Analysis And Display Of Human Wrist Motion

Abstract The three-dimensional kinematic analysis of the wrist is a complex problem. A method uti­ lizing high speed stereocinematography has been developed to accurately measure the motion of the bones in the wrist. Both relative and absolute motions can be obtained using this system. The system has been shown to accurately locate a point to + 0.003 inch. The three-dimensional motion characteristics of the capitate in radial ulnar devTation were analyzed using this system, and the results are presented. A computer graphics program, developed by the authors, is used to display the motion characteristics of the carpal bones. In this program, the bone surface, defined using a special stereopointer and bicubic surface fitting algorithms, is displayed along with the kinematic data.introductionAnalyzing the three-dimensional kinematics of the human wrist is a complex problem. The wrist is composed of eight bones connected by an intricate network of ligament tissue. The bone surfaces and ligaments provide constraint forces which cause the joint to move in a specific manner. If part of the system is not working properly, due to disease or injury, abnormal motion results. The complex nature of the wrist's structure makes it difficult, if not impossible, to analyze using conventional kinematic techniques. At the University of Minnesota, an analysis procedure is being developed which combines concepts from classical kinematics with computer analysis to create a useful tool for the biomechanical engineer and orthopaedic surgeon.MethodsA main component of the analytical process is a high speed stereo motion picture system. The camera system uses mirrors to split the 16 mm film plane, generating two images of the wrist (see Figure 1). Light emitting diode (LED) target frames are securely mounted in the bones of a cadaver specimen using screws and cement. The trajectory of the LEDf s is filmed at 50 frames per second while the wrist is passively moved through some specified motion. After the film has been developed, the stereophotographs are fed into the computer using an automatic digitizer.-*- The computer reconstructs the three-dimensional paths produced by the LEDf s using standard photogrammetric techniques. This system can accurately locate a point in space to within + 0.003 inch in a field of view of roughly 8 cubic feet.Figure 2 shows the motion of four diodes mounted in the right hand capitate of a cadaver. The motion was produced by moving the wrist in radial-ulnar deviation (RUD). The graph shows a dorsal view of the motion data references to a LED target fixed in the radius. Robbin, et al., provide a full description of the experimental procedure.In order to analyze the wrist's motion, trajectories of the LED frames must be con­ verted into a representation of the actual carpal bone relative motion. One common method of representing spatial motion is the screw displacement axis, or twist axis.3 The twist axis describes the motion between two discrete positions as a rotation about the axis and a translation along that axis. The magnitude of the rotation is called the intensity of the twist, and the displacement is linearly related to the intensity by pitch of the screw axis. The twist axis provides a simple way of representing the motion of rigid objects.The twist axes are calculated using a least squares algorithm described by Lenox.4 The algorithm can be broken into two steps. In the first step, the Rodrigues vector, or rota­ tion axis, is calculated using a least squares technique developed by Schut.^ This least squares method allows the motion of the rigid body to be specified by more than three diodes the minimum number of points needed to specify the position and orientation of a body in three-dimensional space. The least squares technique locates the twist axis more accurately than other methods. A minimum rotation angle constraint has also been added to the program to reduce "noise" created by the camera/digitizer system. The twist axis calculation is completed by finding the location of the twist axis with respect to the origin of the coor­ dinate system and calculating the rigid body translation parallel to the axis. Kane and Linkins^ developed two vector expressions that relate these twist parameters to the Rodrigues vector and a vector describing the displacement of any point p on the rigid body. These equations are: