Rigid Body Mechanics Research Articles

Continuum Mechanics Applied to the Biomechanics of Motion.

Continuum Mechanics is the discipline that studies the motion and deformation of material bodies, and is at the basis of both Solid Mechanics and Fluid Mechanics. This works aims at highlighting how a basic education in modern Continuum Mechanics can be of fundamental importance not only in the Biomechanics of Tissue, but also in the Biomechanics of Movement. The latter is largely based on Rigid Body Mechanics, which can be considered as a simple particular case of the general theory of Continuum Mechanics. As an example, a straightforward methodology for the extraction of the angular velocity from motion analysis data is illustrated. The method is based on a quantity that is more primitive than the angular velocity: the spin tensor.

The Character of Couples and Couple Stresses in Continuum Mechanics

In this paper, the concepts of moments and couples in mechanics are examined from a fundamental perspective. Representing a couple by its moment vector is very useful in rigid body mechanics, where the states of internal stresses and deformation are not studied. This is because only the moment of couples appears in the governing equation of moment equilibrium. On the other hand, when considering the state of internal stresses and deformation in continuum mechanics, not only the moment of couples but also the line of action of their constituent parallel opposite forces must be specified. In defining a well-posed problem for a continuum, including the governing equations of moment equilibrium or motion, boundary conditions, and constitutive relations, only the moment of couples (e.g., body couples, couple tractions, couple stresses) appear without specifying the line of action of the constituent parallel forces. Nevertheless, the physical state of stress and deformation in the continuum must be unique and determinate. Therefore, this physical requirement imposes some restrictions on the form of body couples, couple tractions, and couple stresses. Here, the uniqueness of interactions in the continuum is used to establish that the continuum does not support a distribution of body couples or a distribution of surface twisting couple tractions with normal moments. Furthermore, the mechanism of action of the couple traction as a double layer of shear force tractions is established, along with the skew-symmetric character of the couple stress moment tensor.

Ambiguity, invisibility, and negativity *

Many widely different problems have a common mathematical structure wherein limited knowledge leads to ambiguity that can be captured conveniently using a concept of invisibility that requires the introduction of negative values for quantities that are inherently positive. Here I analyze three examples taken from perception theory, rigid body mechanics, and quantum measurement.

A Real Test and Simulation Result Comparison of Selected Properties of Hybrid Composite Materials

In this study, the notion of composite materials is thoroughly assessed. Actual and simulation in a specific computer software stress testing of hybrid composites are investigated. The paper deals with the mechanics of rigid bodies, their elasticity, strength, and stiffness. In addition to a general overview of the former’s behavior and properties, this paper presents the possibility of calculating the bearing capacity of various materials in relevant computer programs. The production and testing process of the composite samples are described. The latter are then subjected to simulated tests in computer software. The main objective of this study is to compare real test results of hybrid composites, namely combined carbon fibers, glass fibers, aramid-carbon fibers, aramid honeycomb, and metal mesh with the simulation findings.

Static Analysis and Optimization Design of Bridge Structures under Different Load Conditions

The research is the optimization design of the bridge from the structure of the bridge, proper material utilization, and improving the performance of the bridge. First, the static model of the bridge structure was established, and then the finite analysis and rigid body mechanics models were utilized to separately detail the dead load, live load, and exceptional load. Based on the above analyses, optimization methods such as mathematical programming and genetic algorithms were used for optimizing the design of bridge structures. The tests demonstrated that the bridge’s weight can be significantly reduced by optimal design, the efficiency of usage in materials is enhanced, and the rigidity and stability of the structure advanced significantly. It is verified through checking the comparative analysis before and after optimization that the efficiency of the optimization method has been proved and the critical application value of optimization design in bridge engineering. The research conclusions provide new ideas and methods for bridge structure design, which has important theoretical and practical significance.

Stick–Slip Vibration Characteristics Study of the Drill String Based on PID Controller

In order to address the issue of drill string stick–slip vibration, which leads to drill bit wear and reduces the drilling velocity, we conducted a study on the characteristics of stick–slip vibration using a proportional-integral-derivative (PID) controller. By applying the principles of rigid body mechanics, we established a two-degree-of-freedom torsional dynamics equation and derived the first-order differential dynamics equation for the drill string. Subsequently, we designed a PID controller and obtained an equation for the control of stick–slip vibration. The research findings indicate that variations in the difference between the static and dynamic friction coefficients directly impact the nature of the limit cycles in the phase plane. As this difference decreases, the limit cycle narrows and the stick–slip vibrations weaken progressively. When the static and dynamic friction coefficients are equalized, no stick–slip vibrations occur within the drill string. The implementation of PID control effectively manages stick–slip vibrations in the drill string, with greater efficiency observed in controlling the turntable velocity compared to the drill bit velocity. This research provides valuable insights for the development of control strategies aimed at mitigating stick–slip vibrations in drilling engineering applications, thereby facilitating the efficient and safe extraction of oil and gas resources.

Efficient generation of random rotation matrices in four dimensions.

Four-dimensional (4D) rotations have applications in the fields of robotics, computer vision, and rigid-body mechanics. In the latter, they can be used to transform between equimomental systems of point masses. Here we provide an efficient algorithm to generate random 4D rotation matrices covering an arbitrary, predefined range of rotation angles. These matrices can be combined with Monte Carlo methods for the efficient sampling of the SO(4) group of 4D rotations. The matrices are unbiased and constructed such that repeated rotations result in uniform sampling over SO(4). The algorithm can be used to optimize the mass partitioning in coarse-grained simulation models of molecules involving coupled constraints for stable time integration.

Multidimensional optical tweezers synthetized by rigid-body emulated structured light

Structured light with more extended degrees of freedom (DoFs) and in higher dimensions is increasingly gaining traction and leading to breakthroughs such as super-resolution imaging, larger-capacity communication, and ultraprecise optical trapping or tweezers. More DoFs for manipulating an object can access more maneuvers and radically increase maneuvering precision, which is of significance in biology and related microscopic detection. However, manipulating particles beyond three-dimensional (3D) spatial manipulation by using current all-optical tweezers technology remains difficult. To overcome this limitation, we theoretically and experimentally present six-dimensional (6D) structured optical tweezers based on tailoring structured light emulating rigid-body mechanics. Our method facilitates the evaluation of the methodology of rigid-body mechanics to synthesize six independent DoFs in a structured optical trapping system, akin to six-axis rigid-body manipulation, including surge, sway, heave, roll, pitch, and yaw. In contrast to previous 3D optical tweezers, our 6D structured optical tweezers significantly improved the flexibility of the path design of complex trajectories, thereby laying the foundation for next-generation functional optical manipulation, assembly, and micromechanics.

Performance of rocking frames with friction tension-only devices

The implementation of a new friction tension-only “GripNGrab” device attached to a rocking steel frame is described. The device, when subject to significant tension dissipates energy via sliding in the frictional component. When the device is loaded in the compression direction, almost no compressive force is carried, but displacement occurs in the ratchetting component. This absence of any significant compressive force within the dissipative system means that the rocking frame will always recentre after uplift from earthquake shaking. A 9 m tall 4.75m wide 3-storey steel concentrically braced rocking frame is designed for low-damage seismic performance. Restoring forces are provided by (i) gravity, (ii) friction “GripNGrab” (GNG) tension-only dissipation devices at the base, and (iii) beam-slab effects. The initial fundamental period of the structure was 0.16s. The initial structure used a 10mm GNG ratchet pitch, and had a GNG strength to not slide under serviceability level shaking. Elastic, pushover, cyclic pushover, as well as time history analyses, with different shaking intensities are conducted using OpenSEES software. The scope of work is limited to a single building and a single ground motion. Parameters varied included the presence of beam-slab effects, and the GNG device stiffness, strength and tooth pitch. It is shown that the full behaviour of the frame could be understood considering cyclic pushover analysis. The peak uplift displacement was conservatively estimated from the peak roof displacement using rigid body mechanics and the tension-only device provided no resistance to full frame recentring. For the frames considered, cumulative uplift displacements, necessary to determine the inelastic displacement capacity of the tension only device, were up to 28 times the peak uplift displacement, not necessarily occurring at the maximum shaking intensity. Maximum frame base shear force demands were up to 1.43 times that from pushover analysis. When the beam-slab, connecting the rocking frame to the rest of the structure, increased the lateral force resistance, the base shear increased significantly, reduced peak roof displacements, and increased the effective number of peak uplift displacement cycles (NPUDc). For large shaking intensities, yielding of the beam-slab occurred resulting in permanent peak roof and uplift displacements. The GNG device strength, stiffness and tooth pitch variations for the cases studied did not significantly affect the response. Initial stiffness, and secant stiffness, based methods to predict the response of rocking frames were non-conservative for these short-period structures with small energy dissipation, and a simple improvement to match the behaviour was developed for the case studied based on the R-T-m relationship for a range of shaking intensity.

Investigation on the basic principles of human-machine contact force, based on screw theory

In this paper, to introduce a spatial rigid body mechanics analytical method and start the analysis, the human-machine contact force is equivalent to a spatially rigid body: the mechanism and skin surfaces are equivalent to two different rigid planes, and the motion between the mechanism and skin surfaces is equivalent to virtual branches motion. By considering the elastic deformation of each virtual branch axis, an equivalent human-machine contact force model is established, along with the deformation coordination equation of each virtual branch. The analytical solution of the tension/compression and the expression of the internal force of each virtual branch are obtained by solving the pseudo inverse and weighted generalized inverse solutions of the human-machine contact force. The physical meaning of the internal force of each virtual branch is also denoted. In addition, this paper contains an experimental platform for testing human-machine contact force, in which the linear stiffness of each branch is evaluated, therefore simulating and verifying the theoretical model introduced above. The contact force model proposed in this paper provides a theoretical basis for the development of human-machine synergetic motion.

“RULES-BASED MOTION” REANIMATION OF THE CARPUS

Using a reverse engineering capability to quantify the factors that control the rigid body mechanics of the wrist, a mathematical forward animation capability and model of wrist motion that allows the carpus to move under its own rules is being developed. This characterises the isometric connections, from which was developed the Stable Central Column Theory of Carpal Mechanics - which incorporates the Law of Rules Based Motion.This work has now advanced to the ability to reapply the extracted rules to allow rules-based rigid body reanimation of an individual wrist. As each wrist is unique, there is a given reality that each reanimation must be based on an individual wrist's unique rules, and the aspiration to create a standard or normal wrist is unrealistic.Using True Life Anatomy (Adelaide, Aust) analysis software, the specific rules (morphology / connectivity / interaction / loading) of individual wrists have been characterised, and then reapplied in a rigid body reanimation environment using Adams (MSC Software, U.S.) software.In the preliminary application of this biomechanics environment, by using the reverse engineering / forward reanimation process, wrist motion can be recreated - based purely on the unique rules, extracted from individual wrists. Instability of the proximal scaphoid was evident in several of the animations, and there was confirmation that the spatial attachment points of the isometric constraints are very exacting. The actual attachment and specific morphology of the carpal bones varied between individual wrists.Using a reverse engineering and then forward reanimation process, we have been able to recreate wrist motion using the rigid body mechanics based on the Law of Rules Based Motion. Further work is required, but the potential to apply “what if” virtual surgery options to an individual injured wrist and more precisely characterise and test solutions to wrist dysfunction are becoming realised.

STRUCTURE OF THE COMPUTER COMPLEX FOR CALCULATING THE STRENGTH OF PRISMATIC BODIES BASED ON THE SEMI-ANALYTIC METHOD OF FINITE ELEMENTS

One of the main and responsible stages of creating an apparatus for numerical analysis of structures using the finite element method is its implementation in the form of a set of programs. The principles of complex construction should take into account modern requirements for strength calculation software in modern calculation complexes. Among them, first of all, automation of the main stages of the computing process, rational use of the resources of the operating and external memory of storage devices, non-closedness in relation to the classes of problems to be solved, algorithms for the task of input data, the method of discretization and solution of systems of equations and etc. In addition, the structure of the programs should take into account the specifics of the semi-analytical method of finite elements, for which such a large experience of creating developed systems of mathematical support for the search of spatial structures has not yet been accumulated, as when using the traditional version of FEM. Considerable experience in solving finite element mechanics problems, accumulated over the past decades, has been reflected in a number of industrial commercial software complexes of domestic (LIRA, SCAD) and foreign (ANSYS, Nastran, ABAQUS) production. The developed finite element base of these software complexes allows you to obtain solutions to a wide range of problems of the mechanics of a deformable rigid body for objects of different dimensions, including for massive spatial bodies, and convenient means of input-output of information and processing of the obtained results make them very accessible to a wide circles of users and allow to display the obtained results with the maximum degree of visibility. There are also object-oriented complexes created at manufacturing enterprises and research institutes, for example at the Institute of Strength Problems of the National Academy of Sciences of Ukraine, at the Dnipropetrovsk National University. The conducted research will determine the most optimal ways of solving the listed problems from the point of view of computing costs and complexity of implementation, as well as outline the circle of unsolved issues.

Non-stationary problem of high earth dam under seismic impact

The design, construction, and operation of high earth dams on the territory of seismogenic zones of Uzbekistan set the task for researchers to improve the calculation methods and algorithms for various kinds of loads to which the structure is subjected. At present, the application of the dynamic method (a wave theory) to the calculation of an earth structure, i.e., the dynamic stress-strain state of high earth dams under seismic impact within the framework of wave theory, is the most difficult problem in the mechanics of a deformable rigid body. In the example of the operating Charvak high earth dam, the numerical method of finite differences solved the problem of studying the stress-strain state with shear dynamic impact on the base (such as the records of a real seismogram of an earthquake). At the boundaries of the considered finite region of the base, the so-called radiation conditions are set, i.e., diffraction is not considered. The result of solving the non-stationary problem is presented as isolines of displacements and stresses along the dam's body, depending on time. At that, the most vulnerable zones of the considered earth dam were identified.

IMPLEMENTATION OF STRENGTH CALCULATION SOFTWARE BASED ON THE SEMI-ANALYTICAL METHOD OF FINITE ELEMENTS

One of the main and responsible stages of creating an apparatus for numerical analysis of structures using the finite element method is its implementation in the form of a set of programs. The principles of complex construction should take into account modern requirements for strength calculation software in modern calculation complexes. Among them, first of all, automation of the main stages of the computing process, rational use of the resources of the operating and external memory of storage devices, non-closedness in relation to the classes of problems to be solved, algorithms for the task of input data, the method of discretization and solution of systems of equations and etc. In addition, the structure of the programs should take into account the specifics of the semi-analytical method of finite elements, for which such a large experience of creating developed systems of mathematical support for the search of spatial structures has not yet been accumulated, as when using the traditional version of FEM. Considerable experience in solving finite element mechanics problems, accumulated over the past decades, has been reflected in a number of industrial commercial software complexes of domestic (LIRA, SCAD) and foreign (ANSYS, Nastran, ABAQUS) production. The developed finite element base of these software complexes allows you to obtain solutions to a wide range of problems of the mechanics of a deformable rigid body for objects of different dimensions, including for massive spatial bodies, and convenient means of input-output of information and processing of the obtained results make them very accessible to a wide circles of users and allow to display the obtained results with the maximum degree of visibility. There are also object-oriented complexes created at manufacturing enterprises and research institutes, for example at the Institute of Strength Problems of the National Academy of Sciences of Ukraine, at the Dnipropetrovsk National University.
 The conducted research will determine the most optimal ways of solving the listed problems from the point of view of computing costs and complexity of implementation, as well as outline the circle of unsolved issues.

ТЕОРИЯ О ДЕГРАДАЦИИ МЕХАНИЧЕСКИХ СВОЙСТВ ЛИТЫХ СТАЛЕЙ КЛАССА 20Л

The paper considers negative changes of mechanical properties and cyclic fracture toughness of 20L class steel that is used for cast solebars and bolsters of bogies for freight cars and also for petrochemical equipment for 25–41 years of operation. The main reason of embrittlement of steel is a high content of manganese and silicon as a result of long-term cyclic operating time. The paper presents an experimental kinetic curve of change of cyclic fracture toughness depending on life of a bogie bolster of a freight car. The paper also shows model curves of degradation of an elasticity coefficient and fracture deformation depending on relative operating time in cycles. On the basis of established effects the author has formulated an integrated theory on degradation of mechanical properties of 20L cast steel after the cyclic operating time for two chapters of mechanics — mechanics for rigid body and fracture mechanics. The reliability of the theory is confirmed by experimental tests.

A rigid body framework for multicellular modeling.

Off-lattice models are a well-established approach in multicellular modeling, where cells are represented as points that are free to move in space. The representation of cells as point objects is useful in a wide range of settings, particularly when large populations are involved; however, a purely point-based representation is not naturally equipped to deal with objects that have length, such as cell boundaries or external membranes. Here we introduce an off-lattice modeling framework that exploits rigid body mechanics to represent objects using a collection of conjoined one-dimensional edges in a viscosity-dominated system. This framework can be used to represent cells as free moving polygons, to allow epithelial layers to smoothly interact with themselves, to model rod-shaped cells such as bacteria and to robustly represent membranes. We demonstrate that this approach offers solutions to the problems that limit the scope of current off-lattice multicellular models.

Dynamic modeling and simulation of a novel mechanism for adhesive capture of space debris

Flexible capture has high applicability in the removal of space debris. In this paper, a novel adhesive capture mechanism is proposed, the multibody dynamic modeling method of the capture system is detailed, and an investigation of the adhesive capture process by numerical simulation is presented. First, the passive trigger mechanism of the capture device is described. Second, based on the classical rigid body mechanics and the fully parameterized ANCF beam element, the multibody model of the capture device is detailed. A contact detection algorithm is proposed to take the failure of adhesive connection into account, and its robustness and effectiveness are demonstrated. Finally, investigations of the dynamics during the capture process in two typical capture conditions are described and the impact of some system parameters on the capture effectiveness is discussed. The simulation results provide key parameters for the selection of the adhesive material and show the practical applicability of the capture mechanism.

Techno-economic analysis of energy supply to personal rapid transit (PRT) systems

Personal Rapid Transit (PRT) is an innovative form of urban transportation which might provide an alternative to car use. PRT is conceptualized by an array of autonomous pods, providing shared riding service to a small number of travelers per vehicle, on a dedicated guideway. PRT is considered by many to be a travel mode that reduces energy use and emissions levels, compared with traditional cars. To evaluate the cost effectiveness and benefits associated with the energy consumed by a typical urban PRT system, a detailed techno-economic analysis of two energy supply alternatives is presented. The technologies considered are: battery storage and third-rail conductors. This paper demonstrates a methodological approach to evaluate PRT energy costs, illustrated by a case study: the city of Herzliya (ISR). First, a PRT system model was developed, including both infrastructure design and operational characteristics, with a total track length of 12.5 km. Then, vehicles tractive and grid energy requirements were derived from the case study data using rigid body mechanics and lumped powertrain properties. Following, an economic evaluation was carried out taking into account capital costs as well as operating costs based on tractive, auxiliary and parasitic energy requirements. In both cases, the energy consumption is about 0.08 [kWh/p-km], while the energy costs are 0.031 and 0.100 [$/p-km] for the battery and third rail, respectively. Future research is discussed in the directions of further modeling development and extending the scope of alternatives.

A Biomechanical Analysis of Muscle Force Changes After Bilateral Sagittal Split Osteotomy.

A basic procedure affecting maxillofacial geometry is the bilateral sagittal split osteotomy. During the surgery, the bony segments are placed in a new position that provides the correct occlusion. Changes in the geometry of the mandible will affect the surrounding structures and will have a significant impact on the functioning of the masticatory system. As a result of the displacement of the bone segment, the biomechanical conditions change, i.e., the load and the position of the muscles. The primary aim of this study was to determine the changes in the values of the muscular forces caused by mandible geometry alteration. The study considered the translation and rotation of the distal segment, as well as rotations of the proximal segments in three axes. Calculations were performed for the unilateral, static loading of a model based on rigid body mechanics. Muscles were modeled as spring elements, and a novel approach was used to determine muscle stiffness. In addition, an attempt was made, based on the results obtained for single displacements separately, to determine the changes in muscle forces for geometries with complex displacements. Based on the analysis of the results, it was shown that changes in the geometry of the mandibular bone associated with the bilateral sagittal split osteotomy will have a significant effect on the values of the masticatory muscle forces. Displacement of the distal segment has the greatest effect from −21.69 to 26.11%, while the proximal segment rotations affected muscle force values to a less extent, rarely exceeding 1%. For Yaw and Pitch rotations, the opposite effect of changes within one muscle is noticed. Changes in muscle forces for complex geometry changes can be determined with a high degree of accuracy by the appropriate summation of results obtained for simple cases.

The Effectivenes of Modeling Instruction Learning on Students’ Conceptual Understanding of Rotational Dynamic

Rotational Dynamics is one of the physics topics which is quite difficult for students. Several previous studies showed students’ difficulties on this topic, one of which is the aspect of students’ conceptual understanding. Modeling instruction is the effective approach to improve students’ understanding. This model is in line with constructivist theory and cognitive model theory. This research aimed to examine the effectiveness of modeling instruction that we developed to improve students' conceptual understanding of rigid body mechanics, where the knowledge of particle mechanics serve as anchor or bridging to develop model of rigid body. This research used mixed method with embedded experimental design. It used one group pretest-posttest design and involved 65 students of a high school in Malang as the subject. Data were gathered using test consisting of 17 multiple-choice items with explanation. The students’ scores were analyzed quantitatively using t-test and N-gain to measure the improvement of students’ understanding, while the students' reasons were analyzed qualitatively. The results showed the average students’ score increased from 1.62 to 9.92 with N-gain of 0.54 (in upper medium category). We concluded that the modeling instruction was effective to improve students’ conceptual understanding.