Six kinematic parameters are needed to fully describe three-dimensional (3D) bone motion at a joint. At the knee, the relative movements of the femur and tibia are often represented by a 1-degree-of-freedom (1-DOF) model with a single flexion–extension axis or a 2-DOF model comprising a flexion–extension axis and an internal–external rotation axis. The primary aim of this study was to determine the accuracy with which 1-DOF and 2-DOF models predict the 3D movements of the femur, tibia and patella during daily activities. Each model was created by fitting polynomial functions to 3D tibiofemoral (TF) and patellofemoral (PF) kinematic data recorded from 10 healthy individuals performing 6 functional activities. Model cross-validation analyses showed that the 2-DOF model predicted 3D knee kinematics more accurately than the 1-DOF model. At the TF joint, mean root-mean-square (RMS) errors across all activities and all participants were 3.4°|mm (deg or mm) for the 1-DOF model and 2.4°|mm for the 2-DOF model. At the PF joint, mean RMS errors were 4.0°|mm and 3.9°|mm for the 1-DOF and 2-DOF models, respectively. These results indicate that a 2-DOF model with two rotations as inputs may be used with confidence to predict the full 3D motion of the knee-joint complex.