THE JACOBIAN MATRIX BASED ON THE TRANSFER MATRICES

Adina CRISAN, Iuliu NEGREAN

Abstract


The main purpose of this paper is to present a mathematical model which can be applied to determine one of the most important differential matrix from robot kinematics also known as the Jacobian matrix or the velocities transfer matrix. The velocity of a robot link with respect to the previous link usually depends on the type of joint that connects them. The velocity of the end effector is a result of the contribution made by local velocities from each joint of the robot. The translation joint is characterized only by a linear velocity which is transferred to the end effector. In case of a rotation driving joint, both, angular velocity and linear velocity will be transferred at the end effector. In this paper is defined a  matrix called Jacobian matrix which establishes the mathematical relation between the velocities from each robot joint and the corresponding linear and angular velocities at a given point on the end-effector. Also, are presented the linear and angular transfer matrices based on which the Jacobian matrix is defined.  

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References


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Key words: kinematics, mechanics, Jacobian matrix, transfer matrix, robotics.


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