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Kinematic structures are very common in the real world. They range from simple articulated objects to complex mechanical systems. However, despite their relevance, most model-based 3D tracking methods only consider rigid objects. To overcome this limitation, we propose a flexible framework that allows the extension of existing 6DoF algorithms to kinematic structures. Our approach focuses on methods that employ Newton-like optimization techniques, which are widely used in object tracking. The framework considers both tree-like and closed kinematic structures and allows a flexible configuration of joints and constraints. To project equations from individual rigid bodies to a multi-body system, Jacobians are used. For closed kinematic chains, a novel formulation that features Lagrange multipliers is developed. In a detailed mathematical proof, we show that our constraint formulation leads to an exact kinematic solution and converges in a single iteration. Based on the proposed framework, we extend ICG, which is a state-of-the-art rigid object tracking algorithm, to multi-body tracking. For the evaluation, we create a highly-realistic synthetic dataset that features a large number of sequences and various robots. Based on this dataset, we conduct a wide variety of experiments that demonstrate the excellent performance of the developed framework and our multi-body tracker.