We present an approach for model-free markerless motion capture of articulated kinematic structures. This approach is centered on our method for generating underlying nonlinear axes (or a skeleton curve) of a volume of genus zero (i.e., without holes). We describe the use of skeleton curves for deriving a kinematic model and motion (in the form of joint angles over time) from a captured volume sequence. Our motion capture method uses a skeleton curve, found in each frame of a volume sequence, to automatically determine kinematic postures. These postures are aligned to determine a common kinematic model for the volume sequence. The derived kinematic model is then reapplied to each frame in the volume sequence to find the motion sequence suited to this model. We demonstrate our method on several types of motion, from synthetically generated volume sequences with an arbitrary kinematic topology, to human volume sequences captured from a set of multiple calibrated cameras.