ISSN ONLINE(23198753)PRINT(23476710)
Faijubhai R.Malek Assistant Professor, Dept of Mechanical Engineering, G.H.Patel College of Engineering and Technology, VallabhVidya Nagar, Gujarat, India 
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In this paper forward kinematic analysis and differential motion analysis of the SCOROT ER Vplus robotic system, which is a 5 d.o.f articulated robotic manipulator, following a specified trajectory is reported. Forward kinematic analysis uses DH formulation and Differential motion uses Jacobians and determines angular positions and endeffector‟s translational and angular velocity at each via point of its trajectory in the Cartesian space coordinates respectively. A trajectory passing through initial point, lift off point, set down point and final point is interpolated in the joint space using cubic splines. The trajectory scheme assumes two more intermediate points on trajectory. Thus, there are five segments of the entire trajectory. A MATLAB source code is developed to obtain all the kinematics parameters and important conclusions are reported from the values obtained.
Keywords 
Robot, Forward Kinematics, Jacobians, DH matrix, Trajectory.Introduction. 
Nomenclature 
Ve is a (6 x 1) vector of endeffectorâs translational and angular velocity with respect to fixed base 
J(q) is a (6 x n) matrix known as a jacobian matrix relative to fixed base 
q is a (n x 1) vector representing rotational velocities of various joints of robot 
n is a number showing degrees of freedom of the robot 
i1Ti a transformation matrix relating coordinate frame {i} with the frame {i1} 
5j jacobian matrix relative to the tool frame {5} 
INTRODUCTION 
The motion of an industrial robot manipulator is generally specified either in terms of the motion of various joints of the manipulator or that of the endeffectors in the Cartesian space. An accurate direct measurement of endeffectorâs position is a complex task and the implementation of a motion control system in Cartesian space can be very difficult. Thus, in practice motion of various joints is converted in the endeffectors motion using forward kinematics. 
Kinematic parameters are necessary to consider in design and specifications planning, in trajectory planning (programming), and in dynamic computations. A common feature of many of the application problems is the fact that the position of the arm end (end effectors) is frequently described by the user in Cartesian world coordinates [9]. 
Robot arm kinematics deals with the analytic study of the geometry of motion of a robot arm with respect to a fixed reference coordinate system as a function of time without considering the forces and/or moments that cause the motion. Thus, it deals with the analytical description of the spatial displacement of the robot as a function of time, in particular the relations between the joint variable space and the position and orientation of the robotâs endeffectors [5]. 
However, control of link motions is achieved through driving and measuring (for the feedback purposes) of joint coordinates. If the kinematic parameters of the end effectors are expressed in terms of joint parameters, the transformation is called direct or forward kinematics. 
As a rule, the endeffectors of a robot is programmed to follow a set of desired positions and orientations in the Cartesian space. When it is required to determine how each infinitesimal joint motion affects the infinitesimal motion of the manipulator endeffectors, one has to develop a mapping scheme between the joint motion and the corresponding endeffectorâs motion. This mapping is defined by a jacobian. 
The forward kinematics at the differential level can be represented by a linear system, 
APPLICATION 
A numerical example has been developed by referring to a SCORBOT ERVplus robot [8] with five revolute joints. The illustrative manipulator task consists of transporting an object from an initial point to a final one. In this task the robot first lift the object from the initial point to an intermediate point called „liftoffâ point. From this point it brings it to another intermediate point called „setdownâ point, which comes just before the final point. The robot joint positions for these four points are given in table2. 
The trajectory passing through these points is interpolated in the joint space using cubic splines. This trajectory scheme assumes two more intermediate points on the trajectory. Thus there are five segments of the entire trajectory. 
CONCLUSIONS 
This paper presents a general method of carrying out differential motion analysis of a robot manipulator of industrial type, considering its geometric and kinematic parameters. The joint trajectories have been modeled using 5cubic type of trajectory planning scheme whose coefficients have been determined by using MATLAB codes. Proper trajectory between given initial and final point of the robot hand motion is of considerable importance. The trajectory should give a smooth motion of joints and hence robot hand. Moreover, minimum jerk trajectory is desirable for its similarity to human joints movements and to limit excessive wear on the robot and the excitation of resonance so that the robot life span is long. 
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