Dextrous manipulation based on techniques for non-linear dimension reduction and manifold learning is an upcoming field of research and offers promising opportunities. Still, many problems remain unsolved and researchers are seeking for new representations that combine efficient learning of examples and robust generalisation to unseen situations. Here, we propose a manifold representation of hand postures, which due to its structural clarity lends itself to simple and robust manipulation control schemes. Focussing on cyclic movements, we describe extensions to the dimensionality reduction algorithm Unsupervised Kernel Regression (UKR) that allow to incorporate structural hints about the training data into the learning yielding task-related structures in the manifold’s latent space. We present the resulting manifold representation and a simplified controller using this representation for manipulation in the example of turning a bottle cap in a physics-based simulation.