In-vitro measurement of the human knee joint motion during quadriceps leg raising

This paper represents a three-dimensional motion analysis of the human knee joint under given conditions of loading and constraint. As the knee is extended by a known force applied to the quadriceps tendon, relative displacements of the femur, tibia, and patella are measured using a video motion analysis system. The most prominent motion of the tibia is external rotation and anterior displacement relative to the femur during knee extension. The patellar flexion angle decreases from 70° to 0°. The moment arm of the knee extensor mechanism exhibits a characteristic bell shape which peaks somewhere in the 40°–60° region of flexion. In general, the quadriceps force results primarily from an increase in the torque exerted by the weight of the lower leg. In the range of 20°–60°, the quardricep force needed to extend the leg remains relatively constant. As the knee approaches full extension, the moment arm decreases due to the fact that the posterior capsule and the ACL begin to tighten in this region. Consequently, the quadriceps force increases rapidly.     

The effects of trochlear groove geometry on patellofemoral joint stability--a computer model study

The effect of the variation in the femoral groove geometry on patellofemoral joint stability was studied using a two-dimensional transverse plane model with deformable articular surfaces. The femoral and patellar bony structures were modelled as rigid bodies with their profiles expressed by splines. The articular cartilage was discretized into compression springs, distributed along the femoral and patellar profiles, based on the rigid-body spring model. The medial and lateral retinacula were modelled as linear tensile springs, and the quadriceps muscles and patellar tendon as strings with known tension. The anatomical data were obtained from the transverse plane magnetic resonance images of a normal knee flexed at 20 degrees and from the literature. A dynamic analysis approach was employed to solve the governing equations of the model, i.e. three static equilibrium equations of the patella and a constraint equation for each cartilage spring, explicitly. The results of the model suggest that alteration of the sulcus angle from 139 degrees to 169 degrees causes a lateral shift and tilt of less than 3 mm and 4 degrees. This effect increased slightly with increasing total quadriceps force, however, to significantly more than 7 mm and 18 degrees respectively when the medial retinaculum was released. It was suggested that this might be the combined effect of the medial retinaculum deficiency and trochlear dysplasia that is responsible for patellar subluxation and, particularly, dislocation disorders.     

The variation in the orientations and moment arms of the knee extensor and flexor muscle tendons with increasing muscle force: a mathematical analysis

The orientations and moment arms of the knee extensor and flexor muscle tendons are evaluated with increasing values of muscle force during simulated isometric exercises. A four-bar linkage model of the knee in the sagittal plane was used to define the motion of the joint in the unloaded state during 0-120 degrees flexion. The cruciate and collateral ligaments were represented by arrays of elastic fibres, which were recruited sequentially under load or remained buckled when slack. A bi-articular model of the patello-femoral joint was used. Simple straight-line representation was used for the lines of action of the forces transmitted by the model muscle tendons. The effects of tissue deformation with increasing muscle force were considered. During quadriceps contraction resisted by an external flexing load, the maximum change in moment arm of the patellar tendon was found to be 2 per cent at 0 degree flexion when the quadriceps force was increased tenfold, from 250 to 2500 N. The corresponding maximum change in orientation of the tendon was 3 degrees at 120 degrees flexion. During hamstrings contraction resisted by an external extending load, the maximum change in moment arm of the hamstrings tendon was 8 per cent at 60 degrees flexion when the hamstrings force was increased tenfold, from 100 to 1000 N. During gastrocnemious contraction, the corresponding maximum change for the gastrocnemious tendon was 3 per cent at 0 degree. The orientations of the flexor muscle tendons in this range of force either remained constant or changed by 1 degree or less at any flexion angle. The general trend at any flexion angle was that, as the muscle force was increased, the moment arms and the orientations approached nearly constant values, showing asymptotic behaviour. It is concluded that experimental simulations of knee muscle action with low values of the externally applied load, of the order of 50 N, can provide reliable estimates of the relationships between muscle forces and external loads during activity.     

Mechanics of the passive knee joint. Part 2: interaction between the ligaments and the articular surfaces in guiding the joint motion

The aim of this study was to examine how the interaction between ligament tensions and contact forces guides the knee joint through its specific pattern of passive motion. A computer model was built based on cadaver data. The passive motion and the ligament lengthening and force patterns predicted by the model were verified with data from the literature. The contribution of each ligament and contact force was measured in terms of the rotational moment that it produced about the tibial medial plateau and the anterior-posterior (AP) force that it exerted on the tibia. The high tension of the anterior cruciate ligament (ACL) and the geometric constraints of the anterior horns of the menisci were found to be key features that stabilized the knee at full extension. The mutual effect of the cruciates was found as the reason for the screw-home mechanism at early flexion. Past 300, the AP component of contact force on the convex geometry of the lateral tibial plateau and tension of the lateral collateral ligament (LCL) were identified as elements that control the joint motion. From 60 degrees to 90 degrees, reduction in the tension of the ACL was determined as a reason for continuation of the tibial anterior translation. From 90 degrees to 120 degrees, increase in the tension of the posterior cruciate ligament and the AP component of the contact force on the convex geometry of the lateral tibial plateau pushed the tibia more anteriorly. This anterior translation was limited by the constraining effects of the ACL tension and the AP component of the contact force on the medial meniscus. The important guiding role observed for the LCL suggests that it should not be overlooked in knee models.     

Three-dimensional contact dynamic model of the human knee joint during walking

It is well known that the geometry of the articular surface has a major role in determining the position of articular contact and the lines of action for the contact forces. The contact force calculation of the knee joint under the effect of sliding and rolling is one of the most challenging issues in this field. We present a 3-D human knee joint model including sliding and rolling motions and major ligaments to calculate the lateral and medial condyle contact forces from the recovered total internal reaction force using inverse dynamic contact modeling and the Least-Square method. As results, it is believed that the patella, muscles and tendon affect a lot for the internal reaction forces at the initial heel contact stage. With increasing flexion angles during gait, the decreasing contact area is progressively shifted to the posterior direction on the tibia plateau. In addition, the medial side contact force is larger than the lateral side contact force in the knee joint during normal human walking. The total internal forces of the knee joint are reasonabe compared to previous studies.     

A technique for the measurement of patellar tracking during weight-bearing activities using ultrasound

A new fixation device, the femoral clamp, was developed in this study for the ultrasound measurement of patellar medio-lateral motion during sitting and squatting knee flexion/extension. Seventeen subjects, 6 males, 11 females, aged between 18 and 40 years were recruited for the test. Results showed that the patella moved medially then laterally from extension to flexion when sitting. Weight-bearing knee motion produced a more laterally tracked patella without the presence of the initial medial patellar translation. The tracking patterns of the patellae were similar regardless of knee movement direction. The patellar lateral position was greatly affected by the movement task (p < 0.0005), and was also influenced by gender for maximum medial position (p < 0.05). The reproducibility of the measurement was between 0.29 and 0.90 for the intra-rater and 0.34-0.75 for the inter-rater reliability. The accuracy of the ultrasound measurement was validated by interventional magnetic resonance (iMR) imaging of the patella and the mean error of the measurement was 1.4 +/- 3.2 mm. Although further research is needed to improve the accuracy and reliability of this method, it has demonstrated the feasibility of obtaining patellar tracking data during load-bearing activities.     

Maximum finger force prediction using a planar simulation of the middle finger

Maximum isometric finger-grip forces were predicted using a biomechanical model for plane motion of the middle finger. In the course of this study, mathematical representations of tendon displacement, the moment arm of tendon at the finger joints and muscle force-length relationship were investigated. The information gathered was applied to the model to estimate the maximum grip force of the middle finger gripping cylinders of different sizes. Muscle force per unit physiological cross-section area of 30 N/cm2 resulted in good agreement with measured force. However, for finger postures having an acute proximal interphalangeal joint angle, the estimated force was greater than that measured. Various joint angles were applied to the model to simulate the wrist and finger postures not limited to the cylinder grip. In general the finger force was greatest with the wrist in its extended position and at acute flexion of the proximal interphalangeal joint. The maximum finger force occurred at reduced metacarpophalangeal joint angles as the wrist joint changed from an extended position to a flexed one. It is also postulated that muscle force-length relationship is an important factor in muscle force predictions. The data obtained by this research are useful for the design of handles and the current model is applicable to the analysis of hand postures for workers using hand tools.     

An optimal control model for determining articular contact forces at the human knee during rising from a static squat position

A two-dimensional dynamic model of the knee joint was incorporated into a four-segment, eight-muscle model of the human body to determine the muscle, ligament, and articular contact forces transmitted at the knee as humans stand up from a static squatting position. Our optimal control model predicted peak tibiofemoral contact forces 8 times as high as body weight. Furthermore, ligament forces, especially those in the anterior-cruciate, were nearly body weight as knee flexion approached 90 degrees. Ligament and tibiofemoral contact loads were dominated by the forces exerted by muscles during the movement.     

Method of generating and measuring static small force using down-slope component of gravity

A method of generating and measuring static small forces at the micro-Newton level is proposed. In the method, the down-slope component of gravity acting on a mass on an inclined plane is used as a static force. To realize a linear motion of the mass with a small friction, an aerostatic linear bearing is used. The forces acting on the mass, such as the down-slope component of gravity and the dynamic frictional force, are determined by the levitation mass method. In an experiment, a static small force of approximately 183 microN is generated and measured with a standard uncertainty of approximately 2 microN.     

Mechanical properties of different anatomical sites of the bone-tendon origin of lateral epicondyle

A series of rabbit common extensor tendon specimens of the humeral epicondyle were subjected to tensile tests under two displacement rates (100 mm/min and 10 mm/min) and different elbow flexion positions 45°, 90° and 135°. Biomechanical properties of ultimate tensile strength, failure strain, energy absorption and stiffness of the bone-tendon specimen were determined. Statistically significant differences were found in ultimate tensile strength, failure strain, energy absorption and stiffness of bone-tendon specimens as a consequence of different elbow flexion angles and displacement rates. The results indicated that the bone-tendon specimens at the 45° elbow flexion had the lowest ultimate tensile strength; this flexion angle also had the highest failure strain and the lowest stiffness compared to other elbow flexion positions. In comparing the data from two displacement rates, bone-tendon specimens had lower ultimate tensile strength at all flexion angles when tested at the 10 mm/min displacement rate. These results indicate that creep damage occurred during the slow displacement rate. The major failure mode of bone-tendon specimens during tensile testing changed from 100% of midsubstance failure at the 90° and 135° elbow flexion to 40% of bone-tendon origin failure at 45°. We conclude that failure mechanics of the bone-tendon unit of the lateral epicondyle are substantially affected by loading direction and displacement rate.     

Study on damping characteristics of hydropneumatic suspension unit of tracked vehicle

Hydropneumatic suspension unit is an important part of tracked vehicles to absorb external impact load exerted from the non-paved road and the cannon discharge. Its absorption performance is strongly influenced by both damping and spring forces of the unit. In this paper, we numerically analyze the damping characteristics of the in-arm-type hydropneumatic suspension unit (ISU) by considering four distinet dynamic modes of the ISU damper: jounce-loading, jounce-unloading, rebound-loading and rebound-unloading. The flow rate coefficients determining the oil flow rate through the damper orifice are decided with the help of independent experiments. The wheel reaction force, the flow rate at cracking and the damping energy are parametrically investigated with respect to the orifice diameter and the wheel motion frequency.     

深海采矿整体系统动力学建模及联动开采作业过程快速仿真分析

以国际海底区域多金属结核开采及我国深海采矿1000 m海试系统技术方案为工程背景,针对整体系统联动开采作业过程模拟研究的需要,提出并开发海底履带式集矿机单刚体快速动力学仿真模型。根据深海采矿系统整体运动与约束关系,将集矿机单刚体模型与扬矿管三维离散元模型相连接,组成深海采矿整体系统快速动力学仿真模型。提出两种新的整体联动开采作业方式——纵向联动折返式与横向联动折返式。通过分析、设计及仿真控制,实现两种整体联动开采作业方式的快速仿真分析。讨论集矿机按两种新提出的采集路径行走,同时采矿船拖曳扬矿管跟随集矿机运动时,整体系统的纵向与横向联动作业动力学特性。仿真分析结果表明,整体系统联动作业过程中各子系统均能保持在各自的稳定范围内运动,进而证明两种新提出的集矿机采集路径的可行性以及整体系统纵向与横向联动折返式作业方式的合理性。深海采矿系统整体联动开采作业过程动力学分析将为整体联动控制研究奠定基础,并为将来的深海采矿海试以及商业开采过程操控提供重要的理论分析基础与技术参考。     

Modeling the lateral pedestrian force on a rigid floor by a self-sustained oscillator

The main goal of this paper is the definition of a nonlinear single-degree-of-freedom oscillator able to accurately predict the lateral walking force of a pedestrian. The force exerted on the floor corresponds to its restoring force. The rigid floor case is analyzed, leading to an autonomous oscillator. Even though such an oscillator is a simplified representation of the human body, it should be able to reproduce two experimentally observed phenomena: (i) the time-history of lateral force is an approximately periodic signal; (ii) the walking motion is self-sustained, in the sense that the pedestrian/oscillator produces by itself the energy needed to sustain its motion. This implies that such an oscillator must be self-sustained. In addition, the self-sustained character entails that the autonomous oscillation has a natural amplitude and frequency, representing the natural walking amplitude and frequency of the pedestrian. An original model is proposed by modifying the so-called hybrid Van der Pol/Rayleigh oscillator, already used for applications in the field of robotics. A dynamic analysis of this oscillator is then performed through an energetic approach and a perturbation technique in order to get the stable limit cycle. The model parameters are finally identified from the experimental force signals, resulting from a test campaign on a population of 12 pedestrians: the agreement between model and experimental results is very good.     

裂纹角的大小对裂纹转子振动特性的影响

将离心叶轮转子系统简化为Jeffcott转子系统,在考虑非线性油膜力的基础上,综合考虑了系统的流体激振力,建立了含有裂纹故障转子的动力学模型。运用数值积分法分析了不同裂纹角下系统响应随转速变化的分岔图、相图和Poincare映射图等,结果表明,裂纹深度一定的情况下,随着裂纹角的增大,流体激振力和非线性油膜力对转子系统分岔特性的影响也逐渐增大。     

Frictional characteristics of an aerostatic linear bearing

Frictional characteristics of an aerostatic linear bearing are evaluated in detail by means of a developing method. In the method, the resultant force acting on the moving part of the bearing is measured highly accurately as the inertial force using an optical interferometer. The velocity dependence of dynamic friction is focused on in this paper. The component of dynamic frictional force, which is almost independent of the absolute value of velocity, is detected in the experiment, in addition to the force component that is proportional to velocity. Before this study, dynamic frictional force had only been explained as the viscous frictional force acting inside the air film, which is proportional to the velocity.     

轮式移动仿人机器人的动力学建模与分析

利用高效迭代牛顿-欧拉方法对一个21自由度的轮式移动仿人机器人进行了整体动力学建模,该模型虽然维数较高,但消除了分块建模中需要对模块之间相互作用力进行建模的难点问题,并且由于机器人双臂的对称结构,当合理规划双臂运动时,动力学模型将得到部分简化。本文还对某关节运动时在各个关节所产生的力或力矩进行了仿真分析。解析及仿真结果表明,合理规划上臂各关节的协调运动,将极大地削弱车体及腰部各关节所受的力或力矩扰动,为基于动力学的机器人运动控制以及稳定性分析提供理论依据。     

动态测量中测量力的确定

在动态测量中应使测量头与工件保持接触,因此,必须合理地确定测量力的大小.本文讨论了动态测量中影响测量力大小的因素,导出了动态测量力的计算公式.     

Analytical model for estimating intersegmental forces exerted on human lower limbs during walking motion

Existing methods for evaluating the intersegmental forces acting on the human lower limbs during walking generally measure the ground reaction force exerted on the feet using force plates and estimate the intersegmental forces using an inverse dynamics approach. However, force plates are inconvenient and expensive. Accordingly, the present study proposes an approach for evaluating the intersegmental forces without the need for force plates by modeling the human lower limbs as a seven-link manipulator system. In the proposed approach, the intersegmental forces are derived directly from the analytical model using Newton–Euler theory based on the posture information obtained from a system of gyroscopes and accelerometers during walking motion. The results obtained from the analytical model are compared with the experimental data obtained using load cells. It is found that the estimated results are in good agreement with the measured results. Thus, the basic validity of the proposed analysis system is confirmed.     

Concentric and eccentric shoulder rehabilitation biomechanics

The use of an impulse-momentum (IM) exercise technique was investigated for end-stage shoulder rehabilitation. The objectives of this study were to: (a) quantify the net shoulder joint forces and moments while using an IM system and (b) test the influence of gender and muscle loading type (concentric or eccentric) on kinetic and kinematic parameters. Fourteen healthy adults (eight males, six females) performed a repeated measures experiment on an instrumented device utilizing a cabled shuttle system. While maintaining 90 degrees of shoulder abduction and 90 degrees of elbow flexion, the subjects externally rotated their upper arm from 0 degrees to 90 degrees (concentric acceleration) and then internally rotated their upper arm back from 90 degrees to the 0 degrees position (eccentric deceleration). Shoulder joint forces and moments as well as rotational work and power were calculated using inverse dynamics (free-body forces and moments calculated at intersegmental joint centres). Overall concentric peak forces and moments were greater than eccentric peak forces and moments (P < 0.0001). Joint forces and moments reached a maximum during the initial phase of concentric loading (0 degrees to 45 degrees) compared with any other rotational position in the loading cycle (concentric 45 degrees to 90 degrees or eccentric 90 degrees to 0 degrees). The results also indicate that males experienced higher (P < 0.0001) average resultant peak joint forces (concentric 0 degrees to 45 degrees = 108.0 N and eccentric 90 degrees to 45 degrees = 87.2 N) than females (concentric 0 degrees to 45 degrees = 74.7 N and eccentric 45 degrees to 0 degrees = 56.0 N). In addition, males experienced higher (P < 0.0001) average resultant peak joint moments (concentric 0 degrees to 45 degrees = 30.4 N m and eccentric 45 degrees to 0 degrees = 21.0 N m) than females (concentric 0 degrees to 45 degrees = 19.7 N m and eccentric 45 degrees to 0 degrees = 12.8 N m).     

Biomechanical simulation of an amputated forearm with and without a prosthesis

In this study a computer simulation was developed for analysing the performance of a below-elbow amputated forearm, with and without a prosthesis. The upper extremity was represented in terms of two rigid bodies, the arm and the forearm. Five muscles, three elbow flexors and two elbow extensors, were included in the model. The muscle model used was the five-component model, including the contractile, parallel, series and viscous elements and the muscle mass. Dynamic and static simulations were conducted, with and without prosthesis, to study parametrically the effects of stump length, tendon distal transfer, tendon or muscle shortening and muscle physiological cross-sectional area. The performance measures which were the most affected included flexion moment of the forearm about the elbow, muscle moment, force in the joint, flexion rate and mechanical energy. The simulation presented an interesting case when the amputation site is more proximal than the anatomical insertion point of a muscle, necessitating shortening of the muscle to avoid the situation where it exerts no force. It was also found that, of the changeable parameters, the most beneficial changes in the forearm parameters for improved dynamic performance were: (a) tendon distal transfer and (b) increase of the muscle cross-sectional area, the latter achievable by means of physical training.