LESSON

# Introduction to velocity kinematics in 2D

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In this lecture, what I want to do is talk about the velocity of the robot's end-effector. So the last couple of lectures, we have looked at concepts like forward kinematics and forward kinematics is the relationship between the joint angles and the robot's end-effector pose, so I put in the joint angles and I get out the end-effector pose.

The inverse kinematics is sort of the opposite. I say what I want the end-effector pose to be and what comes out of the algorithm of the joint angles that I need in order to achieve that end-effector pose.

The problem, what we are going to talk about in this particular lecture is velocity transform. If the joints move at this particular velocity, what is the velocity of the robot's end-effector and you note that I have written the velocity of the joints as q-dot, so dot represents the time rate of change. It is a common notation in differential calculus and the pose of the robot's end-effector I have been using this symbol, psi E, to represent the pose of the end-effector and we have talked about how that is combination of position and orientation.

So, in this particular case, what we are talking about now is cosine dot. We are talking about the rate of change of a pose and that is an interesting and not necessarily intuitive thing; so first of all we are going to talk about what does the rate of change of a pose mean, what kind of mathematical object do we use to represent that and then what is the relationship between that thing, the psi dot, and the rate of change of the joint angles of the robot itself.

So, that is what this lecture is about. It is about understanding relationship between velocity of the joints and the rate of change of pose.

We will learn about the relationship, in 2D, between the velocity of the joints and the velocity of the end-effector — the velocity kinematics. This relationship is described by a Jacobian matrix which also provides information about how easily the end-effector can move in different Cartesian directions.

### Skill level

Undergraduate mathematics

This content assumes high school level mathematics and requires an understanding of undergraduate-level mathematics; for example, linear algebra - matrices, vectors, complex numbers, vector calculus and MATLAB programming.