## Reachability and Singularity

In Robotics | No commentFor 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.

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.

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

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.

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.

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.

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.

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

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

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.

This video gives summary of Robot Manipulator Arms.

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

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.

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?

We learn a method for succinctly describing the structure of a serial-link manipulator in terms of its Denavit-Hartenberg parameters, a widely used notation in robotics.

We learn the concepts of a robot’s task space and its configuration space, and the relationship between the dimensions of these two spaces.

We consider the most general type of serial-link robot manipulator which has six joints and can position and orient its end-effector in 3D space.

We consider a robot with four joints that moves its end-effector in 3D space.

We consider a robot with three joints that moves its end-effector on a plane.

We consider a robot, which has two rotary joints and an arm.

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