Ball-socket Joint Research Articles

Simulation of the dynamics of a flexible fiber in the swirling airflow in a nozzle containing cylindrical and divergent conical sections

Swirling airflow plays a key role in textile production processes. The structure and properties of a textile processed by utilizing swirling airflow depend to a large extent on the dynamics of the fibers in the flow. This work presents a numerical investigation of the dynamics of a flexible fiber in the tangentially injected swirling airflow in a nozzle containing cylindrical and divergent conical sections, which is frequently encountered during textile production. Simulation of the three-dimensional, transient, compressible and turbulent swirling airflow field in the nozzle is first conducted. A model for the particle-level simulation of a flexible fiber in a wall-bounded flow is consequently adopted for studying the fiber motion in the nozzle. This model assumes the fiber to be composed of several massless elastic rods connected by rigid ball–socket joints where various forces and torques are exerted. The stretching, bending and twisting deformations of the fiber as well as the fiber–wall collision can all be modeled. The motional characteristics of the flexible fiber can be obtained by solving the translational and rotational equations for all the ball–socket joints in the fiber model. Based on the model, the effects of two process and nozzle geometric parameters – the nozzle pressure and radial position of the injectors – on the fiber motion are studied. The results show that the model and methods presented in this work can provide effective and useful insights into the dynamics of flexible fiber in the swirling airflow field inside complex-structured nozzles employed in the textile production processes.

Gyroscopic Optimization for Aerospace Applications

This paper describes a Gyroscope balancing device which is gravity operated. The device is mounted at the base of the gyroscopes which are installed in the aircrafts. The device is for vertical gyroscopes. When the aircraft turns or heads upwards or downwards an error is introduced in the gyroscopes, as the base of the gyroscopes get inclined. In order to reduce this error, the inventions has four rectangular compartments in which metallic balls are placed which slide to the other end when the planes inclines in a particular direction and activate a touch switch which magnetizes the magnet at the opposite end which pull a disc mounted on a ball socket joint placed at the center of the four compartments, and on this disc the gyroscope is mounted. As the disc is attracted by a magnet it inclines in that direction which is opposite to the inclination of the aircraft and therefore keeps the gyroscope straight.

Mechanical testing setups affect spine segment fracture outcomes

The purpose of the work presented here was to establish an experimental testing configuration that would generate a bending compression fracture in a laboratory setting. To this end, we designed and fabricated a fixture to accommodate a three level spine segment and to be able to perform mechanical testing by applying an off-centric compressive loading to create a flexion-type motion. Forces and moments occurring during testing were measured with a six-channel load cell. The initial testing configuration (Fixture A) included plates connected to the superior potted vertebral body and to the ball-socket joint of the testing system ram. Surprisingly, while all cadaveric specimens underwent a similar off-centric compressive loading, most of the specimens showed extension outcomes as opposed to the intended pure-flexion motion. The extension was due to fixture size and weight; by applying an off-centric load directly on the top plate, unintended large shear forces were generated. To resolve the issue, several modifications were made to the original fixture configuration. These modifications included the removal of the superior plates and the implementation of wedges at the superior surface of the fixture (Fixture B). A synthetic sample was used during this modification phase to minimize the number of cadaveric specimens while optimizing the process. The best outcomes were consistently observed when a 15°-wedge was used to provide flexion-type loading. Cadaveric specimens were then experimentally tested to fracture using the modified testing configuration (Fixture B). A comparison between both fixtures, A and B, revealed that almost all biomechanical parameters, including force, moment, and displacement data, were affected by the testing setup. These results suggest that fixture design and implementation for testing is of extreme importance, and can influence the fracture properties and affect the intended motion.

Advances on the study of movable artificial vertebral body

At present, artificial vertebral implants have proven to be effective in the treatment of spinal tumors, infections, fractures and other diseases. However, the fusion artificial vertebral body can cause adjacent intervertebral joint degeneration and loss of original physiological curvature and activity. The movable artificial vertebral body can, to some extent, restore the normal physiological movement and reduce biomechanical changes of the spine, reducing the occurrence of complication. The design of movable artificial vertebral body is to equip movable device when the basis of reliable stability is obtained. According to its principle it can be divided into ball socket joint or elastic deformation. However the overall design of movable artificial vertebral body needs further improvement. Traditional mechanical processing methods are difficult to process complex prostheses and the agreement rate between traditional produced prostheses and lesions was low. While the emerging 3D printing technology can achieve individualized improvement of prosthesis, its slow rate and high cost need to be improved. The materials of movable artificial vertebral body includes metal, ceramics, biomaterials, high polymer materials and so on. Titanium alloy is the main material in metal materials, which is widely used, but its modulus of elasticity is still far from that of human bone and it lacks ideal bone fusion. Ceramic materials are rich in variety but fragile and poor in wear resistance. Biomaterials include autogenous bone, allogeneic bone, etc., with limited source and complicated operation. There are many kinds of polymer and biodegradable materials which obtain excellent and ideal properties. But their properties and applications need to be further studied. The movable artificial vertebral body still needs to be promoted and developed. The clinical experimental data is still insufficient, and long-term curative effect needs to be further observed and studied. This paper reviews the development, advantages, design, processing and materials of movable artificial vertebral bodies and provides useful reference for optimization design, processing and clinical application of movable artificial vertebral bodies.

A model for the particle-level simulation of multiple flexible fibers moving in a wall-bounded fluid flow

Airflow has wide and important applications in textile manufacturing. The dynamic behavior of fibers in the airflow can have a decisive influence on the structure and performance of the resultant textiles. In this paper, a three-dimensional model for the particle-level simulation of the dynamic behavior of multiple flexible fibers in a wall-bounded fluid flow of finite Reynolds number is proposed. The fiber is modeled as made up of a series of massless elastic rods connected by rigid ball-socket joints. In the model, both the internal and fluid forces and torques are applied on the ball-socket joints while the elastic rods only serve to transmit the internal forces and maintain the connectivity of the fiber without interacting with the ambient fluid. Each pair of adjacent elastic rods can bend and twist at the ball-socket joint connecting them, thus the stretching, bending and twisting deformations of the fiber can all be modeled. The motions of the fibers are governed by the translational and rotational equations for each ball-socket joint and both the fiber–fiber and fiber–wall interactions can be solved based on the hard sphere model. Using the proposed model, the regimes of the motion of a threadlike particle in a shear flow and the interaction of a single rigid fiber with a solid wall in Poiseuille flow are successfully reproduced, which agrees with the experimental results found in literature. The model is applied to the simulation of the motions of multiple flexible fibers in the airflow field inside the fiber transfer channel of the rotor spinning machine. Based on the simulation, the motional characteristics of the fibers as well as the effect of the transfer channel on the straightness and parallelization of the fibers are analyzed. The results indicate that the model proposed in this paper can provide an effective means of studying the dynamic behavior of the flexible fibers in the flow field involved in the textile production processes and a promising way of optimizing the design of the key components of textile machines.

Non-spherical ball-socket joint design for Delta-type robots

Delta-type robots are commonly used for positioning purposes in medical surgery. In such applications, the loading position accuracy of the end effector is of critical importance. However, the positioning accuracy is determined by the loading deflection, which depends in turn on the link flexibility and joint clearance within the system. Importantly, the loading deflection is posture/position dependent. This characteristic greatly complicates the task of improving the positioning accuracy using traditional compensation control methods. Accordingly, the present study proposes a non-spherical ball-socket joint design to improve the loading stiffness of the robot over the entire workspace. An analytical model is derived to quantify the loading deflection as a function of the link flexibility and joint clearance. The experimental results show that the non-spherical ball-socket joint design reduces the total variation in the loading deflection of the end effector by up to 81.04% compared to that of a traditional robot with spherical ball-socket joints when performing positioning over the entire workspace at the assigned height.

An Investigation on Rigidity of Ball-Socket Hip Joint Replacement

A 3-dimensional hip joint implant model was constructed which separates into three individual parts namely femoral stem with neck, femoral head and acetabular cup. Each part were assigned with the specific materials and a total of 3000 N loads was applied to mimic the body weight of an adult in static position or in double leg standing position. The results of the stress distribution were obtained from the finite element analysis for the difference diameter for each component of ball-socket and neck as well as the difference materials. The results showed that an optimum diameter of femoral ball-socket with 36 mm and titanium alloy have design rigidity which provided better performance and longer life span based on 13.922 Mpa equivalent stress .

An algorithm to allow humerus translation in the indeterminate problem of shoulder abduction

The shoulder is one of the most complex joints of the human body, mainly because of its large range of motion, but also because of its active muscular stabilisation. Actually, the numerous stabilizing muscles and degrees of freedom yield indeterminate biomechanical models. To solve this indeterminate, most models use reverse dynamics with a simplified ball-socket joint, preventing therefore the natural humerus translation. In this paper, an algorithm was specifically developed to solve the indeterminate problem by a feedback control of muscle activation, allowing the natural humerus translation. Abduction was considered in the scapular plane, accounting for the three deltoid parts and the rotator cuff muscles. The major aim of this study was to validate the numerical algorithm, which was here restricted to two-dimensions in order to compare the numerical solution to a known algebraic one. This comparison gave a relative error below 0.1%. The joint reaction force was comparable to other models and the humerus translation was in agreement with in vivo or in vitro studies.

Brownian dynamics simulations of needle chain and nugget chain polymer models--rigid constraint conditions versus infinitely stiff springs.

It is well known that orientational correlations appear in polymer chain models when the subunits are linked by ball-socket joints implemented as rigid constraint conditions. These correlations do not appear when the subunits are connected by springlike potential forces, even in the limit of infinitely stiff springs. In a widely used class of algorithms for Brownian dynamics simulations, inertia effects are ignored. However, in the recently introduced needle chain and nugget chain algorithms, the rigid constraint correlations depend on the mass and moment of inertia. This inconsistency does not appear in the bead-rod (Kramers) polymer chain model, which also has orientational correlations introduced by rigid constraint conditions. Explicit expressions for the correlation functions are given for thermodynamic equilibrium states. Analytical expressions for the associated forces ("metric forces") and simulation results showing how the rigid constraint correlations influence dynamical properties, are also presented. Further we discuss the physical relevance of these correlations and show via simulations that their influence on stationary and dynamical properties depend significantly on chain length. We further show that if the metric forces are removed, algorithms designed with rigid constraint conditions describe a chain of segments connected by infinitely stiff springs. Finally we show that the results presented here for needle chains are relevant also for the bead-rod (Kramers) chain model, making it possible to simulate a bead-spring chain with infinitely stiff springs.

Rotational diffusion of two-segmented macromolecules with a ball–socket joint: A kinetic theory approach

Semiflexible polymers are often modelled as consisting of rigid segments connected by rigid rods, ball–socket joints or springs. In this paper we focus on polymers consisting of two identical segments connected by a frictionless ball–socket joint. This introduces rigid constraints, resulting in the number of degrees of freedom being reduced. Using kinetic theory we derive the effective hydrodynamic mobility tensor of each segment in the chain, expressed in terms of the hydrodynamic mobility of an identical free segment. The result is used to obtain analytical and numerical expressions for the slowest decay mode in a typical transient electrically induced birefringence experiment. We show that under typical experimental conditions only this single mode will be present. The results we obtain are significantly different from results for a similar once-broken rod published by Wegener and co-workers and Garcia de la Torre and co-workers. In the last part of the paper Brownian dynamics simulations of the two-segment model is used to verify our analytically obtained expressions for the mobility tensor and decay modes and to obtain results for situations where analytical results are unavailable. The model assumes no hydrodynamic interaction between the segments.

Brownian dynamics simulation of rigid bodies and segmented polymer chains. Use of Cartesian rotation vectors as the generalized coordinates describing angular orientations

The three Eulerian angles constitute the classical choice of generalized coordinates used to describe the three degrees of rotational freedom of a rigid body, but it has long been known that this choice yields singular equations of motion. The latter is also true when Eulerian angles are used in Brownian dynamics analyses of the angular orientation of single rigid bodies and segmented polymer chains. Starting from kinetic theory we here show that by instead employing the three components of Cartesian rotation vectors as the generalized coordinates describing angular orientation, no singularity appears in the configuration space diffusion equation and the associated Brownian dynamics algorithm. The suitability of Cartesian rotation vectors in Brownian dynamics simulations of segmented polymer chains with spring-like or ball-socket joints is discussed.

Brownian dynamics of bead–rod–nugget–spring polymer chains with hydrodynamic interactions

With Brownian dynamics simulations of solutions containing complex biological macromolecules in mind we have formulated a polymer chain model consisting of a selectable sequence of spherical subunits (beads) and nonspherical subunits of arbitrary shapes (nuggets) connected by rigid rods, rigid ball–socket joints, or springs. Many physical properties of both subunits and connections are selectable. First a very general diffusion equation of polymer kinetic theory is employed. Next the equivalent Itô stochastic differential equation of motion is established and finally an effective Brownian dynamics simulation algorithm is presented. In all these steps it is assumed that the numerical values of the subunit steady state mobility tensor are obtainable. The important and previously unanswered question of how to include translational–rotational hydrodynamic interactions in Brownian dynamics simulations of polymer chains containing nonspherical subunits linked by rigid constraints is resolved rigorously here. This means that during the formal derivation of the presented Brownian dynamics simulation algorithm all subunit hydrodynamic interactions of the proposed bead–rod–nugget–spring polymer chain model have in principle been taken fully into account. In addition the model includes rigid constraints to fixed points in the laboratory coordinate system, solvent flow, external forces, excluded volume effects, and bending and torsional stiffness between polymer chain subunits. Bead–spring, bead–rod–spring, needle–spring, needle polymer chains and liquid crystals are all special cases of the bead–rod–nugget–spring polymer chain model. The validity of the algorithm presented is limited to the diffusion time domain.

Stabilized interference fringes on the retina.

A METHOD of producing a stabilized retinal image (that is, an image which is stationary on the retina) was first described in Nature 1, and other work has been reported elsewhere2–4. Here we describe a method of producing a stabilized image with interference fringes. A cylindrical unit 6 mm. in diameter and 3 mm. thick is formed by cementing a calcite crystal between two pieces of ‘Polaroid’. This unit is cemented to a steel ball which fits tightly into a ball-socket joint on a stalk fixed to a contact lens as shown in Fig. 1.