Instantaneous Center Research Articles

Cervical Disc Arthroplasties Fail to Maintain Physiological Kinematics Under Lateral Eccentric Loads.

In vitro human cadaveric biomechanical analysis. Optimization of prostheses for cervical disc arthroplasties (CDA) reduces the risk of complications. The instantaneous helical axis (IHA) is a superior parameter for examining the kinematics of functional spinal units. There is no comprehensive study about the IHA after CDA considering all 3 motion dimensions. Ten human functional spinal units C4-5 (83.2 ± 7.9yrs.) were examined with an established measuring apparatus in intact conditions (IC), and after CDA, with 2 different types of prostheses during axial rotation, lateral bending, and flexion/extension. Eccentric preloads simulated strains. The IHA orientation and its position at the point of rest (IHA0-position) were analyzed. The results confirmed the existing data for IHA in IC. Lateral preloads showed structural alterations of kinematics after CDA: During axial rotation and lateral bending, the shift of the IHA0-position was corresponding with the lateral preloads' applied site in IC, while after CDAs, it was vice versa. During lateral bending, the lateral IHA orientation was inclined, corresponding with the lateral preloads' applied site in the IC and oppositely after the CDAs. During flexion/extension, the lateral IHA orientation was nearly vertical in the IC, while after CDA, it inclined, corresponding with the lateral preloads' applied site. The axial IHA orientation rotated to the lateral preloads' corresponding site in the IC; after CDA, it was vice versa. Both CDAs failed to maintain physiological IHA characteristics under lateral preloads, revealing a new aspect for improving prostheses' design and optimizing their kinematics.

Damping control of polodes, inertia and natural frequencies: Theory and application to automotive suspensions

This paper shows how tunable dampers can help control the instant centre of rotation of a 2D rigid body and its polode in planar motion, which in turn implies that the inertia tensor can also be controlled. For mechanisms equipped with some elasticity the results show that damping can also control their natural frequencies. The foundation of a general theory to control the polode is presented, exploring the chance of an optimal control formulation of the problem via a variational control principle, approached by the LQR (Linear Quadratic Regulator) method, after a suitable linearization. Application to automotive suspension linkages is presented that demonstrates the control of the instant roll centre and axis and consequently its instant roll vibration frequency to optimize the response, when excited by lateral inertia forces.

Animation of cycloid and spiral curves in companion with instantaneous center of rotation and radius of curvature

ABSTRACT In this paper, the animations for the 2D cycloid and the 3D spiral curves are done. The trajectories of instantaneous rotation center and the corresponding radius of curvature are given. We prove that the trajectory of the instantaneous center of rotation is also a cycloid. For a 3D spiral curve, the two radii and the two instantaneous centers of rotation for the spiral curve are also given. It is interesting to find that the two parameters in the Frenet equation have the same meaning of radius of curvature but in different planes. In a similar way of the 2D experience, we also confirm that the trajectory of the instantaneous center of rotation for a spiral curve is also a spiral curve. An example is also given to discuss the Puyuma express incident, a major accident in 2018. The curve of rail is interpolated and the radius of curvature is determined. Discussions on the radius of rail curve and the speed of train for the failure are done. Finally, the animation is implemented by using the MATLAB and the Mathematica software. Not only theoretical derivation for the curvature of a curve but also its real application to rail engineering is proposed.

Singularity analysis of spatial single-DOF mechanisms based on the locations of the instantaneous screw axes

The instantaneous kinematics of a mechanism can be fully described through the instantaneous screw axes (ISAs) associated to the relative motions between mechanism's links. Characterizing the instantaneous kinematics of a mechanism includes its singularity analysis, which is the identification of mechanism configurations (singularities) where the instantaneous degrees-of-freedom (DOFs) of the mechanism “somehow” change. In single-DOF mechanisms with time-independent either holonomic or first-order non-holonomic constraints, the locations of the instantaneous screw axes only depend on the mechanism configuration. This property is fully exploited in planar single-DOF mechanisms where all the singularity conditions have been associated to the coincidence of particular instant centers (ICs), thus making the singularity identification possible with a simple analysis of the mechanism configuration. Differently, for single-DOF spatial mechanisms, the geometric conditions on ISAs that identify a singular configuration have not been enunciated for the general case, yet. This paper fills this lack by providing the explicit expressions of all the possible instantaneous input-output relationships, the exhaustive enumeration of the geometric conditions on the ISAs that identify singular configurations and a geometric and analytic technique for the singularity analysis of spatial single-DOF mechanisms, which is the natural extension of the IC-based ones conceived for planar single-DOF mechanisms.

Interspinous-Interbody Fusion via a Strictly Lateral Surgical Approach: A Biomechanical Stabilization Comparison to Constructs Requiring Both Lateral and Posterior Approaches.

Objective Lumbar fusion performed through lateral approaches is becoming more common. The interbody devices are generally supported by supplemental posterior fixation implanted through a posterior approach, potentially requiring a second incision and intraoperative repositioning of the patient. A minimally invasive lateral interspinous fixation device may eliminate the need for intraoperative repositioning and avoid disruption of the supraspinous ligament. The objective of this in vitrobiomechanical study was to investigate segmental multidirectional stability and maintenance of foraminal distraction of a lateral interspinous fixation device compared to commonly used pedicle screw and facet screw posterior fixation constructs when combined with lumbar interbody cages. Methods Six human cadaver lumbar spine specimens were subjected to nondestructive quasistatic loading in the following states: (1) intact; (2) interspinous fixation device alone and (3) with lateral interbody cage; (4) lateral lumbar interbody cage with bilateral pedicle screws; (5) lateral lumbar interbody cage with unilateral pedicle screws; and (6) lateral lumbar interbody cage with facet screws. Multidirectional pure bending in 1.5 Nm increments to 7.5 Nm, and 7.5 Nm flexion-extension bending with a 700 N compressive follower load were performed separately with optoelectronic segmental motion measurement. Relative angular motions of L2-L3, L3-L4, and L4-L5 functional spinal units were evaluated, and the mean instantaneous axis of rotation in the sagittal plane was calculated for the index level.Foraminal height was assessed during combined flexion-extension and compression loading for each test construct. Results All implant configurations significantly restricted flexion-extension motion compared with intact (p < 0.05). No significant differences were found in flexion-extension when comparing the different posterior implants combined with lateral lumbar interbody cages. All posterior fixation devices provided comparable neuroforaminal distraction and maintained distraction during flexion and extension. Conclusions When combinedwith lateral lumbar interbody cages, the minimally invasive lateral interspinous fixation device effectively stabilized the spine and maintained neuroforaminal distraction comparable to pedicle screw constructs or facet screws. These results suggest the lateral interspinous fixation device may provide a favorable alternative to other posterior systems that require patient repositioning during surgery and involve a greater disruption of native tissues.

Dört Çubuk Mekanizmalı Diz Protezlerinin Arı Algoritması ve Genetik Algoritma ile Boyut Optimizasyonu

: In knee prostheses, the curve of the instantaneous center of rotation (ICR) and, therefore, stability of the prothesis are the most important parameters to be considered. The ICR curve depends on many parameters. One of them and the most effective one is the dimensions of four bar mechanism. In polycentric knee mechanisms, it has become inevitable to use optimization techniques while determining the dimensions of the mechanism for the stability of the prosthesis in the stance position. In this study, definitions of knee prostheses and polycentric knee mechanisms are given, optimization studies written in this field are mentioned thorough literature research. The study aims to find mechanism dimensions that gives ICR curve close to the reference curve by optimizing the mechanism dimensions of four-bar knee mechanisms. The Bees Algorithm and Genetic Algorithm (GA) were used for this purpose. The limits and objective function for the optimization were determined, and after many trials, separate mechanism dimensions with The Bees Algorithm and the Genetic Algorithm are obtained. By comparing the results, it has been observed that the dimensions obtained by The Bees Algorithm produced a better approximation to the reference instantaneous center of rotation curve.

Characteristics of wind turbine wakes for different blade designs

In this work, we investigate the characteristics of wind turbine wakes for three different blade designs (i.e. the NREL-Ori, NREL-Root and NREL-Tip designs, where the NREL-Ori refers to the baseline offshore 5 MW wind turbine designed by the US National Renewable Energy Laboratory) under turbulent inflows using large-eddy simulations with the actuator surface model. The load on the blade is higher near the blade root/tip for the NREL-Root/NREL-Tip designs when compared with the NREL-Ori design, while their thrust coefficients are the same. The results show that the blade designs influence the velocity deficit in the near wake, turbulence kinetic energy and wake meandering (both amplitude and frequency). In the near-wake region, the magnitude of the velocity deficit from the NREL-Root design is higher. As for the turbulence kinetic energy, its maximum in the near wake is higher for the NREL-Tip design, while in the far wake, it is higher for the NREL-Root design. Analyses of the instantaneous spanwise wake centre positions show higher meandering amplitude for the NREL-Root design, with the magnitudes of the low-frequency components approximately the same as the other two designs under the same inflow. The dominant meandering frequencies from different designs are different, with lower values for the NREL-Root design for which the vortex structures near the hub of low frequency play leading roles, and higher values for the NREL-Tip design for which the flow structures of high frequency in the tip shear layer are more important.

Design and Evaluation of a Smooth-Locking-Based Customizable Prosthetic Knee Joint

Abstract Limb loss affects many people from a variety of backgrounds around the world. The most advanced commercially available prostheses for transfemoral amputees are fully active (powered) designs but remain very expensive and unavailable in the developing world. Consequently, improvements of low-cost, passive prostheses have been made to provide high-quality rehabilitation to amputees of any background. This study explores the design and evaluation of a smooth-locking-based bionic knee joint to replicate the swing phase of the human gait cycle. The two-part design was based on the condyle geometry of the interface between the femur and tibia obtained from magnetic resonance (MR) images of the human subject, while springs were used to replace the anterior and posterior cruciate ligaments. A flexible four-bar linkage mechanism was successfully achieved to provide not only rotation along a variable instantaneous axis but also slight translation in the sagittal plane, similar to the anatomical knee. We systematically evaluated the effects of different spring configurations in terms of stiffness, position, and relaxion length on knee flexion angles during walking. A good replication of the swing phase was achieved by relatively high stiffness and increased relaxation length of springs. The stance phase of the gait cycle was improved compared to some models but remained relatively flat, where further verification should be conducted. In addition, 3D printing technique provides a convenient design and manufacturing process, making the prosthesis customizable for different individuals based on subject-specific modeling of the amputee’s knee.

Instantaneous center of rotation in the canine femorotibial joint: Ex vivo assessment of a tool to evaluate joint stabilization surgeries

Cranial cruciate ligament rupture is a common cause of femorotibial joint instability in the dog. Numerous techniques including several tibial osteotomies have been described for stabilization, but there is no current consensus on the best method. The instantaneous center of rotation (ICR) can aid investigations of pathological joint movement, but its use is problematic in the femorotibial joint due to combined rotation and translation during flexion and extension. Using fluoroscopic images from an earlier cadaveric study of canine joint stability, an interpolation method was used to create repeatable rotational steps across joint situations, followed by least squares approximation of the ICR. The ICR in intact joints was located mid-condyle but displaced significantly (P < 0.001) proximally following cranial cruciate ligament transection and medial meniscal release. Individual joints appear to respond differently to destabilization. Triple tibial osteotomy partially restored ICR location during early movement from flexion to extension. Joint instability significantly altered the proportions of rolling and gliding movement at the joint surface (P < 0.02), which triple tibial osteotomy partially improved. While triple tibial osteotomy restores joint stability ex vivo and clinically, normal biomechanics of the joint are not restored. The methods described here may prove useful for comparison of osteotomy techniques for stabilization of the cranial cruciate ligament deficient femorotibial joint in dogs.

Finite element analysis of optimized novel additively manufactured non-articulating prostheses for cervical total disc replacement.

Ball-and-socket designs of cervical total disc replacement (TDR) have been popular in recent years despite the disadvantages of polyethylene wear, heterotrophic ossification, increased facet contact force, and implant subsidence. In this study, a non-articulating, additively manufactured hybrid TDR with an ultra-high molecular weight polyethylene core and polycarbonate urethane (PCU) fiber jacket, was designed to mimic the motion of normal discs. A finite element (FE) study was conducted to optimize the lattice structure and assess the biomechanical performance of this new generation TDR with an intact disc and a commercial ball-and-socket Baguera®C TDR (Spineart SA, Geneva, Switzerland) on an intact C5-6 cervical spinal model. The lattice structure of the PCU fiber was constructed using the Tesseract or the Cross structures from the IntraLattice model in the Rhino software (McNeel North America, Seattle, WA) to create the hybrid I and hybrid II groups, respectively. The circumferential area of the PCU fiber was divided into three regions (anterior, lateral and posterior), and the cellular structures were adjusted. Optimal cellular distributions and structures were A2L5P2 in the hybrid I and A2L7P3 in the hybrid II groups. All but one of the maximum von Mises stresses were within the yield strength of the PCU material. The range of motions, facet joint stress, C6 vertebral superior endplate stress and path of instantaneous center of rotation of the hybrid I and II groups were closer to those of the intact group than those of the Baguera®C group under 100N follower load and pure moment of 1.5 Nm in four different planar motions. Restoration of normal cervical spinal kinematics and prevention of implant subsidence could be observed from the FE analysis results. Superior stress distribution in the PCU fiber and core in the hybrid II group revealed that the Cross lattice structure of a PCU fiber jacket could be a choice for a next-generation TDR. This promising outcome suggests the feasibility of implanting an additively manufactured multi-material artificial disc that allows for better physiological motion than the current ball-and-socket design.

Optimization Design and Performance Analysis of a Bionic Knee Joint Based on the Geared Five-Bar Mechanism.

Animal joint motion is a combination of rotation and translational motion, which brings high stability, high energy utilization, and other advantages. At present, the hinge joint is widely used in the legged robot. The simple motion characteristic of the hinge joint rotating around the fixed axis limits the improvement of the robot's motion performance. In this paper, by imitating the knee joint of a kangaroo, we propose a new bionic geared five-bar knee joint mechanism to improve the energy utilization rate of the legged robot and reduce the required driving power. Firstly, based on image processing technology, the trajectory curve of the instantaneous center of rotation (ICR) of the kangaroo knee joint was quickly obtained. Then, the bionic knee joint was designed by the single-degree-of-freedom geared five-bar mechanism and the parameters for each part of the mechanism were optimized. Finally, based on the inverted pendulum model and the Newton-Euler recursive method, the dynamics model of the single leg of the robot in the landing stage was established, and the influence of the designed bionic knee joint and hinge joint on the robot's motion performance was compared and analyzed. The proposed bionic geared five-bar knee joint mechanism can more closely track the given trajectory of the total center of mass motion, has abundant motion characteristics, and can effectively reduce the power demand and energy consumption of the robot knee actuators under the high-speed running and jumping gait.

A novel approach for determining instantaneous centers of rotation of the mandible with an intraoral scanner: A preliminary study.

Recording and reproducing mandibular movements have been of key importance in the practice of dentistry for over a century. Recently, it has become possible to use digital technologies for these tasks. This study presents a preliminary method to try to identify the mandibular instantaneous centres of rotation based solely on intraoral scanners. The dentitions of four participants were scanned, multiple inter-occlusal registrations and buccal scans were performed in closed and opened positions. Blender software was used to align the meshes during the post-scan digital workflow. Bite alignment accuracy was assessed and then improved with a strict exclusion protocol. An automated algorithm was used to find rotations between closed stage and open stage meshes. Our exclusion protocol reduced the bite alignment error significantly (p = 0.001) and the root-mean-square error value of the meshes decreased from 0.09 mm (SD = 0.15) to 0.03 mm (SD = 0.017). However, the remaining translational error caused an unexpectedly large shift in the axis of rotation (mean = 1.35 mm, SD = 0.77) with a 41.83: 1 ratio. As found in other studies, our results showed even a small amount of error during registration can shift the axis of rotation a large amount. This phenomenon will compromise the results of common pantographic methods which assume a rotation axis of the condyle. It also adds valuable information to the concept of instantaneous centers of rotation by revealing their true characteristics.

Performance Research of Dual Power Flow Continuous Differential Steering System for Tracked Vehicle

The tracked vehicle has good passability and adaptability for different complex environments, and also can maintain a stable posture with the ability to regulate flexible posture. Therefore, it is necessary to design a steering system with continuous and accurate steering radius and high transmission efficiency. The dynamic model of differential steering system was established including input rotate speed and output rotate speed. The dynamic model between input rotate speed and steering radius was obtained according to the relationship of output rotate speed and steering radius. The dynamic model of steady steering including the length, gauge, ground instantaneous center offset and so on of tracked vehicle was built, which could be used to predict the steady state steering characteristic of tracked vehicle.

Design and Optimization of Lower Limb Rehabilitation Exoskeleton with a Multiaxial Knee Joint.

To facilitate rehabilitation training for patients, we proposed the implementation of an anthropomorphic exoskeleton structure that incorporates a variable instantaneous center of rotation (ICR). This design considers the variability in knee ICR among individuals, resulting from the irregular form of the human knee joint, and leverages a double-degrees-of-freedom (2DOF) five-bar mechanism to adapt to these differences. The walking gait of the human lower limb and the corresponding knee ICR were measured and calculated using an optical 3D motion capture system. The optimal dimension parameters of the five-bar mechanism were then obtained through the optimization of human movement position inputs and rod length constraints to minimize the error in knee ICR, gait angle, and ankle trajectory between the human and the exoskeleton. Finally, we established an exoskeleton prototype to conduct relevant experimental tests. The experiment results showed that the average errors of knee ICR trajectory, hip angle, knee angle, and ankle trajectory were 5.52 × 10-4 m, 0.010 rad, 0.014 rad, and 1.57 × 10-3 m, respectively. The experimental results demonstrated that the exoskeleton's movement trajectory was close to the human's, reducing the human-mechanism interaction force and improving patient comfort during rehabilitation training.

AXOIDS OF HOOKE’S JOINT

The analysis of literary sources devoted to the research and construction of cardan transmissions using the Hooke's joint showed that the peculiarities of the spherical movement of the cardan joint crosspiece are insufficiently covered. This is explained by the relatively small weight of the crosspiece, due to which it almost does not affect the dynamics of the cardan transmission. The need to take into account the mass-geometric parameters of the crosspiece and to analyze comprehensively its movement may arise during accurate calculations of high-speed cardan transmissions. In this case, it is convenient to consider the movement of the crosspiece as rolling without sliding of the moving axoid on the stationary axoid. This approach makes it possible to more fully investigate the peculiarities of the spherical movement of the crosspiece and gives a visual representation of the orientation of its instantaneous axis of rotation in fixed and moving coordinate systems. Based on this, this work is devoted to the construction of a kinematic model of the Hooke's joint crosspiece, the movement of which is considered as rolling without sliding of a moving axoid on a stationary one.&#x0D; As a result of the kinematic analysis of the Hooke's joint, the equations of the hodographs of the vector of the absolute angular velocity of the crosspiece in the fixed and moving coordinate systems were obtained, and the parameters of the fixed and moving axoids of the crosspiece of the cardan joint were determined. It is proved that the stationary axoid of the crosspiece of the Hooke's joint is an oblique elliptic cone with the apex in the center of the crosspiece, and its opposite generatrices, crossing the major axis of the guide ellipse, coincide with the axes of the drive and driven shafts of the joint. The moving axoid of the crosspiece is a closed conical surface with a variable opening angle, the maximum value of which is equal to twice the value of the interaxial transmission angle. With small values of the interaxial angle, which occur in the practice of using a single Hooke’s joint, a moving axoid can be approximately considered as a straight circular cone with a vertex in the center of the crosspiece and an opening angle equal to twice the value of the interaxial transmission angle. The error of this assumption increases rapidly with the increase of the interaxial transmission angle. The correctness of the obtained mathematical model was confirmed by computer modeling in the Autodesk Inventor environment.&#x0D; The obtained results can be used in the study of dynamic processes that occur in cardan transmissions using Hooke's joint.

Corneal topographic changes in patients with thyroid eye disease: A retrospective cross-sectional study

PurposeThis study aimed to evaluate corneal topographic findings in patients with thyroid eye disease (TED) using a Galilei camera and compare their corneal topographic parameters with those of control patients. MethodsThis retrospective cross-sectional study included 52 eyes of 26 patients with TED (study group) and 40 eyes of 20 controls treated at a tertiary medical center in Taiwan between January and December 2021. All participants underwent basic ophthalmological examinations, corneal topography examination using a Galilei dual Scheimpflug camera, thyroid function examination, and orbital computed tomography. The corneal topographic parameters and cross-sectional area of the extraocular muscles were compared between the TED and control groups. ResultsSeveral corneal topographic parameters, including the Inferior-Superior Index, Keratoconus Prediction Index, Surface Asymmetry Index, Surface Regularity Index, simulated keratometry astigmatism, and anterior instantaneous astigmatism axis, differed significantly between the groups (P ≤ 0.05). The anterior instantaneous astigmatism axis was more oblique in the TED group than in the control group. A scatter plot revealed a more scattered distribution in the anterior instantaneous astigmatism axis in the TED group than in the control group. However, the corneal topographic parameters did not differ significantly among the different thyroid dysfunction groups. ConclusionsThe corneas of patients with TED are suspicious and keratoconus-like, and TED can increase anterior corneal astigmatism in the oblique axis, albeit with large variations in the extent of change. These TED-related corneal changes may aid in the early diagnosis of TED, especially “silent” TED.

Effect of non-specific neck pain on the path of the instantaneous axis of rotation of the neck during its flexion-extension movement

Non-specific neck pain is a common musculoskeletal disorder with a high prevalence and involves impaired joint movement pattern. Therefore, this study aimed to compare the trajectory of the instantaneous axis of rotation(IAR) in flexion-extension movements of the neck between people with and without nonspecific neck pain, using functional data analysis techniques. Furthermore, possible relationships between neck kinematics and perceived pain and disability were explored.Seventy-three volunteers participated in this cross-sectional study. They were allocated in a non-specific pain group (PG, n = 28) and a control group (CG, n = 45). A cyclic flexion-extension movement was assessed by a video photogrammetry system and numerical and functional variables were computed to analyze IAR trajectory during movement. Moreover, to explore possible relationships of these variables with pain and neck disability, a visual analogue scale (VAS) and the neck disability index (NDI) were used.The instantaneous axis of rotation trajectory during the flexion-extension cyclic movement described a path like Greek letter rho both in the CG and the PG, but this trajectory was shorter and displaced upward in the PG, compared to the CG. A reduction of the displacement range and a rise in the vertical position of the IAR were related to VAS and NDI scores.Non-specific neck pain is associated with a higher location of the instantaneous axis of rotation and a decrease in length of the path traveled during the flexion-extension movement. This study contributes to a better description of neck movement in people with non-specific neck pain, which would help to plan an individualized treatment.

Equivalent system based inverse dynamics analysis of transfemoral prosthetic legs: Validation and application.

Inverse dynamics analysis of prosthetic legs with polycentric knees is complex due to increased number of links. The present work proposes a simple and general method called equivalent system (ES) analysis. The ES analysis provides forces and moment at hip joint as well as at the functional knee centre (FKC), the instant centre of the polycentric knee. The input to the ES analysis is the motion data. For validation of the proposed method, synthetic motion data for the swing phase of walking with prosthetic legs having different knees are generated by simulations using ADAMS. The hip kinetics evaluated by the proposed method is compared with that from ADAMS. The root mean square errors of the ES analysis are lower than 17 (10-6) N for hip reaction forces and 2.6 (10-6) Nm for the hip moments, thereby validating the proposed method. In order to demonstrate the application of the proposed methodology, the motion data of two transfemoral amputees using single-axis and four-bar knee prostheses are obtained during gait trials. The hip kinetics as well as kinetics at FKC are computed using ES analysis. Hip power during the swing phase is also evaluated and compared. The results are presented in this paper and discussed. The ES analysis is shown to be a versatile tool to provide insights into the human-mechanism interaction.

Biomechanical consequences of the intervertebral disc centre of rotation kinematics during lateral bending and axial rotation

The location of the instantaneous centre of rotation (ICR) of a lumbar unit has a considerable clinical importance as a spinal health estimator. Consequently, many studies have been conducted to measure or estimate the ICR during rotations in the three anatomical planes; however the results reported are widely scattered. Even if some inter-subjects variability is to be expected, such inconsistencies are likely explained by the differences in methods and experiments. Therefore, in this paper we seek to model three behaviours of the ICR during lateral bending and axial rotation based on results published in the literature. In order to assess the metabolic and mechanical sensibility to the assumption made on the ICR kinematics, we used a previously validated three dimensional non-linear poroelastic model of a porcine intervertebral disc to simulate physiological lateral and axial rotations. The impact of the geometry was also briefly investigated by considering a 11^circ wedge angle. From our simulations, it appears that the hypothesis made on the ICR location does not significantly affect the critical nutrients concentrations but gives disparate predictions of the intradiscal pressure at the centre of the disc (variation up to 0.7 MPa) and of the displacement fields (variation up to 0.4 mm). On the contrary, the wedge angle does not influence the estimated intradiscal pressure but leads to minimal oxygen concentration decreased up to 33% and increased maximal lactate concentration up to 13%. While we can not settle on which definition of the ICR is more accurate, this work suggests that patient-specific modeling of the ICR is required and brings new insights that can be useful for the development of new tools or the design of surgical material such as total lumbar disc prostheses.

A geometric and analytic technique for the determination of the instantaneous screw axes in single-DOF spatial mechanisms

In single-degree-of-freedom (single-DOF) mechanisms, the location of the instantaneous screw axes (ISAs) of the relative motions between any two links depends only on the mechanism configuration. In the literature, this property together with the Aronhold-Kennedy (AK) theorem was exploited to devise geometric and analytic techniques that determine ISAs in planar mechanisms, where the ISAs are located by the instant centers (ICs). Despite the fact that an extended Aronhold-Kennedy (EAK) theorem has been demonstrated for spatial mechanisms, too, since 1959, the spatial counterpart of these techniques has not been proposed, yet. Relating ISA locations to the mechanism configuration is important during the mechanism design and provides a deeper comprehension of the mechanism motion by disclosing the role each link plays. Here, a geometric and analytic technique based on the EAK theorem is presented for the ISA determination in single-DOF spatial mechanisms. The proposed method is indeed the extension to spatial mechanisms of those techniques used for the IC determination in planar mechanisms. The effectiveness of the proposed technique is also illustrated through two relevant case studies.