Foundation of Robot Kinematics: Mathematical Modeling for Robotics

Have you ever wondered how robotic arms calculate their exact movements in three-dimensional space? This text-based course introduces you to the foundational mathematical models and kinematic principles that power modern robotics. You will transition from basic geometric concepts to advanced spatial representations, gaining the skills to model and analyze the motion of robotic manipulators. By studying clear written explanations and step-by-step mathematical derivations, you will learn how to describe positions, orientations, and joint movements with absolute precision. What you'll learn: Learn the core concepts of degrees of freedom and rigid-body motion in space. Represent rotations and translations using rotation matrices and homogeneous transformations. Formulate forward kinematics using modern Product of Exponentials (PoE) and Denavit-Hartenberg parameterizations. Calculate inverse kinematics to determine the joint angles required for target tool positions. Analyze velocity kinematics using Jacobians to map joint speeds to end-effector velocities. Apply these mathematical models to modern collaborative robots and industrial manipulators. The course begins with fundamental definitions of space and motion, gradually building up to complex multi-joint kinematic chains and velocity profiles. It is designed specifically for beginners, engineers, and students looking for a structured, mathematical entry point into robotics without requiring prior advanced robotics experience. Start reading today to build a solid mathematical foundation for your robotics career.