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In this contribution we introduce the Shape Flow algorithm (SF), a novel method for spatio-temporal 3D pose estimation of a 3D parametric curve. The SF is integrated into a tracking system and its suitability for tracking human body parts in 3D is examined. Based on the example of tracking the human hand-forearm limb it is shown that the use of two SF instances with different initializations leads to an accurate and temporally stable tracking system. In our framework, the temporal pose derivative is available instantaneously, therefore we avoid delays typically encountered when filtering the pose estimation results over time. All necessary information is obtained from the images, only a coarse initialisation of the model parameters is required. Experimental investigations are performed on 5 real-world test sequences showing 3 different test persons in an average distance of 1.2-3.3 m to the camera in front of cluttered background. We achieve typical pose estimation accuracies of 40-100 mm for the mean distance to the ground truth and 4-6 mm for the pose differences between subsequent images.