Differential inverse kinematics is a core robotics problem whose state-of-the-art solutions are currently based on quadratic programming. In this paper, we revisit it from the perspective of augmented Lagrangian methods (AL) and the related alternating direction method of multipliers (ADMM). By embracing AL techniques in the spirit of the rigid-body dynamics algorithms proposed by Featherstone, we introduce a method that solves equality-constrained differential IK problems with linear- time complexity. Combined with the ADMM strategy popularized by OSQP, we handle the same class of problems as QP-based differential IK, but scaling linearly with problem dimensions rather than cubically. We implement our approach as C++ open- source software and evaluate it on a benchmark of robotic-arm and humanoid-locomotion tasks. We measure computation times 2–3× shorter than the QP-based state of the art.