Forward Kinematics From Scratch

Key Insight

Forward kinematics answers the most basic question in robotics: given the angle of every joint, where in space is the hand? You compute it by multiplying one homogeneous transform per joint, walking outward from the robot's base frame to its end-effector, so the whole computation is just a chain of 4×4 matrix products. It is always solvable and always cheap — unlike inverse kinematics, its much harder mirror image — which is why coding it from raw NumPy and checking the result against a trusted library like Pinocchio is the rite of passage that makes Jacobians, control, and planning concrete later on.