The study of joint kinematics and dynamics has broad clinical applications, including the identification of pathological motions or compensation strategies and the analysis of dynamic stability. High-end motion capture systems, however, are expensive and require dedicated camera spaces with lengthy setup and data processing commitments. Depth cameras, such as the Microsoft Kinect, provide an inexpensive, marker-free alternative at the sacrifice of joint-position accuracy. In this work, we present a fast framework for adding biomechanical constraints to the joint estimates provided by a depth camera system. We also present a new model for the lower lumbar joint angle. We validate key joint position, angle, and velocity measurements against a gold standard active motion-capture system on ten healthy subjects performing sit to stand (STS). Our method showed significant improvement in mean absolute error and intraclass correlation coefficients for the recovered joint angles and position-based metrics. These improvements suggest that depth cameras can provide an accurate and clinically viable method of rapidly assessing the kinematics and kinetics of the STS action, providing data for further analysis using biomechanical or machine learning methods.