FABRIK
An iterative inverse-kinematics solver that drags a bone chain toward its target back and forth along the joints instead of computing angles.
FABRIK (Forward And Backward Reaching Inverse Kinematics) treats the chain as points at fixed distances. A backward pass first moves the end — the hand or the foot — exactly onto the target and then pulls each earlier joint after it, keeping bone lengths; a forward pass re-anchors the root and works outward. The passes repeat until the end is close enough, usually after a handful of rounds.
Andreas Aristidou and Joan Lasenby published the method in 2011. Its strength is that it avoids matrices and trigonometry entirely and simply moves points, which makes it fast, stable and free of the jumps that hit Jacobian-based solvers near singularities. It is widely used in games and VR for arms, legs, spines and tentacles, and handles long chains better than most alternatives.