#### Analyzing a robot arm that moves in 3D

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We consider a robot with four joints that moves its end-effector in 3D space.

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We consider a robot with four joints that moves its end-effector in 3D space.

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We introduce the relationship between the velocity of the robot’s joints and the velocity of the end-effector in 3D space.

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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 a real 6-link robot our previous approach to computing the Jacobian becomes unwieldy so we will instead compute a numerical approximation to the forward kinematic function.

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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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We consider a robot, which has two rotary joints and an arm.

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We repeat the process of the last section but this time consider it as an algebraic problem.

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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 consider the simplest possible robot, which has one rotary joint and an arm.

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We revisit the simple 2-link planar robot and determine the inverse kinematic function using simple geometry and trigonometry.