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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.  

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.  

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.  

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.  

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.  

Robot Workspace

The workspace of a robot arm is the set of all positions that it can reach. This depends on a number of factors including the dimensions of the arm.  

Base and Tool transforms

The pose of the working part of a robot’s tool depends on additional transforms. Where is the end of the tool with respect to the end of the arm, and where is the base of the robot with respect to the world?  

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