We present a framework for monocular 3D kinematic pose tracking and viewpoint estimation of periodic and quasi-periodic human motions from an uncalibrated camera. The approach we introduce here is based on learning both the visual observation manifold and the kinematic manifold of the motion using a joint representation. We show that the visual manifold of the observed shape of a human performing a periodic motion, observed from different viewpoints, is topologically equivalent to a torus manifold. The approach we introduce here is based on the supervised learning of both the visual and kinematic manifolds. Instead of learning an embedding of the manifold, we learn the geometric deformation between an ideal manifold (conceptual equivalent topological structure) and a twisted version of the manifold (the data). Experimental results show accurate estimation of the 3D body posture and the viewpoint from a single uncalibrated camera.