A rigid-body method for finding centers of rotation and angular displacements of planar joint motion

A rigid-body method for determining the center of rotation (CR) and the angular displacement in a plane is developed. A comparison of this method to the graphical method of Reuleaux (Theoretische Kinematik: Grundzüge einer Theorie des Maschinenwerens, 1875) is found to have fewer constraints while meeting or exceeding the Reuleaux method in accuracy. The rigid-body method is not constrained by the location of the markers, as they can be placed radially or juxtapositioned about the CR. Magnitude of the rotation angle does not affect the accuracy in calculating the rotation angle. When applying both methods to locate the CR in a simulated knee joint, a substantial decrease in error is found with the new method. In a comparison of optimal marker angles used to locate the CR and find the angular displacement, the rigid-body method is found to be more accurate in both the mean and range of error. Effects of parameters specified by Panjabi (J. Biomechanics 12, 911-920, 1979) are applied to both methods. Results are then used in setting up guidelines for increasing accuracy with the rigid-body method.