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Motion in 3D

A body moving in 3D space has a translational velocity and a rotational velocity. The combination is called spatial velocity and is described by a 6-element vector.  

Introduction to Velocity Kinematics in 3D

We will learn about the relationship, in 3D, 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. To do this in 3D we need to learn about rate of change of orientation and the concept of angular velocity.  

Velocity Ellipse in 2D

The end-effector is not able to move equally fast in all directions, and that in fact depends on the pose of the robot. We will introduce the velocity ellipse to illustrate this.  

Introduction to Velocity kinematics in 2D

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.  

Joint Interpolated Motion

To move a robot smoothly from one pose to another we need smooth and coordinated motion of all the joints. The simplest approach is called joint interpolated motion but it has some limitations.  

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