Goal: Motion capture is used for recording complex human movements that is increasingly applied in medicine. We describe a novel algorithm of combining a machine learning approach with biomechanics to enable robust analysis of motion capture data to obtain joint angles. Methods: A multilayer perceptron and a recurrent neural network were compared in their capacity to estimate the joint angles of the human arm. The networks were pre-trained using a kinematic model of the human arm. We evaluated our models on a dataset containing movements with three degrees of freedom comprising wrist flexion/extension, wrist abduction/adduction, and hand pronation/supination. Results: A recurrent neural network model with long short-term memory architecture can solve the inverse kinematics problem for three rotational degrees of freedom with the least error; it performed faster than real time. Conclusions: This shows that it is feasible to rely on pre-trained neural networks for real-time calculation of joint angles.