## Rigid-Body Dynamics

In Robotics | No commentWe can factorise the joint torque expression into an elegant matrix equation with terms that describe the effects of inertia, Coriolis and centripetal and gravity effects.

We can factorise the joint torque expression into an elegant matrix equation with terms that describe the effects of inertia, Coriolis and centripetal and gravity effects.

In a serial-link manipulator arm each joint has to support all the links between itself and the end of the robot. We introduce the recursive Newton-Euler algorithm which allows us to compute the joint torques given the robot joint positions, velocities and accelerations and the link inertial parameters.

We start by considering the effect of gravity acting on a robot arm, and how the torque exerted will disturb the position of the robot controller leading to a steady state error. Then we discuss a number of strategies to reduce this error.

We will learn about the forces that are exerted on a robot’s joint by gravity acting on links, friction, and the coupling forces where the motion of one joint imparts a force on other joints.

This video gives Summary of Robot Actuators and Control.

In this video we will study the limits of electric motor performance.

We will use Simulink to create a dynamic model of a single robot joint and simulate its operation.

A robot joint controller is a type of feedback control system which is an old and well understood technique. We will learn how to assemble the various mechatronic components such as motors, gearboxes, sensors, electronics and embedded computing in a feedback configuration to implement a robot joint controller.

All mechanical systems exhibit friction and we learn about two broad classes of friction: linear and non-linear.

Electric motors are typically quite weak, they produce a low torque, so it’s very common to add a reduction gearbox.

We can model a DC motor as a resistor and a voltage source, and then understand the implications of controlling either the voltage or current supplied to the motor. We also learn about common methods for motor control such as the H-bridge driver and pulse width modulation.

If your knowledge of dynamics is a bit rusty then let’s quickly revise the basics of second-order systems and the Laplace operator. Not rusty? Then go straight to the next section.

The most common type of actuator is a rotary electric motor so let’s look at the basic principles.

Actuators are the components that actually move the robot’s joint. So let’s look at a few different actuation technologies that are used in robots.

A robot joint is a mechatronic system comprising motors, sensors, electronics and embedded computing that implements a feedback control system.

We will learn about how we make the the robot joints move to the angles or positions that are required in order to achieve the desired end-effector motion. This is the job of the robot’s joint controller and in this lecture we will learn how this works. This journey will take us in to the realms of control theory.

This video gives summary of Velocity kinematics in 3D.

A robot manipulator may have any number of joints. We look at how the shape of the Jacobian matrix changes depending on the number of joints of the robot.

Now we introduce a variant of the Jacobian matrix that can relate our angular velocity vector back to our rates of change of the roll, pitch and yaw angles.

We previously learnt how to derive a Jacobian which relates the velocity of a point, defined relative to one coordinate frame, to the velocity relative to a different coordinate frame. Now we extend that to the 3D case.