The Kinematic Theory of rapid human movements and its Sigma-Lognormal model enables to model human gestures, in particular complex handwriting patterns such as words, signatures and free gestures. This paper investigates the extension of the theory and its Sigma-Lognormal model from two dimensions to three, taking into account new acquisition modalities (motion capture), multiple subjects, and unconstrained motions. Despite the increased complexity and the new acquisition modalities, we demonstrate that the Sigma-Lognormal model can be successfully generalized to describe 3D human movements. Starting from the 2D model, we replace circular with spherical motions to derive a representation of unconstrained human movements with a new 3D Sigma-Lognormal model. First experiments show a high reconstruction quality with an average signal-tonoise ratio (SNR) of 18.52 dB on the HDM05 dataset. Gesture recognition using dynamic time warping (DTW) achieves similar recognition accuracies when using original and reconstructed gestures, which confirms the high quality of the proposed model.