Three-dimensional Digitizer Research Articles

Modelling and development of transformation matrices for a three-dimensional digitiser

The conceptual design of a three-dimensional digitiser, capable of reporting the three-dimensional coordinates of a point in space is discussed in this paper. The design uses spherical coordinate systems to represent the motion of the mechanical linkages of the system. A mathematical transformation is developed to obtain the three-dimensional location of the tip of the digitiser. The device was designed to interface with a standard personal computer such as an IBM personal computer. The proposed design will offer an accuracy of 0.001 in (0.025mm) with a working volume of at least 0.085 cubic metres. The complete system including the software is expected to cost less than $25,000 making it a viable entry into the coordinate measuring machine (CMM) market.

A knowledge-based user interface for the interactive design of three-dimensional objects

A critical problem with existing computer-based geometric modeling is the labor intensive task involved in specifying data input for the description of three-dimensional (3-D) objects. This paper describes a new, 3-D input system aimed at alleviating this problem. It is based on the use of a three-dimensional digitizer for the direct input of spatial coordinates, and an intelligent interactive user interface. The intent of this system is to create a high level, intelligent interface between the designer and a geometric solid modeler which would lighten the designer's burden in performing arduous 3-D geometric description tasks. The user interface is developed around the Knowledge Craft expert system building tool, using the rule-based Carnegie Representation Language OPS5 (CRL-OPS). The system uses schematic networks or frames and production rules to encode knowledge about geometric primitive digitization methods, object feature operators, solid modeler requirements, and input command functions. It also employs a forward-chaining inference strategy to direct the knowledge. This ensures that only a minimal amount of valid data entry is required by the user. However, if excessive data is entered the intelligent interface has the capability to extract the required information. As a result, the solid modeler can automatically create the appropriate object “primitive” or the specific object “feature” upon recognition by the expert system. It will be demonstrated that these capabilities can simplify the 3-D model description process.

Three-dimensional digitizer (neuronavigator): New equipment for computed tomography-guided stereotaxic surgery

A new device was invented as an adjunct for computed tomography (CT)-guided stereotaxic or open neurosurgery. It is composed of a multijoint three-dimensional digitizer (sensor arm) and a microcomputer, which indicates the place of the sensor arm tip on preoperative CT images. Computed tomography scan is performed pre-operatively with three markers placed on the nasion and ears. At surgery, after fixing the patient's head and the sensor arm, sampling of the standard points was done to translate the position of the tip of the sensor arm onto the CT images displayed on a computer screen. In this way positional data from conventional preoperative CT scan can be directly transferred into the surgical field. This system has the unique feature of introducing CT-guided stereotaxis into conventional open neurosurgery.

Sensitivity of Insertion Locations on Length Patterns of Anterior Cruciate Ligament Fibers

A technique is demonstrated, employing an instrumented spatial linkage, for the determination of the length patterns of discrete fiber bundles within a ligament under controlled loading conditions. The instrumented spatial linkage was used to measure the three-dimensional joint motion. The linkage was also used as a three-dimensional coordinate digitizer to determine the spatial location of bony landmarks and the ligament's insertion areas. The length of pseudo fiber bundles was determined as the straight line distance between bone attachments. A comparison is presented, showing good agreement, between elongation patterns obtained from this method and those measured using an instrumented fine wire cable fiber. A sensitivity analysis was performed to evaluate the influence of tibial and femoral attachment location on the length pattern of fiber bundles of the anterior cruciate ligament. It was found that the relationship between fiber elongation and knee flexion depended strongly on the fibers femoral attachment location but not on its tibial attachment location.

Creative computer imaging

Creative computer imaging

Three-dimensional measurement of stone cast deformation. Part 2. Effects of types of impression material and mold on the dimensional stability of stone casts.

Three different types of dies (straight, tapered and undercut) obtained using three types of impression materials (alginate, polysulfide and addition-curing silicone) were measured for height and the dimension of the diameter with a three-dimensional digitizer. Assuming that the value obtained by adding the amount of free-setting expansion of the die material to the dimension of the original represents the highest accuracy, the difference in dimension according to the types of impression material used would be as follows : 1. The die made with alginate : In the case of the straight type, both the height and diameter increased somewhat uniformly. In the case of the tapered type, the height was correct but the diameter was slightly larger, especially in the upper portion. In the case of the undercut type, the height was fairly large and the diameter was large in all portions, especially in the lower portion as though spreading had occurred.2. The die made with polysulfide : In the case of the straight type, the height was particularly large but the diameter was correct. In the case of the tapered type, the height was slightly larger, and the diameter was a little larger in the upper portion, correct in the central portion, but slightly smaller in the lower portion. In the case of the undercut type, the height was almost as large as that of the die made with alginate and the diameter was large on the whole, showing a form swollen in the middle.3. The die made with addition-curing silicone : In the case of the straight type, the height was slightly large and the diameter was correct in the upper portion but was slightly small in the lower portion. In the case of the tapered type, both the height and diameter were accurate but the diameter became slightly small in the lower portion. In the case of the undercut type, both the height and diameter were almost uniformly larger, although only slightly. However, in the case of the die made with silicone, the undercut recovery was found to be better than that of the dies made with the two other impression materials.

The inertial and geometrical properties of helmets.

The center of gravity (CG) and the principal mass moments of inertia about the CG of Army aviator, American football, and bicycle helmets were experimentally determined by a variation of the classic differential weighing and torsional pendulum techniques. In the course of these experiments, an innovative method for three-dimensional (3D) digitization was found. An electronic caliper, which measured length, was used with a computer algorithm to achieve 3D digitization. The results of the above measurements show that the weight of the helmet and the distances from the CG to the orthogonal coordinate axes intercepts with the outer shell surface were highly correlated with its principal mass moments of inertia. A set of regression equations was derived on theoretical considerations and served to unify the experimentally obtained data. Our results indicate that the principal mass moments of inertia of helmets vary linearly with its mass but nonlinearly with size and shape. For a helmet, given its weight and certain geometrical distances, the regression equations estimate the principal mass moments of inertia to within 5% of its experimentally-determined values. For the helmets studied in this series, a modified linear-regression relationship between the principal mass moments of inertia and its mass was found. This result is reasonable because the mass distribution of the current generation of helmets are set primarily by the head size and secondarily by helmet size, shape, and materials.

An experimental study of the displacement of the maxillary complex, produced by extraoral forward traction: Toshiaki Tanabe, Kenji Suginome, Yasuhiko Yoshida, and Sadahiko NishiguchiJ. Jpn. Orthod. Soc. 42:322–335, 1983

analyze jaw movement quantitatively within a small range around the mandibular postural resting position, and to assess the reliability of this method. In order to investigate the amount of distortion involved in the MKG data, a parallel-sliding system was developed and connected with a three-dimensional digitizer (Gradicon) which was connected by an aluminum rod, in turn, to the magnet centered in the MKG sensor array. This assembly then was capable or registering the true X-Y-Z coordinates of the magnet’s position. The original MKG data were recorded directly by reading a digital tester at each of the magnet’s 168 positions, distributed at regular intervals with a range ofminus2toplus2mminX,minus2toplus lOinY, and 0 to minus 10 in Z coordinates. The formula for the correction, expressed by a dual equation of the second degree, was arrived at by inversely converting the equation which represents the distortion of the measured value received from the MKG. Then the true coordinates were compared to both the distorted original coordinates and the logically corrected coordinates for each dimension. The results showed that the distorted MKG data were sufficiently corrected to reduce the error to as small as 0.1 to 0.2 mm, and that this correction method had a good reliability for studying the jaw movements within a limited space around the mandibular postural resting position. T. M. Graber

An in-vitro study of the kinematics of the normal, injured and stabilized cervical spine

The relative motion between various vertebrae of multi-level cervical ligamentous spinal segments (C2-T2), using Bryant angles, is described. A three-dimensional sonic digitizer was utilized to study the motion in flexion, extension, right lateral bending and right axial rotation. Effects of a number of injuries and stabilization (interspinous wiring and acrylic cement, PMMA) on the motion behavior of C5–C6 (injured) and C4–C5 (superior to injured) levels were investigated. The data were normalized with respect to intact specimens. The injury to capsular ligaments at C5–C6 produced a significant increase in the relative motion at C4–C5. Although the interspinous wiring reduced the motion at C5–C6 the C4–C5 motion was still higher. The application of PMMA made the motion at C4–C5 comparable to the intact specimen.

An in-vivo study of normal wrist kinematics.

The motion of the hand relative to a reference frame embedded in the radius is described using the screw displacement axis (SDA) concept. A three-dimensional sonic digitizer was utilized in a study of the dominant wrist of 15 normal subjects to determine the location and orientation of the SDAs based on the endpoints of flexion-extension motion (FEM) and radial-ulnar deviation (RUD) of the hand. The length of the common perpendicular between the SDAs of FEM and RUD was as large as 6 mm in some individuals; however, in some subjects the FEM SDA was distal of the RUD SDA while in others it was proximal. Considering the group of 15 subjects, the SDAs of FEM and RUD for the normal group nearly intersect in the head of the capitate in the neutrally positioned wrist and forearm.

The Three-dimensional Rotational Behaviors of the Carpal Bones

The rotational behaviors of the carpal bones of ten fresh cadaver forearms were determined using a three-dimensional sonic digitizer, as the hands were passively moved through planar constrained motions. Changing forearm orientation from supination to pronation results in an increase in the magnitudes of extension of the proximal and distal carpal row bones and a reduction in the magnitudes of flexion of the distal carpal row bones. The included angles between each carpal bone screw displacement axis (SDA) and third metacarpal SDA for corresponding intervals of motion are significantly greater than zero, regardless of forearm orientation. The included angles of the proximal carpal row bones are significantly greater than those of the distal carpal row bones during third metacarpal radial-ulnar deviation. The carpal bone rotation magnitudes are significantly attenuated relative to the prescribed rotation magnitudes of the third metacarpal, with the exception of the trapezoid during third metacarpal extension. The rotational attenuation is greatest in the proximal carpal row bones and is most pronounced during third metacarpal flexion-extension motion and ulnar deviation. Evidence from this investigation favors a carpal row concept of wrist motion, as opposed to a carpal column model.

An investigation of carpal bone motion using a three-dimensional sonic digitizer

Normal carpal kinematics were studied in 22 cadaver specimens using a biplanar radiography method. The kinematics of the trapezium, capitate, hamate, scaphoid, lunate, and triquetrum were determined during wrist motion in sagittal and coronal planes. The results were expressed using the concept of the screw displacement axis and converted to describe the magnitude of rotation about and translation along three axes (X-axis: pronation-supination axis, Y-axis; flexion-extension axis, and Z-axis: radial-ulnar deviation axis) commonly used for the wrist. The orientation of these axes is expressed relative to the radius.Within the proximal carpal row, considerable differences of carpal behavior around the Y-axis were observed during sagittal plane motion of the wrist. The scaphoid exhibited the greatest magnitude of rotation, and the lunate the least. The magnitude of rotation of the carpal bones around the X-axis during sagittal plane motion of the wrist was small. The proximal carpal bones exhibited some ulnar deviation in 60° of wrist flexion. During coronal plane motion of the wrist, the magnitude of radial-ulnar deviation of the distal carpal bones was mutually similar and generally of a greater magnitude than that of the proximal carpal bones. The proximal carpal bones experienced some flexion during radial deviation of the wrist and extension during ulnar deviation of the wrist. Translation was generally minimal in all carpal bones throughout wrist motion.This study reports results from the largest cadaver wrist kinematics study completed to date. The accuracy of the current method was improved when compared to previous studies. A sufficient number of specimens to allow statistical comparison was used and minimal interspecimen variability was noted. This study enabled a precise description of quantitative analyses of normal carpal kinematics relative to the radius.

A biomechanical investigation of wrist kinematics

This paper describes a biomechanical investigation to determine the overall kinematic behavior of the human wrist or carpus. The hand and forearm segments are modeled as rigid bodies, and the three-dimensional kinematic characteristics of the wrist are obtained by studying two clinically significant planar motions of the hand relative to the forearm: flexion-extension motion, and radial-ulnar deviation. The three mechanical quantities used to describe the kinematic behavior of the wrist are the functional range of motion, the looseness locus, and the instantaneous center of rotation locus. In vivo and in vitro experimental data are collected using biplanar X-ray films, and a three-dimensional sonic digitizer interfaced with a small laboratory computer. Validation tests using a metal universal joint with known kinematic properties indicate the accuracy and reliability of the experimental results. Data for one normal subject and one rheumatoid patient, examined both pre and post operatively, are presented and discussed.

Computer Applications in Radiology—1970

Computer applications in radiology are evolving rapidly, tied to incremental improvements in hardware, software, and methods. In computer hardware, the emergence of dramatically improved graphic and computational performance for engineering workstations enables their use for visualization. Major changes in networking, storage, and display technology play a major role in influencing applications. The use of three-dimensional digitizers to perform localization of real three-dimensional points in conjunction with images and the rendering of objects using rapid prototyping methods, such as stereolithography, were recently reported. Major software advances have taken place through the availability of applications packages that are operated with menu-driven or point-and-click user interfaces, data flow languages, or complete turnkey applications. Imaging methods including CT, MR imaging, digital radiography, biomagnetism, and optical range sensing, which take advantage of advanced computer technology, are new this year. Image processing for multimodality fusion or image registration, visualization, reconstruction, and quantification of images, have been reported at a wide variety of conferences and in key publications. New computer methods to fabricate custom orthopaedic implants, and to improve imaging technology assessment were introduced.