Instrumented Linkage Research Articles

Novel Arthrometer for Quantifying In Vivo Knee Laxity in Three Planes Following Total Knee Arthroplasty

BackgroundKnee instability is a leading cause of dissatisfaction following total knee arthroplasty (TKA). Instability can involve abnormal laxity in multiple directions including varus-valgus (VV) angulation, anterior-posterior (AP) translation, and internal-external rotation (IER). No existing arthrometer objectively quantifies knee laxity in all three of these directions. The study objectives were to verify the safety and assess reliability of a novel multiplanar arthrometer. MethodsThe arthrometer utilized a five degree-of-freedom instrumented linkage. Two examiners each conducted two tests on the leg that had received a TKA of 20 patients (mean age 65 years (range, 53-75); 9 men, 11 women), with nine and eleven distinct patients tested at 3-month and 1-year postoperative time points, respectively. AP forces from −10 to 30 Newtons, VV moments of ±3 Newton-meters, and IER moments of ±2.5 Newton-meters were applied to each subject’s replaced knee. Severity and location of knee pain during testing were assessed using a visual analog scale. Intraexaminer and interexaminer reliabilities were characterized using intraclass correlation coefficients. ResultsAll subjects successfully completed testing. Pain during testing averaged 0.7 (out of possible 10; range, 0-2.5). Intraexaminer reliability was >0.77 for all loading directions and examiners. Interexaminer reliability and 95% confidence intervals were 0.85 (0.66-0.94), 0.67 (0.35-0.85), and 0.54 (0.16-0.79) in the VV, IER, and AP directions, respectively. ConclusionThe novel arthrometer was safe for evaluating AP, VV, and IER laxities in subjects who had received TKA. This device could be used to examine relationships between laxity and patient perceptions of knee instability.

A Composite Athletic Tape With Hyperelastic Material Properties Improves and Maintains Ankle Support During Exercise

Controlled laboratory testing using a single-group, prospective, repeated-measures design. To compare the material properties of a hyperelastic athletic tape to a conventional tape and to compare the passive ankle support of these tapes before and after exercise. The near-linear material properties of conventional athletic tape may interfere with ankle motion, resulting in reduced athletic performance. Conventional athletic tape is also known to lose much of its initial support during exercise. It was assumed that a tape constructed of Kevlar fibers embedded in a silicon matrix would possess hyperelastic material properties that would improve ankle support. A tensile testing machine was used to determine the tensile material properties of 11 samples of conventional and hyperelastic tape. The ankles of 11 young, healthy athletes were taped, one ankle with conventional tape and the other ankle with hyperelastic tape. The passive ankle support of each tape was measured with an instrumented linkage (the ankle flexibility tester) before and after 30 minutes of exercise. The composite tape had a significantly higher load to failure than the conventional tape. It had significantly lower initial stiffness and higher late stiffness than conventional tape, thus demonstrating highly hyperelastic behavior. The hyperelastic tape maintained a significantly higher portion of its support during the 30 minutes of exercise than the conventional tape. Composite athletic tape with highly hyperelastic properties can be constructed and maintains a larger portion of its support during short-duration exercises (less than 30 minutes) than conventional athletic tape.

KINEMATIC ANALYSIS AND PERFORMANCE EVALUATION OF 6R INSTRUMENTED SPATIAL LINKAGES

Six-degree-of-freedom instrumented spatial linkages are often used to measure anatomical joint motion for clinical studies or research applications in biomechanics. Their appropriate design is a fundamental issue to allow for accurate measurements and ease of application, and this mainly relies on addressing the kinematic analysis of the linkage. The aim of this paper is to integrate and extend past literature in the field by giving a generalized set of guidelines and ready-to-use mathematical relationships to approach the whole kinematic analysis of a general instrumented spatial linkage in a systematic way. The direct kinematics is formulated using common robotics formulation and, with reference to a specific linkage architecture, a geometrical approach is proposed to solve for the inverse kinematics in closed-form. Kinematic error analysis is addressed in a generalized way by using differential transformation theory, and it is then applied to the specific case under study. By the proper definition of a virtual joint, the inverse kinematics is used to estimate the static performance of the linkage over its specific task space.

Design and Evaluation of a New General-Purpose Device for Calibrating Instrumented Spatial Linkages

Because instrumented spatial linkages (ISLs) have been commonly used in measuring joint rotations and must be calibrated before using the device in confidence, a calibration device design and associated method for quantifying calibration device error would be useful. The objectives of the work reported by this paper were to (1) design an ISL calibration device and demonstrate the design for a specific application, (2) describe a new method for calibrating the device that minimizes measurement error, and (3) quantify measurement error of the device using the new method. Relative translations and orientations of the device were calculated via a series of transformation matrices containing inherent fixed and variable parameters. These translations and orientations were verified with a coordinate measurement machine, which served as a gold standard. Inherent fixed parameters of the device were optimized to minimize measurement error. After parameter optimization, accuracy was determined. The root mean squared error (RMSE) was 0.175 deg for orientation and 0.587 mm for position. All RMSE values were less than 0.8% of their respective full-scale ranges. These errors are comparable to published measurement errors of ISLs for positions and lower by at least a factor of 2 for orientations. These errors are in spite of the many steps taken in design and manufacturing to achieve high accuracy. Because it is challenging to achieve the accuracy required for a custom calibration device to serve as a viable gold standard, it is important to verify that a calibration device provides sufficient precision to calibrate an ISL.

Development and Evaluation of an Instrumented Linkage System for Total Knee Surgery

The principles and application of total knee surgery using optical tracking have been well demonstrated, but electromagnetic tracking may offer further advantages. We asked whether an instrumented linkage that attaches directly to the bone can maintain the accuracy of the optical and electromagnetic systems but be quicker, more convenient, and less expensive to use. Initial testing using a table-mounted digitizer to navigate a drill guide for placing pins to mount a cutting guide demonstrated the feasibility in terms of access and availability. A first version (called the Mark 1) instrumented linkage designed to fix directly to the bone was constructed and software was written to carry out a complete total knee replacement procedure. The results showed the system largely fulfilled these goals, but some surgeons found that using a visual display for pin placement was difficult and time consuming. As a result, a second version of a linkage system (called the K-Link) was designed to further develop the concept. User-friendly flexible software was developed for facilitating each step quickly and accurately while the placement of cutting guides was facilitated. We concluded that an instrumented linkage system could be a useful and potentially lower-cost option to the current systems for total knee replacement and could possibly have application to other surgical procedures.

Validation of a calibration technique for 6-DOF instrumented spatial linkages

This paper presents a practical and effective approach to the calibration of instrumented spatial linkages for biomechanical applications. A 6-DOF mechanical linkage with rotational transducers is designed and in-house manufactured for this purpose. In order to assess the validity of the proposed calibration technique and to distinguish between geometrical and electrical parameters uncertainties, high-precision optical encoders are used and calibration is addressed from a kinematic point of view only. The proposed technique is based on a closed-loop method, in which the end segments of the linkage are connected to each other by revolute joints. A parametrical model of the system is formulated using a standard link-to-link transformation matrices approach. Continuous data collection is carried out and a recursive identification of kinematic parameters is implemented by the use of an extended Kalman filter algorithm. Results shows that the proposed technique, despites its simplicity, is effective in improving the accuracy of the system up to its theoretically computed resolution, which limits the performance of the real system.

The Effect of Anterior Cervical Fusion on Neck Motion

Prospective cohort study. To precisely measure the effect of anterior cervical fusion on neck motion. Anterior cervical decompression and stabilization procedures are successful in treating recalcitrant cervical radiculopathy and cervical myelopathy. Most assume that these "fusion" procedures result in a loss of neck motion, although changes in overall motion following anterior cervical fusion have never been precisely quantified. Twenty-five consecutive patients undergoing anterior cervical fusion of one to four levels underwent cervical range of motion testing in three planes using an unconstrained instrumented linkage before surgery and more than 3 months after surgery. These data were compared with that of 10 volunteers with no prior history of neck complaints. Motion data were compared between patients and volunteers, and between the patients before surgery and at last follow-up, using RMANOVA and Fisher's PLSD post hoc test. Before surgery, the patients had significantly less motion than the volunteers in all directions. Following surgical fusion, patients gained a statistically significant amount of motion in all planes, although they did not achieve the motion seen among the volunteers. Gains in motion were seen among all patients, including those undergoing four-level fusions, and there was no correlation between postoperative motion and the number of levels fused. Patients undergoing anterior cervical fusion have diminished neck motion compared with normal volunteers. Following surgery, they may be expected to gain motion, even when undergoing multilevel fusions. However, these patients are unlikely to regain the neck motion seen among normal individuals without neck complaints.

Design and Demonstration of a New Instrumented Spatial Linkage for Use in a Dynamic Environment: Application to Measurement of Ankle Rotations During Snowboarding

Joint injuries during sporting activities might be reduced by understanding the extent of the dynamic motion of joints prone to injury during maneuvers performed in the field. Because instrumented spatial linkages (ISLs) have been widely used to measure joint motion, it would be useful to extend the functionality of an ISL to measure joint motion in a dynamic environment. The objectives of the work reported by this paper were to (i) design and construct an ISL that will measure dynamic joint motion in a field environment, (ii) calibrate the ISL and quantify its static measurement error, (iii) quantify dynamic measurement error due to external acceleration, and (iv) measure ankle joint complex rotation during snowboarding maneuvers performed on a snow slope. An "elbow-type" ISL was designed to measure ankle joint complex rotation throughout its range (+/-30 deg for flexion/extension, +/-15 deg for internal/external rotation, and +/-15 deg for inversion/eversion). The ISL was calibrated with a custom six degree-of-freedom calibration device generally useful for calibrating ISLs, and static measurement errors of the ISL also were evaluated. Root-mean-squared errors (RMSEs) were 0.59 deg for orientation (1.7% full scale) and 1.00 mm for position (1.7% full scale). A custom dynamic fixture allowed external accelerations (5 g, 0-50 Hz) to be applied to the ISL in each of three linear directions. Maximum measurement deviations due to external acceleration were 0.05 deg in orientation and 0.10 mm in position, which were negligible in comparison to the static errors. The full functionality of the ISL for measuring joint motion in a field environment was demonstrated by measuring rotations of the ankle joint complex during snowboarding maneuvers performed on a snow slope.

Quantitative measurement of ankle passive flexibility using an arthrometer on sprained ankles

Objective. The purpose of this study was to quantitatively examine the flexibility of sprained ankles using an arthrometer device and compare the differences in flexibility between ankles following the first sprains and ankles with repeated severe sprains and chronic symptoms. Design. A retrospective in vivo study was used. Background. Many in vitro studies have demonstrated a significant role of joint flexibility in determining mechanical laxity of human cadaveric ankles after sectioning of the lateral ligaments, but few in vivo studies have used the technique to provide objective measurement on the sprained ankles. Furthermore, there is a lack of extensive studies that compared the difference in the ankle flexibility between ankles following the first sprain and ankles with multiple repeated severe sprains and chronic symptoms. Methods. A total of 27 subjects with unilateral ankle sprains participated in this study. The subjects were divided into a first injury group (group A, n=12) and a chronic symptom group (group B, n=15) based on the history of their ankle injuries. The ankle flexibility in anterior drawer and inversion/eversion tests was measured in both ankles of the subjects using an arthrometer device, the ankle flexibility tester – a six-degree-of-freedom instrumented linkage used for measurements of applied forces/moments and resultant rotations and/or translations of the ankle joint complex. The difference in ankle flexibility between the injured ankle and the contralateral intact side was analyzed. Results. The flexibility in anterior drawer test of the injured ankles significantly increased compared to the intact ankles of the same individual in group B, but the same difference was not significant in group A. There were more subjects in group B (46.6%) than in group A (33.3%) who showed a sign of mechanical laxity in their injured ankles. Conclusions. The results indicated that the approach with measurement of ankle flexibility may be a potential tool used to detect the mechanical laxity in the sprained ankles. A tendency was found that patients with multiple ankle sprains and chronic symptoms had a higher occurrence rate of mechanical laxity. The result of the present study may also be interpreted that the ankles with mechanical laxity had higher risk of re-injury and leading to chronic symptoms. Relevance A non-invasive and objective measurement of ankle flexibility has potential to be developed into a diagnostic tool for the mechanical laxity of sprained ankles. The finding of this study may help clinicians in the plan of patient treatment.

1997 Volvo Award winner in biomechanical studies. Kinematic behavior of the porcine lumbar spine: a chronic lesion model.

Experimental models of intervertebral disc and facet joint degeneration were created in vivo in the porcine lumbar spine for studying spinal kinematics, using a dynamic technique. To quantify the changes in spinal kinematics and the stabilizing capacity of the lumbar musculature caused by chronic lesions in the intervertebral disc and facet joints. Segmental kinematics are detrimentally altered by acute injury to passive structures of the motion segment. However, stimulation of the surrounding musculature adds stability to the motion segment. The in vivo kinematics of a degenerated lumbar motion segment and the stabilizing function of the surrounding musculature have not been quantified dynamically. Forty-four pigs were used in six chronic lesions models: sham, disc anulus, disc nucleus, facet capsule, facet joint slit, and facet joint wedge. Three months after injury, an instrumented linkage was used to measure continuously the sagittal kinematics of the L3-L4 motion segment during flexion-extension, with and without stimulation of the lumbar paraspinal musculature. Flexion-extension end point and maximum ranges of motion, and hysteresis were analyzed. Significant alterations in the kinematics caused by chronic lesions were observed, particularly when using the maximum range of motion and when comparing changes in axial translation. Muscular stimulation reduced the hysteresis in the sham, facet capsule, and disc nucleus groups; however, increased hysteresis was observed in the remaining lesion groups. The kinematic behavior of motion segments with chronic lesions was established. The maximum range of motion, which must be measured using a dynamic technique, was a more sensitive parameter for identifying changes in segmental kinematics caused by chronic lesions than was the end range of motion. The lumbar musculature was less efficient overall in stabilizing the motion segment, possibly because of altered mechanisms in the neuromuscular feedback system.

Changes in the flexibility characteristics of the ankle complex due to damage to the lateral collateral ligaments: an in vitro and in vivo study.

This study was part of a long-term effort to develop a reliable diagnostic procedure for ankle ligament injuries. Earlier efforts led to the development and validation of a six-degrees-of-freedom instrumented linkage capable of measuring the flexibility characteristics of the ankle complex in vitro and in vivo. The major goal of the present study was to determine if these flexibility measurements are sufficiently sensitive to detect the presence of damage to the lateral collateral ligaments of the ankle joint both in vitro and in vivo. The in vitro testing was conducted on the legs from six fresh cadavers before and after serial sectioning of the anterior talofibular ligament and the calcaneofibular ligament. The flexibility in inversion-eversion, anterior drawer, and internal-external rotation was measured before and after resection of the ligaments. The in vivo testing was conducted on five patients with unilateral injuries to the ankle ligament. The flexibility evaluation used for in vitro specimens was also performed on both the injured and the intact ankles. For the in vitro testing, the data analysis was based on comparison of flexibility values before and after resection of the ligaments, whereas the data analysis for the in vivo testing was based on comparison of the flexibility of the injured joint with that of the intact contralateral joint. The results of the in vitro study indicated that both an isolated rupture of the anterior talofibular ligament and combined damage of the anterior talofibular and calcaneofibular ligaments produce statistically significant changes in flexibility. Furthermore, the most sensitive parameters to the presence of ligament injuries were found to be early flexibility in anterior drawer, early flexibility in inversion, and the amount of coupling between internal rotation and inversion. These parameters provided a basis for differentiating between an isolated injury to the anterior talofibular ligament and a combined anterior talofibular and calcaneofibular ligament injury. For an isolated anterior talofibular ligament injury, a significant increase in flexibility in anterior drawer was present, whereas the increase in inversion flexibility or in the amount of coupling was insignificant. However, the increases in inversion flexibility and the amount of coupling became significant when both ligaments were involved. The results of the in vivo study indicated that significant changes in flexibility can be detected in patients with lateral ankle injuries. Finally, both the in vitro and in vivo results suggest that development of a reliable diagnostic test for ankle ligament injury based on changes in passive flexibility may be possible.

A six-degrees-of-freedom instrumented linkage for measuring the flexibility characteristics of the ankle joint complex

Diagnosis of ligament injuries to the ankle joint complex is a difficult clinical problem which relies primarily on manual physical examination and on radiographic evaluations. In an attempt to develop a reliable, quantitative diagnostic tool for such injuries we developed a six-degrees-of-freedom instrumented linkage: (Ankle Flexibility Tester—AFT), capable of measuring the flexibility characteristics of the ankle joint complex in vivo. The unique non-serial structure of this linkage was such that these characteristics were recorded directly in an anatomical coordinate system which enhanced clinical interpretation. The goal of the present study was to develop this linkage and to test its accuracy and its test-retest reliability. The positional accuracy of the AFT was measured and was found to be better than 0.5 mm for translation and 1.2° for rotations. The results obtained from a study conducted on two cadaveric specimens indicate negligible effect of loading rate on the flexibility characteristics within the range of possible manually applied loads. Finally, the reliability of the AFT was examined from test-retest studies conducted on a total of thirteen young healthy volunteers. The intraclass correlation coefficient: (ICC),, calculated from the test-retest data, indicated a reliability higher than 0.85. It was concluded that the high reliability and accuracy of the AFT, its simplicity of operation, the easy alignment procedure, the on-line load-displacement results, and the elimination of complex data processing render this device suitable for use in the clinic as well as in the research laboratory.

Experimental instability in the lumbar spine.

An in vivo animal model of lumbar segmental instability, involving both passive and active stabilizing components of the spine, was developed. The aim of this investigation was to dynamically study the alterations in segmental kinematics as a result of interventions to the passive stabilizing components and to the lumbar musculature. Segmental instability in the lumbar spine is associated with abnormal intervertebral motion. The majority of biomechanical studies have examined the in vitro effects of transecting individual stabilizing structures (i.e., intervertebral disc, facet joints, and ligaments), and have not simultaneously considered the effects of active musculature on spinal kinematics, which exist in the in vivo environment. Also, few studies have evaluated the kinematic behavior in the neutral region, for example, the transition phase between flexion and extension. Four experimental groups comprised 33 pigs, each of which followed different surgical injury sequences to the L3-L4 motion segment. An instrumented linkage attached to the L3-L4 motion segment was used to measure the sagittal kinematics during dynamic flexion-extension after each surgical injury and after bilateral stimulation of the lumbar paraspinal musculature. Injuries to the disc resulted in greater overall axial translation. Graded injuries to the facet joint mainly caused changes in sagittal rotation and shear translation. When the facet injuries were compounded by removal of the transverse processes, there was significantly greater coupled motion and increased hysteresis in the neutral region for rotation. Extensive muscular stimulation after each of the injuries caused significantly greater rotation and shear translation, along with a tendency toward reduced axial translation, when compared to the unstimulated case. Although increasing the range of motion, increased muscular activity stabilized the injured motion segment by smoothing the erratic rotation pattern of motion, particularly in the neutral region. Because of the direct attachment to the vertebrae, both passive and active strain from the musculature influence the spinal kinematics in normal or destabilized motion segments. Although increasing the range of motion, stimulation of the musculature surrounding the injured motion segment has a stabilizing effect by reducing abrupt kinematic behavior, particularly in the neutral region where the muscles are under reduced tension. A facetectomy produces a paradoxical kinematic behavior, which enhances the unstable condition of the motion segment. Surgical and rehabilitative treatments for patients with segmental instability need to consider the physiologic influences of the spinal musculature.

A New Stress Test for the Diagnosis of Hip Dysplasia: A Preliminary Study on a Manikin

Early detection of hip dysplasia remains elusive due to lack of a safe and objective diagnostic screening test. A new hip stress test sequence for improving the diagnosis of hip dysplasia is proposed: firstly the Barlow manoeuvre is performed, followed by an instrumented hip stiffness test and lastly the Ortolani test. Both the Barlow and the Ortolani tests consist of manual manipulative examinations which produce characteristic vibration in abnormal hips. The clinical examiner detects this vibration using finger-tip sensation. To verify this three-phase technique, the test was performed on a commercially available patient simulator. The force applied to the hip joint was measured using a force plate, and the hip laxity measured with an instrumented linkage. Significant differences in hip stiffness were found between dislocated and reduced hips. Further clinical testing will allow the theory to be finally verified and the technique to be refined.

An instrumented linkage for the measurement of the rotatory stability of the human ankle complex

Objective: To develop an analytical model of the lumbar motion segment and to determine the following under the application of flexion physiological loads: (1) the force displacement relationships of the lumbar motion segment; (2) the forces in the ligaments, disc, and facet joints; (3) the strains in the ligaments; and (4) the effect of the transection of the ligaments. Design: Computer modeling. Setting: Spinal Ergonomics and Joint Research Laboratory at The National College of Chiropractic. Procedure: Computer model simulation of external loads and simulation of ligament transection. Measures: The following parameters were predicted in flexion by means of a computer model: (1) the load-displacement relationships of the lumbar motion segment; (2) the loads in the ligaments, disc and facet joints; (3) the strains in the ligaments; and (4) the effect of the transection of the ligaments. Results: The load sharing among different ligaments predicted by this model under flexion load suggests that the supraspinous ligament carries the greatest load, followed by the yellow ligament, capsular ligament, intertransverse ligament, and interspinous ligament. The ligament strains indicate that the supraspinous ligament undergoes the maximum increase in length, followed by the interspinous ligament, yellow ligament, capsular ligament, and intertransverse ligament. The transection of ligaments increased the flexibility of the joint, the strains on the rest of the ligaments, the loads on all of the rest of the ligaments, as well as the moment on the disc, but does not significantly affect the compressive load on the disc. Conclusions: The analytical model predicts results similar to the experimental data on cadaver motion segments reported in the literature under flexion moment loads. (J Manipulative Physiol Ther 1999;22:201–8)

A method for the intravital measurement of interspinous kinematics

A novel non-radiographic technique for objectively quantifying quasi-static or dynamic intervertebral motion of a spinal motion segment in vivo in human subjects is presented here. The intervertebral motion device (IMD) is an instrumented linkage transducer system which can continuously measure over time two-dimensional sagittal plane rigid-body motion. Three custom-built omega-shaped displacement transducers are utilized. The IMD is rigidly fixed to the spinous processes of the lumbar motion segment by means of two intraosseous pins. Knowing the mechanoelectrical behavior and geometric configuration of the IMD, the relative spatial motion between the vertebral bodies can be resolved into sagittal rotation, axial translation, and anterior-posterior shear translation. Static calibrations of the IMD in the ranges of ±4° rotation and ±4 mm translation determined the absolute maximum errors to be 0.2° and 0.07 mm for rotation and translation measurements, respectively, with corresponding variances of 0.1° and 0.03 mm. For use in the vibration environment, negligible motion artifact content was detected in the IMD output signals when excited at discrete frequencies of 5.0 and 8.0 Hz. The first natural frequency of the IMD, specific for this design, was measured at 16.25 Hz. This technique may be used to study in vivo the spinal kinematics in healthy lumbar motion segments and in patients suspected of having segmental instability, and can perhaps be of clinical diagnostic significance.

Three-dimensional motion analysis of clinical stress tests for anterior knee subluxations.

The three rotations and three translations that comprise total knee motion were simultaneously measured in cadaveric knees during the commonly employed clinical tests for anterior cruciate injury. A second study determined the three-dimensional motions that occurred when known forces and moments were applied. A total of eight whole lower limbs were studied. A 6 degree-of-freedom instrumented linkage (3-D electrogoniometer), rigidly mounted to the tibia and femur, was used. The ligaments sectioned included the lateral extraarticular restraints (iliotibial band, lateral capsule) and the anterior cruciate ligament, both separately and in combination. After sectioning the anterior cruciate ligament alone, anterior displacement of both the medial and lateral tibial condyles increased markedly during the flexion rotation drawer and pivot shift tests. At 30 degrees knee flexion, total anterior-posterior displacement increased 100 percent, but internal-external tibial rotation increased only 15 percent. In all the anterior displacement type of clinical tests (including Lachman's test), there was not a true rigid coupling of knee motions because the examiner controlled the amount of internal tibial rotation and anterior tibial translation. After anterior cruciate sectioning alone, both the lateral and medial tibial condyles displaced anteriorly. Sectioning the medial structures caused additional anterior translation of the medial and lateral tibial condyles. We measured many different combinations of motions that depend on the ligament and capsular structures injured, the clinical test used, and how the clinician performed the test. Differing types of anterior subluxation require that the separate subluxations of the medial and lateral tibial condyles be determined during each stress test.

Reduction of Instrumented Linkage Data for Simple Anatomical Joint Models

When measuring the total, six degree-of-freedom (dof) motion permitted by an anatomical joint, it is convenient to attach the ends of an instrumented linkage to the two bodies meeting at the joint and to measure six independent linkage variables as the bodies move. While this method gives a complete description of the motion, it does not permit the motion to be described in a quantifiable manner that non-technical personnel understand. It is therefore often desirable to model the joint as as simple joint which permits fewer than six dof’s, e.g., as a spherical or even a revolute joint. If this is done, a decision must be made as how the six-dof data will be used to define the motion data associated with these simple models. It is the purpose of this paper to present an approach for doing this based in part on optimization theory.

Anchors 3. The behaviour of grouped inclined anchors in sand : 11F, 3R. GROUND ENGNG. V6, N6, 1973, P34–41

Research into the bahaviour of groups of inclined ground anchors is described. Results of laboratory tests are presented and discussed. The effect of anchor spacing and inclination was investigated in a test rig in which metal discs simulating the underreams were embedded. These were connected by a steel tendon to an instrumental linkage and a motor driven pull-out head. The instrumented linkage containing strain gauges and transducers was connected to a 20 channel bridge and digital voltmeter which produced direct punching of results on tape as the pull-out progressed. The article gives results in graphical form of many tests on groups of three and five anchors covering a range of inclinations and spacings. Differences were found in the loads taken by the 'leading' and 'trailing' anchors which were always compared with the performance of a single control anchor. Using stereo-photogrammetric techniques to record movements within the leighton buzzard sand in which the anchors were embedded, a picture of the 'pressure bulb' around the anchor group was obtained. The change in shape of this bulb with changes in other variables is discussed.