Zaid H. Rashid Supervisor Dr. Hassan M. Alwan Dynamic analysis and motion control of three link robot manipulator (open chain) Zaid H. Rashid Supervisor Dr. Hassan M. Alwan

Introduction The study focuses on the mechanics and control of the common important form of the industrial robot, the serial manipulator through the use of a three link articulated robot. The study is a merely collection of topics taken from mechanics (statics and dynamics), mathematics to describe the spatial motion, control theory to design and evaluating algorithms for desired motion or force application, electrical techniques in connecting electronics to interfacing the robot and computer programming for contributing these devices to perform a desired task.

Search objectives: Model the robot kinematics (forward, inverse , velocity and acceleration). Deriving the rigid body dynamics using Lagrange method. Design a PID controller to control the robot dynamics. Build a three link robot (open chain). Simulate and implement a planning motion.

Search topics Theoretical work Experimental work kinematics forward Inverse jacobian Dynamic equations Lagrange Euler Newton Euler Path planning Polynomials Non Polynomials control Linear PID Non-linear Experimental work Software (computer programs) MATLAB & MATLAB Simulink 3D CAD tool Hardware (robot building) Microprocessor board (Arduino , Rossberry,…etc) Links and actuators (servo motor , stepper motor,..etc)

kinematics Denavit—Hartenberg Notation will be used to produce transformation matrices . the fourth column describes the end effector position to base frame, and the 3*3 matrix represents the rotation matrix for end effector frame to base frame.

Inverse kinematics It’s the computation of the set of joint angles which achieve the desired position and orientation. By decoupling the problem into position and orientations of tool the problem can be solved by any of the following: 1- geometrical approach. 2- algebraic approach. 3- iterative technique N.R. As shown there are four configuration to reach the end effector position. End effector position Shoulder right Elbow up Elbow down Shoulder left

Jacobian The Jacobian is useful for : finding singularities. determining inverse kinematics algorithms. describing the mapping between forces applied to the end-effector and resulting torques at the joints (statics). deriving dynamic equations of motion. designing operational space control schemes. Gives the relationship between the joint velocities and the corresponding end-effector linear and angular velocity. It possible to compute the jacobian via differentiation of the direct kinematics function with respect to the joint variables. termed analytical Jacobian. Or from transformation matrcies with out differentiation, termed geometrical jacobian.

Dynamics The dynamic model of a manipulator provides a description of the relationship between he joint actuator torques and the motion of the structure. The lagrangian The equation of motion given by:

Control It relates the dynamics and kinematics of a robot to a prescribed motion. Path or trajectory planning is a part of control, in which we plan a path followed by the manipulator in a planned time profile. the motion can be controlled linearly with a PID technique or non Linearly with computed torque method.

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