#### Jacobian and Number of Robot Joints

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A robot manipulator may have any number of joints. We look at how the shape of the Jacobian matrix changes depending on the number of joints of the robot.

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A robot manipulator may have any number of joints. We look at how the shape of the Jacobian matrix changes depending on the number of joints of the robot.

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We learn the concepts of a robot’s task space and its configuration space, and the relationship between the dimensions of these two spaces.

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The workspace of a robot arm is the set of all positions that it can reach. This depends on a number of factors including the dimensions of the arm.

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For a redundant robot the inverse kinematics can be easily solved using a numerical approach.

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Let’s recap the important points from the topics we have covered about light, wavelength, spectrums, light sources, reflection, reflectance functions, cone cells, tristimulus and chromaticity space.

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An alternative for smooth motion between poses is Cartesian interpolated motion which leads to straight line motion in 3D space.

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As the illumination level changes so do the red, green and blue tristimulus values, but they are linearly related. We can separate brightness from chromaticity which is a two dimensional representation of color. We discuss briefly the effect of gamma encoding on the color reproduction process.

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To move a robot smoothly from one pose to another we need smooth and coordinated motion of all the joints. The simplest approach is called joint interpolated motion but it has some limitations.

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We learn to compute a trajectory that involves simultaneous smooth motion of many robot joints.

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A body moving in 3D space has a translational velocity and a rotational velocity. The combination is called spatial velocity and is described by a 6-element vector.