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We present a fast continuous collision detection (CCD) algorithm for articulated models using Taylor models and temporal culling. Our algorithm is a generalization of conservative advancement (CA) from convex models [Mirtich 1996] to articulated models with non-convex links. Given the initial and final configurations of a moving articulated model, our algorithm creates a continuous motion with constant translational and rotational velocities for each link, and checks for interferences between the articulated model under continuous motion and other models in the environment and for self-collisions. If collisions occur, our algorithm reports the first time of contact (TOC) as well as collision witness features. We have implemented our CCD algorithm and applied it to several challenging scenarios including locomotion generation, articulated-body dynamics and character motion planning. Our algorithm can perform CCDs including self-collision detection for articulated models consisting of many links and tens of thousands of triangles in 1.22 ms on average running on a 3.6 GHz Pentium 4 PC. This is an improvement on the performance of prior algorithms of more than an order of magnitude.