotation about x axis by α, Trans(x, α ) is translation along x i axis by a distance α i, Rot(z, θ i ) stands for rotation about ez i axis by θ i, and Trans(z, d i ) is the translation along z i axis by a distance d i. 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0 0 = 0 Where the four quantities θ i, a i, d i, α i are the parameters of link i and joint i. The description below illustrates the link frames attached so that frame {i} is attached rigidly to link i. The various parameters in previous equation are given the following are (Length) is the distance from to, measured along ; (Twist), is the angle between and, measured about ; (Offset), is the distance from to measured along ; and (Angle), is the angle between measured about ; In the usual case of a revolute joint, the joint variable with the other three quantities are fixed. The matrix notation used is homogeneous.here H represents a rotation by angle α about the current x-axis followed by a translation of units along the x-axis, followed by a translation of d units along the z-axis, followed by a rotation by angle θ about the z-axis, which is 22
H=,,,, = 0 The most general homogeneous transformation is of the form = = Where the three by three augmented matrix, [R 3x3, represents the rotation, the three by one augmented matrixes, d 3x1, represent the translation; the f 1x3 represents the perspective transformation and S 1x1 is the factor. The direct kinematics made from the composition of homogeneous transformation matrices, where each rotation corresponds to one four by four augmented matrix: MODELING THROUGH MATLAB Our main motive is to investigate and to develop the robot lever arm using MATLAB. The Hartenberg analysis is the most approximate, method for using the direct kinematics using relevant parameters that have been used. In this, analysis, there is a defined coordinate transformation between two frames, where the position and orientation are fixed one with respect to the other and it is possible to work with homogeneous matrix transformations... THE KINEMATIC LINK DIGRAM 23
is a homogenous matrix which is defined to transform the coordinates of a point from frame i to frame i-1. The matrix is not constant, but varies as the configuration of the robot lever arm is changed. However, the assumption that all joints are either revolute or prismatic means that is a function of only a single joint variable, namely qi. The homogenous matrix that transforms the coordinates of a point from frame i to frame j is denoted by (i > j). Denoting the position and orientation of the end joint with respect to the inertial or the base frame by a three dimensional vector and a 3x3 rotation matrix, respectively, we define the homogenous matrix as 0 1 Then the position and orientation of the end joint in the inertial frame has been mentioned as,,.,. Each homogenous transformation is of the form of Hence 0 1 0 1 The matrix expresses the orientation of frame i relative to frame j (i > j) and is given by the rotational parts of the -matrices (i > j) as. The vectors (i> j) are given recursively by the formula THE COORDINATE FRAME Robot lever arm has five rotational joints and a moving grip. Joint 1 represents the shoulder and its axis of motion is z1. This joint provides a angular motion around z 1 axis in x 11 plane. Joint 2 is identified as the Upper Arm and its axis is perpendicular to Joint 1 axis. It provides a rotational angular motion around z2 axis in x2y2 plane. Z3axes of Joint 3 and Joint 4 are parallel to Joint 2. z-axis provides and angular motions in x3y3 and x4y4 planes respectively. Joint five are identified as the grip rotation. And it s z5 axis is vertical to z4 axis and it provides angular motions in x5y5 plane. A graphical view of all the joints has been presented below. 24
THE PARAMETERS COORDINATE FRAME OF ROBOT LEVER ARM The Denavit-Hartenberg analysis is preferred and is the most approximate method.the direct kinematics is determined from some parameters that have been defined, for each mechanism. The homogeneous transformations and matrix has been used for analysis, for coordinate transformation between two frames, where the position and orientation are fixed one with respect to the other it is possible to work with elementary homogeneous transformation operations. D-H parameters for AL5B defined for the assigned frames. i 1 0 0 d 2 90 0 0 3 0 a 0 4 0 a 0 ( -90) * 5-90 0 d 6 0 0 0 Gripper By substituting the parameters from into coordinate equation the transformation matrices T1 to T6 can be obtained. 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 25
0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 Now the link transformations can be calculated to find the single transformation that is relating frames The transformation given here is a function of all five variables. From the robots joint position, the coordinate position and orientation of the last link is computed.the orientation and position of are calculated using: n s c c s s s c s c s s s c s c c s _ )+ _ _ = + KINEMATIC ANALYSIS THROUGH MATLAB In the kinematic window displayed below the main purpose is to compute the position of end joint by entering the angle values.this is the done through the use of MATLAB module. This gives the resulting matrices. 26
LEVER ARM COORDINATE ARRANGEMENT KINEMATIC ANALYSIS USING MATLAB MODULE In this study mathematical and kinematic modeling analysis is done for the lever arm. Robot arm has been mathematically modeled through Hartenberg method using kinematics and is furthered analyzed through MATLAB. 27
RESULT The experimental results of modeling through MATLAB have been analyzed and are used for the robot lever arm physical characteristic analysis. THE KINEMATIC MODULE A initial position angle MATLAB module is given below with zero 0, 0,1,2,,5. The transformation matrix is given and this matrix gives the initial position and orientation of the robot arm. THE INITIAL POSITION KINEMATIC MODULE 0 0 1 347 0 1 0 0 1 0 1 70 From the above matrix we find that the (x, y, and z) position of the end position is equal to (347, 0, and 70). 28
INITIAL ORIENTATION OF LEVER ARM When the following angular are taken for the up position the following matrix is obtained Matrix, T which is the orientation of the base of lever arm is shown. 0.63 0.47 0.61 211 0.76 0.23 0.61 211 0.15 0.85 0.5 205 This equation gives the following module which is [x, y, and z] = [211, 211, and 205]. is analyzed through MATLAB and is the final kinematic solution of the robot arm. INITIAL POSITION OF LEVER ARM 29
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