#### Velocity of 3-Joint Planar Robot Arm

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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 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 with three joints that moves its end-effector on a plane.

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Time varying coordinate frames are required to describe how the end-effector of a robot should move to grab an object, or to describe objects that are moving in the world. We make an important distinction between a path and a trajectory.

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The Jacobian matrix provides powerful diagnostics about how well the robot’s configuration is suited to the task. Wrist singularities can be easily detected and the concept of a velocity ellipse is extended to a 3-dimensional velocity ellipsoid.

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We learn how to describe the position and orientation of objects in the 3-dimensional space that we live in. This builds on our understanding of describing position and orientation in two dimensions.

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The linear algebra approach we’ve discussed is very well suited to MATLAB implementation. Let’s look at some toolbox functions that can simulate what cameras do. If you are using a more recent version of MVTB, ie. MVTB 4.x then please change>> cam.project(PW βTcamβ, transl(0.1, 0, 0)) to >>Β cam.project(PW βposeβ, transl(0.1, 0, 0)).

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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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The simplest smooth trajectory is a polynomial with boundary conditions on position, velocity and acceleration.

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The orientation of a body in 3D can also be described by a unit-Quaternion, an unusual but very useful mathematical object. In the MATLAB example starting at 3:48 I use the Quaternion class. Β For Toolbox version 10 (2017) please use UnitQuaternion instead.

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A problem arises when using three-angle sequences and particular values of the middle angle leads to a condition called a singularity. This mathematical phenomena is related to a problem that occurs in the physical world with mechanical gimbal systems. Note that in Robotics, Vision & Control (second edition) and RTB10.x the default definition of roll-pitch-yaw […]