Computation of Lethal and Non-Lethal Angles of a Spherical Robotic Arm Manipulator from Localized Object Using Homogenous Transformation Matrix Method

Godwin A. Otu, Alabi P. Akubo, Obunike A Ubadike, Stephen E. Iheagwara, Ubadike Osichinaka Chiedu

Abstract: The effectiveness of a robotic arm is for joint angles to align so that the end-effector will position itself with reference to the base frame. This can be used in many applications like car wash system, car spray system, vehicle loading and off-loading systems, since the position of the target object is localized. In this research, the homogenous transformation matrix is effectively used to accurately compute the rotation of each of the joint angles from the base frame to the end-effector frame. Given the joint lengths and the object position, the angles which will perfectly locate and handle the object without harming the object and the end-effector with the ones which can harm both the object and the end-effector can be derived. The product of all the transformation matrices and all the frames from the base frame to the last frame is evaluated. Direct kinematics formulates how these joint angles can be determined from the position vector and given joint lengths while the excel application was used to demonstrate the angle variations and the corresponding effect on the end-effector.

Keywords: direct kinematics, end-effector, homogenous transformation matrix, joint angles, position vector, robotic arm