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

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

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For real robots such as those with 6 joints that move in 3D space the inverse kinematics is quite complex, but for many of these robots the solutions have been helpfully derived by others and published. Let’s explore the inverse kinematics of the classical Puma 560 robot.

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We will introduce resolved-rate motion control which is a classical Jacobian-based scheme for moving the end-effector at a specified velocity without having to compute inverse kinematics.

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We learn a method for succinctly describing the structure of a serial-link manipulator in terms of its Denavit-Hartenberg parameters, a widely used notation in robotics.

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Let’s look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations. For RTB10.x please note that the mask value must be explicitly preceded by the ‘mask’ keyword. For example: >> q = p2.ikine(T, [-1 -1], ‘mask’, [1 1 0 0 0 0])

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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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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.