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Foundations of Robot Manipulators

Introduction to Robotic Manipulators

Robot Links, Joints, and Degrees of Freedom

Coordinate Frames and Homogeneous Transformations

Denavit-Hartenberg Convention for Serial Robots

Forward Kinematics of Robotic Arms

Forward Kinematics Principles

Forward Kinematics for Planar Manipulators

Forward Kinematics for Spatial Manipulators

Inverse Kinematics and Workspace Analysis

Inverse Kinematics Principles

Analytical Inverse Kinematics for Planar Arms

Numerical Inverse Kinematics and Singularities

Jacobians and Differential Kinematics

Jacobian Matrices for Manipulators

Velocity Analysis Using Jacobians

Acceleration, Statics, and Force Relationships

Lagrangian Dynamics of Multi-Joint Manipulators

Dynamic Modeling Fundamentals

Kinetic and Potential Energy of Robot Links

Euler-Lagrange Equations for Manipulators

Lagrangian Dynamics for a Two-Link Planar Arm

Newton-Euler Dynamics and Applied Robot Analysis

Newton-Euler Formulation

Newton-Euler Dynamics for Serial Manipulators

Model Selection, Validation, and Practical Applications

Quiz

Question 1: Robot Manipulator Terminology

Question 2: Forward Kinematics

Question 3: Inverse Kinematics

Question 4: Jacobian Velocity Analysis

Question 5: Manipulator Dynamics

Survey and Feedback

Course Feedback Survey

Welcome to "Kinematics and Dynamics of Multi-Joint Robotic Manipulators," the definitive online course designed to bridge the gap between theoretical robotics and practical application. Whether you are an aspiring roboticist, a mechanical engineer, or a computer scientist looking to master robot motion, this comprehensive program will equip you with the mathematical and analytical tools required to understand, model, and control complex robotic arms.

Welcome to "Kinematics and Dynamics of Multi-Joint Robotic Manipulators," the definitive online course designed to bridge the gap between theoretical robotics and practical application. Whether you are an aspiring roboticist, a mechanical engineer, or a computer scientist looking to master robot motion, this comprehensive program will equip you with the mathematical and analytical tools required to understand, model, and control complex robotic arms. Throughout this course, you will dive deep into the foundational principles of robot manipulators, exploring everything from basic joint configurations to advanced dynamic modeling. We begin by demystifying coordinate frames and the Denavit-Hartenberg convention, laying the groundwork for forward and inverse kinematics. You will learn how to calculate precise end-effector poses and solve complex workspace challenges using both analytical and numerical methods. As you progress, the curriculum transitions into differential kinematics, where you will master Jacobian matrices to analyze velocity, acceleration, and static forces. Finally, you will tackle the core of robot dynamics through both Lagrangian and Newton-Euler formulations, enabling you to calculate joint torques, understand inertia, and optimize robot control systems. By the end of this course, you will possess the expertise to confidently analyze, model, and validate multi-joint robotic systems for real-world industrial and research applications. Join us to unlock the mechanics behind modern automation!

Kinematics and Dynamics of Multi-Joint Robotic Manipulators

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            <p>The study of multi-joint robotic manipulators requires a rigorous understanding of both their geometric motion and the underlying physical forces that govern their behavior. This course provides a comprehensive exploration of robot kinematics, beginning with foundational principles such as coordinate frames, homogeneous transformations, and the standard Denavit-Hartenberg convention. Participants will systematically analyze planar and spatial manipulators through the methodologies of forward and inverse kinematics, establishing the mathematical relationships between joint variables and precise end-effector poses. Furthermore, the curriculum delves into differential kinematics, utilizing Jacobian matrices to evaluate velocity, acceleration, and static force relationships while addressing critical operational constraints such as kinematic singularities and workspace limitations.</p>

<p>Beyond geometric and kinematic analysis, the accurate control, simulation, and design of robotic arms necessitate a profound comprehension of manipulator dynamics. The latter portion of this course focuses on formulating robust dynamic models utilizing two prominent methodologies: the energy-based Lagrangian approach and the recursive Newton-Euler formulation. By evaluating kinetic and potential energy, inertia, Coriolis effects, and gravitational impacts, learners will derive precise equations of motion for complex, multi-joint systems. Ultimately, the course synthesizes these theoretical frameworks, equipping participants with the analytical tools required for rigorous model selection, validation, trajectory planning, and the practical implementation of advanced robotic control strategies.</p>
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