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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.

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

We learn how to create smoothly varying orientation in 3D by interpolating Euler angles and Quaternions. In the MATLAB example starting at 5:44 I use the Quaternion class.  For Toolbox version 10 (2017) please use UnitQuaternion instead.

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.

The orientation of a body in 3D can be described by three angles, examples of which are Euler angles and roll-pitch-yaw angles. Note that in the MATLAB example at 8:24 note that recent versions of the Robotics Toolbox (9.11, 10.x) give a different result: >> rpy2r(0.1,0.2,0.3)ans = 0.9363 -0.2751 0.2184 0.2896 0.9564 -0.0370 -0.1987 0.0978 […]

We summarise the important points from this lecture.