Do you want to know how robots work? Are you interested in robotics as a career? Are you willing to invest the effort to learn fundamental mathematical modeling techniques that are used in all subfields of robotics?
If so, then the "Modern Robotics: Mechanics, Planning, and Control" specialization may be for you. This specialization, consisting of six short courses, is serious preparation for serious students who hope to work in the field of robotics or to undertake advanced study. It is not a sampler.
In Course 2 of the specialization, Robot Kinematics, you will learn to solve the forward kinematics (calculating the configuration of the "hand" of the robot based on the joint values) using the product-of-exponentials formula. Your efforts in Course 1 pay off handsomely, as forward kinematics is a breeze with the tools you've learned. This is followed by velocity kinematics and statics relating joint velocities and forces/torques to end-effector twists and wrenches, inverse kinematics (calculating joint values that achieve a desired "hand" configuration), and kinematics of robots with closed chains.
This course follows the textbook "Modern Robotics: Mechanics, Planning, and Control" (Lynch and Park, Cambridge University Press 2017). You can purchase the book or use the free preprint pdf. You will build on a library of robotics software in the language of your choice (among Python, Mathematica, and MATLAB) and use the free cross-platform robot simulator V-REP, which allows you to work with state-of-the-art robots in the comfort of your own home and with zero financial investment.
Chapter 4: Forward Kinematics
Product of exponentials formula for forward kinematics in the space frame and the end-effector frame.
Chapter 5: Velocity Kinematics and Statics
Velocity kinematics using the space Jacobian and body Jacobian, statics of open chains, singularities, and manipulability.
Chapter 6: Inverse Kinematics
Analytical and numerical inverse kinematics.
Chapter 7: Kinematics of Closed Chains
Forward kinematics, inverse kinematics, velocity kinematics, and statics of closed chains.