 ## 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.

## Inverting the Jacobian Matrix

By inverting the Jacobian matrix we can find the joint velocities required to achieve a particular end-effector velocity, so long as the Jacobian is not singular.

## Velocity of 2-Joint Planar Robot Arm

For a simple 2-link planar robot we introduce and derive its Jacobian matrix, and also introduce the concept of spatial velocity.

## Rate of Change of Pose in 2D

We introduce the relationship between the velocity of the robot’s joints and the velocity of the end-effector in 3D space.

## 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.

## Summary of Inverse Kinematics

This video gives summary of inverse kinematics.

## Cartesian interpolated Motion

An alternative for smooth motion between poses is Cartesian interpolated motion which leads to straight line motion in 3D space.

## 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.

## Redundant Robots

For a redundant robot the inverse kinematics can be easily solved using a numerical approach.

## Reachability and Singularity

For real robots there are a few extra things to think about. Is a particular point actually reachable? Our old friend, singularity or gimbal lock reappears in the wrist.

## Numerical Inverse Kinematics

Let’s look at numerical approaches to inverse kinematics for a couple of different robots and learn some of the important considerations.

## Different Approach to Solving Inverse Kinematics

To simplify the inverse kinematics most robots have a spherical wrist, a particular mechanical wrist design. For robots where the inverse kinematics is too hard to figure out we can solve the problem numerically, treating it as an optimisation problem.

## Robot Arm Configuration Change

A characteristic of inverse kinematics is that there is often more than one solution, that is, more than one set of joint angles gives exactly the same end-effector pose.

## Inverse Kinematics for a General Purpose Robot Arm that moves in a 3D

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.

## Inverse Tanget Function

A really important function when performing inverse kinematics is the inverse tangent or arctan function. We revise how this function works for angles in all quadrants of the circle and introduce a useful variant known as atan2.

## Inverse Kinematics for 2-Joint Robot Arm using Algebra

We repeat the process of the last section but this time consider it as an algebraic problem.

## Inverse Kinematics for 2-Joint Robot Arm using Geometry

We revisit the simple 2-link planar robot and determine the inverse kinematic function using simple geometry and trigonometry.

## Introduction to Inverse Kinematics

We will learn about inverse kinematics, that is, how to compute the robot’s joint angles given the desired pose of their end-effector and knowledge about the dimensions of its links. We will also learn about how to generate paths that lead to smooth coordinated motion of the end-effector.

## Summary of Robot Manipulator Arms

This video gives summary of Robot Manipulator Arms.

## What is Kinematics?

This lecture has been about kinematics and we define that term.