This paper introduces a general optimisation-based method for identification of biomechanically relevant parameters in kinematically determinate and over-determinate systems from a given motion. The method is designed to find a set of parameters that is constant over the time frame of interest as well as the time-varying system coordinates, and it is particularly relevant for biomechanical motion analysis where the system parameters can be difficult to accurately determine by direct measurements. Although the parameter identification problem results in a large-scale optimisation problem, we show that, due to a special structure in the linearised Karush–Kuhn–Tucker optimality conditions, the solution can be found very efficiently. The method is applied to a set of test problems relevant for gait analysis. These involve determining the local coordinates of markers placed on the model, segment lengths and joint axes of rotation from both gait and range of motion experiments.