M-1-MR1: Mathematics for Robotics-1

Introductory mathematics for robotics modelling General Notes

• Visualizations in MATLAB

Syllabus

Prerequisites

• Math 0
• Math 1

MODULE 1: Introduction

• Fundamental Jargon

Link: A link is a rigid body and is a single component of a mechanism that is used transmit motion and forces. Types: Rigid, Flexible and Fluid links. For this module, we shall restrict our discussion to rigid links. Common types of links - Binary, Ternary and Quaternary links.

Joint: A joint can be defined as the connection between two links that constrains their relative motion to a definite type. Main types of joints in robotics: Revolute joint and Prismatic joint; Other types of joints: Cylindrical, Helical, Spherical, Planar, and Universal joints.

Kinematic chain: A set of interconnected links and joints that produces a desired motion according to the constraints imposed by the joints.

Mechanism: A kinematic chain where one joint is fixed (also called the base).

<add an image of a 4-bar mechanism>

• Parts of a Robot A robot is a mechanical system composed of links connected by joints to form a kinematic chain, in which one link is fixed (the base) and the others can move relative to it to achieve a desired motion or task. The kinematic chain may be an open kinematic chain (for example, a robotic manipulator) or a closed kinematic chain (for example, a Stewart platform).

A robot is a mechanical system composed of links and joints to form a kinematic chain, in which one link is fixed (the base) and the other links can move relative to it to achieve a desired motion or task.

Note: The part of the definition of a robot, "a mechanical system composed of links and joints to form a kinematic chain, in which one link is fixed (the base)", can logically be truncated to the term 'mechanism'. The reason it's not done so is that the term 'kinematic chain' emphasises the geometric and mathematical relationships between links and joints (subject of interest when we study robot kinematics in the upcoming modules), while the term "mechanism" emphasises more on the mechanical function (which may be relevant in the area of mechanical design).

• Workspace and Taskspace
• Configuration Space (non-ModernRobotics)

MODULE 2: Transforms

• Frames
• Rotation Matrices
• Homogeneous Transformation Matrices
• Python Libraries

MODULE 3: Forward Kinematics

• Strict Trigonometry and its Drawbacks
• DH Method
  • Classical
  • Modified
• Python Code

MODULE 4: Inverse Kinematics

• Why Simply Inverting DH Doesn't Work
• Analytical Solutions
• Other Jargon

MODULE 5: A Better System

• Screw Theory vs HTM