#### Velocity of 6-Joint Robot Arm – Rotation

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We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

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We resume our analysis of the 6-link robot Jacobian and focus on the rotational velocity part.

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We have a quick revision of the skew-symmetric matrix. If you’re comfortable with this topic then go straight on to the next section.

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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.

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We can also derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame.

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We extend what we have learnt to a 3-link planar robot where we can also consider the rotational velocity of the end-effector.

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The end-effector is not able to move equally fast in all directions, and that in fact depends on the pose of the robot. We will introduce the velocity ellipse to illustrate this.

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By inverting the Jacobian matrix we can find the joint velocities required to achieve a particular end-effector velocity, so long as the Jacobian is not singular.

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For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.

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For real robots there are a few extra things to think about. Is a particular point actually reachable? Our old friend, singularity or gimbal lock reappears in the wrist.

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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.