A rigid body model of the forearm

In this article the forearm, with its complex, continuous motion of masses during pronation/supination, was approximated by a rigid body model consisting of a radial segment rotating around an ulnar segment. The method used to obtain the model parameters is based on three-dimensional voxel data that include velocity information. We propose a criterion that allows the voxels to be attributed to either of the two segments. It is based on the notion that the rotational kinetic energy determined from the voxel data equals the kinetic energy of the rigid body model. To obtain a three-dimensional smoothing we further propose a parameterization of the shape of both segments. These shapes can then be used to determine the dynamic integrals of the segments, i.e. mass, center of mass, and inertia. Using this approach we determined all model parameters for a human forearm from three series of MRI scans in a supinated, a pronated, and an intermediate position. In the appendix, a procedure is described that allows the dynamic quantities to be scaled homogeneously without recalculation of the integrals. Thus, this article provides all essential parameters required for three-dimensional dynamic simulations of general movements of the forearm.