We present a framework for parameter and state estimation of personalized human kinematic models from motion capture data. These models can be used to optimize a variety of human-robot collaboration scenarios for the comfort or ergonomics of an individual human collaborator. Our approach offers two main advantages over prior approaches from the literature and commercial software: the kinematic models are estimated for a specific individual without a priori assumptions on limb dimensions or range of motion, and our kinematic formalism explicitly encodes the natural kinematic constraints of the human body. The personalized models are tested in a human-robot collaborative manipulation experiment. We find that human subjects with a restricted range of motion rotate their torso significantly less during bimanual object handoffs if the robot uses a personalized kinematic model to plan the handoff configuration, as compared to previous approaches using generic human kinematic models.