Abstract
This chapter describes how to obtain the kinematic model of a robot manipulator using the basic Jacobian matrix. This model allows computing the linear and angular velocities of the end-effector in terms of the joint velocities. The Jacobian matrix can be decomposed into two or three matrices containing simpler terms. This chapter also illustrates how to use the Jacobian matrix to analyze the workspace and the velocity space of a robot. The chapter also demonstrates how to use the Jacobian matrix to obtain the static model and highlights the duality of this model with the kinematic model. Finally, the chapter establishes the kinematic models associated with the various representations of the task coordinates. The kinematic model can also be used to find a numerical solution to the inverse geometric problem for a general robot. The necessary tool to obtain this solution is the inverse kinematic model.
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