Abstract: Complex mesh models of man-made objects often consist of multiple components connected by various types of joints. We propose a joint-aware deformation framework that supports the direct manipulation of an arbitrary mix of rigid and deformable components. First we apply slippable motion analysis to automatically detect multiple types of joint constraints that are implicit in model geometry. For single-component geometry or models with disconnected components, we support user-defined virtual joints. Then we integrate manipulation handle constraints, multiple components, joint constraints, joint limits, and deformation energies into a single volumetric-cell-based space deformation problem. An iterative, parallelized Gauss-Newton solver is used to solve the resulting nonlinear optimization. Interactive deformable manipulation is demonstrated on a variety of geometric models while automatically respecting their multi-component nature and the natural behavior of their joints.