THE JACOBIAN MATRIX BASED ON DIFFERENTIAL MATRICES

Adina CRISAN, Iuliu NEGREAN

Abstract


The present paper aims to present a mathematical model of determining the Jacobian matrix by using the differential matrices of the homogenous transformations. The expressions for the Jacobian matrix were developed using the differential matrices of first and second order and are obtained by differentiating the expressions for the locating matrices that define the transformations between the systems. Based on these, are determined the expressions for the Jacobian matrix with projections on the fixed and mobile system. The role of Jacobian matrix is to establish the connection between the generalized velocities and operational velocities, both defining the forward kinematics equations for any robot mechanical structure.

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Key words: kinematics, Jacobian matrix, robotics, kinematics, differential matrix.


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