Sequential Damage Assessment of the Posterolateral Complex of the Knee Joint: A Finite Element Study

Background. The posterolateral complex (PLC), which consists of the popliteus tendon (PT), lateral collateral ligament (LCL), and popliteofibular ligament (PFL), is an indispensable structure of the knee joint. The aim of this study was to explore the functionality of the PLC by determining the specific role of each component in maintaining posterolateral knee stability. Methods. A finite element (FE) model was generated based on previous material property data and magnetic resonance imaging of a volunteer’s knee joint. The injury order of the PLC was set as LCL, PFL, and PT. A 134 N anterior load was applied to the tibia to investigate tibial displacement (TD). Tibial external rotation (TER) and tibial varus angulation (TVA) were measured under bending motions of 5 and 10 Nm. The instantaneous axis of rotation (IAR) of the knee joint under different rotation motions was also recorded. Results. The TD of the intact knee under a 134 N anterior load matched the values determined in previous studies. Our model showed consistent increases in TD, TVA, and TER after sequential damage of the PLC. In addition, sequential disruption caused the IAR to shift superiorly and laterally during varus rotation, and medially and anteriorly during external rotation. In the dynamic damage of the PLC, LCL injury had the largest effect on TD, TVA, TER, and IAR. Conclusions. Sequential injury of the PLC caused considerable loss of stability of the knee joint according to an FE model. The most significant structure of the PLC was the LCL.

Instantaneous center/axis of rotation for planar and three-dimensional motion

This article discusses a direct analytical method for calculating the instantaneous center of rotation and the instantaneous axis of rotation for the two-dimensional and three-dimensional motion, respectively, of rigid bodies. In the case of planar motion, this method produces a closed-form expression for the instantaneous center of rotation based on a single point located on the rigid body. It can also be used to derive closed-form expressions for the body and space centrodes. For three-dimensional, rigid body motion, an extension of the technique used for planar motion locates a point on the instantaneous axis of rotation, which is parallel to the body angular velocity vector. In addition, methods are demonstrated that can be used to map the body and space cones for general rigid body motion, and locate the fixed point for the body.

Moving and fixed axoids of frenet thrihedral of directing curve on example of cylindrical line

If the solid body makes a spatial motion, then at any point in time this motion can be decomposed into rotational at angular velocity and translational at linear velocity. The direction of the axis of rotation and the magnitude of the angular velocity, that is the vector of rotational motion at a given time does not change regardless of the point of the solid body (pole), relative to which the decomposition of velocities. For linear velocity translational motion is the opposite: the magnitude and direction of the vector depend on the choice of the pole. In a solid body, you can find a point, that is, a pole with respect to which both vectors of rotational and translational motions have the same direction. The common line given by these two vectors is called the instantaneous axis of rotation and sliding, or the kinematic screw. It is characterized by the direction and parameter - the ratio of linear and angular velocity. If the linear velocity is zero and the angular velocity is not, then at this point in time the body performs only rotational motion. If it is the other way around, then the body moves in translational manner without rotating motion. The accompanying trihedral moves along the directing curve, it makes a spatial motion, that is, at any given time it is possible to find the position of the axis of the kinematic screw. Its location in the trihedral, as in a solid body, is well defined and depends entirely on the differential characteristics of the curve at the point of location of the trihedral – its curvature and torsion. Since, in the general case, the curvature and torsion change as the trihedral moves along the curve, then the position of the axis of the kinematic screw will also change. Multitude of these positions form a linear surface - an axoid. At the same time distinguish the fixed axoid relative to the fixed coordinate system, and the moving - which is formed in the system of the trihedral and moves with it. The shape of the moving and fixed axoids depends on the curve. The curve itself can be reproduced by rolling a moving axoid over a fixed one, while sliding along a common touch line at a linear velocity, which is also determined by the curvature and torsion of the curve at a particular point. For flat curves, there is no sliding, that is, the movable axoid is rolling over a stationary one without sliding. There is a set of curves for which the angular velocity of the rotation of the trihedral is constant. These include the helical line too. The article deals with axoids of cylindrical lines and some of them are constructed.

KINEMATICS OF A ROLLER CONE BIT WITH A DIRECT FACET TOOTH

The advanced technique of shock-kinematic analysis of the bit roller cone interaction with rock in the process of oil and gas wells drilling is proposed. Preliminary investigations of the interaction of the roller cone bits with rock were based on assumptions far from reality: the concept of the instantaneous axis of rotation of the roller cone constant contact with rock, the absence of slipping, as well as the tooth reforming and sinking into rock. The principle of the roller cones action is the gradual destruction of the surface of the bottomhole due to the cutting-crushing chipping of rock with a bit tooth.The axial roller cone is considered, and the original method of planes projection is used to determine the regulation of tooth motion, taking into account: bit roller cones slipping along the surface of the bottomhole; phases of roller cone tooth sinking into rock; real change in the distance of the axis of rotation of the roller cone to the surface of the bottomhole due to tooth penetration into the rock; the substantiation of the conditions for avoiding the roller cone tooth entering to the previously obtained hole in the process of bottomhole crushing. Besides the moment of the drill string inertia, the moments of roller cones inertia are additionally taken into account under the condition of the oblique impact of the tooth on the rock.The technique allows to calculate the volume of the disintegrated rock on the bottomhole, both taking into account and without taking into account rock chipping and tooth forming. The obtained dependencies allow us to select transmitted ratios from the drill string to the crowns of the roller cones under the condition of avoiding the roller cone tooth to the previously obtained hole during rock destruction on the bottomhole. It allows increasing the efficiency of drilling by roller cones.

Quantitative analysis of in-vivo thumb carpometacarpal joint kinematics using four-dimensional computed tomography

The purpose of this study was to define the normal thumb carpometacarpal joint kinematics in-vivo during opposition and abduction using four-dimensional computed-tomography in four volunteers. Movement of the metacarpal relative to the trapezium was quantified using both Euler and helical axis representations. Articular surface contact patterns were also analysed. The overall axis of rotation for the movement of opposition and abduction passes through the trapezium and the base of the proximal phalanx, respectively. An abrupt change in instantaneous axis of rotation at terminal opposition was found. Ligament modelling shows dorsoradial ligament becomes tauter towards terminal opposition, whereas anterior oblique ligament becomes more slack. These results support the existence of the ‘screw-home’ pivot at terminal opposition and the importance of the dorsoradial ligament for stability in this position. The normal reference set in this study can help establish a diagnostic tool for subtle carpometacarpal instability, or for evaluating efficacy of surgery.