Instantaneous Center Research Articles

On graphical method of mechanical dynamics based on balance equation of rotating moment around moving point

Graphical method is an effective method to verify the results of analytical method. However, the research on graphical method of mechanical dynamics can not be carried out until the moment balance equation of rigid body rotating around moving point (practical equation A) is given in our open paper. The main reason is that the connecting rod is not a body rotating around a fixed point, and its moment balance equation contains too many unknowns. Practical equation A is derived based on the research idea of Fangyan equation. 1) Our 8 previous research results in mechanical dynamics were summarized. The instantaneous centre between two bodies is velocity instantaneous centre. After analysis, there is not necessarily acceleration instantaneous centre between two bodies. 2) A rotation moment balance equation (qualitative equation B) of a rigid body around a moving point was proposed based on qualitative analysis. 3) A crank rocker mechanism is taken as an example. The moment of rotation of a rigid body around the centroid (ordinary equation C) was practiced too. Practical equation A is as correct as ordinary equation C. Practical equation A makes the results of the graphical method of mechanical dynamics feasible.

Knee joint prototype based on cam mechanism – design and video analysis

The paper is focused on a design of mechanism accurately reproducing a complex motion in the sagittal plane of a human knee joint. The desired movement is modelled by applying specially designed shapes of cooperating cam elements based on the fixed and moving centroids of knee joint’s instantaneous centre of rotation. The mechanism’s CAD model and prototype are built using 3D printed elements, providing the possibility of interchanging the elements with cam profiles and adjusting the mechanism’s movement to individual needs. The mechanism movement is measured by analysing a video in Matlab and tracking colour markers on the prototype.

Design and Validation of a Polycentric Hybrid Knee Prosthesis With Electromagnet-Controlled Mode Transition

A hybrid knee prosthesis is proposed in this letter, which consists of a polycentric structure in passive mode for low-torque activities and a single-axis structure in active mode for high-torque activities. A novel mode transition mechanism controls self-holding electromagnets for switching modes between the four-bar linkage and single-axis structure. Compared with the conventional single-axis hybrid knee, the four-bar polycentric mechanism with varying instantaneous center of rotation (ICR) can enhance the geometric stability and increase the toe clearance in passive mode. For active mode, we developed a custom embedded electric system, employed torque control for stance and position control for swing. The results of bench tests indicated that the bandwidth of the controller was suitable for locomotion. The clinical test of level-ground walking without sudden buckling and stumble was validated by three subjects. Regarding climbing stairs, a typical high-torque activity in daily locomotion, all subjects reach the maximum knee torque around 0.95 Nm/kg comparable to the able-bodied.

Combination Strategy for the Geocentric Realization of Regional Epoch Reference Frames

AbstractFor high‐resolution regional geodetic applications, the International Terrestrial Reference Frame (ITRF) is complemented by regional densifications. These are realized either as multi‐year solutions related to a tectonic plate (e.g., EUREF for Europe) or as epoch reference frames (ERFs) to capture nonlinear geophysical station motions caused by, for example, earthquakes or non‐tidal loading (e.g., SIRGAS for Latin America). These Global Navigation Satellite Systems (GNSS)‐only based regional reference frames have in common that their geodetic datum is aligned with the ITRF datum at a specific epoch. The consequence is that their origin represents the Earth's center of figure and does not coincide with the instantaneous center of mass. Here, we present studies on a direct geocentric realization of regional ERFs. We propose to realize the geodetic datum for each epoch by combining global GNSS, Satellite Laser Ranging, and Very Long Baseline Interferometry networks via measured local ties at co‐located sites. A uniformly distributed global GNSS network is used to realize the orientation via a no‐net‐rotation constraint with respect to the ITRF and is densified by the stations of the regional subnetwork. The developed combination and filtering strategy aims to guarantee a stable datum realization for each epoch‐wise solution. Validating our results against global reference frames and geophysical loading models relating to the Earth's centers of mass and figure, we show that the realized displacement time series are geocentric and reflect seasonal geophysical processes. As the approach does not need to rely on co‐location sites in the region of interest, it is conceptually transferable to other regions on the globe.

Anterior-cruciate-ligament reconstruction does not alter the knee-extensor moment arm during gait

BackgroundThe ability of the quadriceps muscles to extend the knee depends on the moment arm of the knee-extensor mechanism, which is described by the moment arm of the patellar tendon at the knee. The knee-extensor moment may be altered by a change in quadriceps force, a change in the patellar tendon moment arm (PTMA), or both. A change in quadriceps muscle strength after anterior-cruciate-ligament-reconstruction (ACLR) surgery is well documented, however, there is limited knowledge about how this procedure affects the PTMA. Research questionDoes ACLR surgery alter the moment arm of the knee-extensor mechanism during gait? MethodsWe measured the PTMA in both the ACLR knee and the uninjured contralateral knee in 10 young active individuals after unilateral ACLR surgery. Mobile biplane X-ray imaging was used to measure the three-dimensional positions of the femur, tibia and patella during level walking and downhill walking over ground. The PTMA was found from the location of the instantaneous axis of rotation at the knee and the line-of-action of the patellar tendon. ResultsThere was a small but statistically significant difference in the mean PTMA calculated over one cycle of level walking between the ACLR knee and the contralateral knee, with the mean PTMA in the ACLR knee being 1.5 mm larger (p < 0.01). In downhill walking, statistically significant differences were found in the range 15°– 25° of knee flexion, where the PTMA was 4.7 mm larger in the ACLR knee compared to the contralateral knee (p < 0.01). SignificanceSignificant differences were evident in the mean PTMA between the ACLR knee and the contralateral knee in both activities, however, the magnitudes of these differences were relatively small (range: 3–10%), indicating that ACLR surgery successfully restores the moment arm of the knee-extensor mechanism during dynamic activity.

Formation of buckling resistance in a transfemoral prosthesis

Introduction. The principles of construction of the knee joint in the transfemoral prosthesis are considered. The design of the knee joint in the transfemoral prosthesis with an original mechanism for ensuring buckling resistance in the prosthesis is proposed. Goal. Create an artificial knee joint, which provides a reliable mechanism of strut stability during walking by quickly blocking the flexion-extension of the artificial knee joint in the prosthetics for high amputations of the lower extremities when resting on the prosthesis. Materials and methods. One of the main problems that exist in the development of knee joints in a femoral prosthesis is the presence in the design of the module of a mechanism that ensures its blocking from bending when walking at the moment of support of the prosthesis in the transfer phase of a healthy limb. In the knee joints of various companies, this issue is solved in different ways. For example, some simple singleaxis knee joints are designed to lock when the disabled person is in a standing position. Walking is carried out without flexion in the knee joint. To unlock, pull the cable (transition to a sitting position). In some single-axis hinges, a locking function is applied using the weight of a disabled person. In the phase of support on a full foot, the hinge closes due to the weight load on it and opens by transferring weight to the toe. In more complex multi-axis module designs, there is a so-called geometric lock. The closure in the stance phase occurs due to the correct arrangement of the axes relative to each other. The opening occurs in the transfer phase. The object of the study. The mechanisms of the knee joint, which provide a handicapped person's resistance to buckling while walking on a transfemoral prosthesis. The subject of the study. The design of the knee joint, which provides self-braking due to a coupling with a split disc. Results. The study made it possible to substantiate the practical possibility of creating a knee joint of prosthetics for high amputation with a braking device made in the form of a split disc clutch. Discussion. Currently, there are various designs of knee joint that have mechanisms of buckling. When considering modern knee joint of well-known manufacturers, the main ways of ensuring buckling resistance are determined. The polycentric knee module of the company "Ossur" implements the principle of knee locking due to the displacement of the instantaneous axis when the knee is extended, thereby providing buckling resistance. In the Ottobock knee joint, the knee axis is automatically closed under the influence of human weight. Domestic manufacturers of knee modules are ORTHOS (Novosibirsk) and Metiz. Also, the scientific and production corporation "Precision Instrument Engineering Systems" (NPC SPP, part of Roscosmos) announced the production of the knee module "Aktiv-2". Due to the restriction of imports of foreign products, state prosthetic and orthopedic enterprises are interested in the development and production of domestic prosthetic and orthopedic products, including artificial knee joints of various designs. Conclusions. The principles of constructing the design of the knee joint of the above knee prosthesis have been formed.

Теоретичне дослідження коливальних рухів гичкозбиральної машини, встановленої спереду агрегатуючого трактора

Goal. To increase the quality of gathering and reliability of the top-gathering machine by minimizing the amplitude of its angular oscillations during movement on the unevenness of the soil surface. Methods. Theoretical studies were carried out using the basic principles of higher mathematics and theoretical mechanics, in particular the dynamics of a mechanical system. Numerical calculations and graphical dependences were obtained using a PC with the help of the developed and standard programs. Experimental studies were carried out according to standard methods of field multivariate experiments. Results. Based on the developed equivalent scheme of the frontally attached to the wheeled tractor top-gathering machine, the differential equation of the angular oscillations of the top-gathering machine to the center of instantaneous rotation of the tractor attachment mechanism was compiled. The analytical solution of this equation was obtained thanks to the law of oscillatory motion of the top-gathering machine in the longitudinal-vertical plane. As a result of numerical calculations, graphical dependences were built of the angle of rotation of the top-gathering machine at different speeds of its translational movement and different values of the coefficient of stiffness and damping of the tires of the copying wheels, as well as at different values of the main design parameters of the machine and the step of the unevenness of the soil surface. Conclusions. To reduce the amplitude of the angular oscillations of the harvester in the longitudinal vertical plane, its supporting wheels should be located as far as possible from the instantaneous center of rotation of the tractor’s front attachment mechanism. The central thrust of this mechanism should also be installed at the greatest possible angle of inclination to the vertical. The greater the step of the unevenness of the soil surface, the more stable will be the movement of the front-mounted top-gathering machine in the longitudinal-vertical plane. According to experimental studies, with amplitudes of oscillations of the lower ends of the knives of the rotary cutting device up to 5 cm, the loss of the sliver is insignificant. However, when the amplitude of these fluctuations increases to 7 cm or more, these losses become more significant and their maximum values can reach more than 12%.

Multi-Objective Instantaneous Center of Rotation Optimization Using Sensors Feedback for Navigation in Self-Reconfigurable Pavement Sweeping Robot

Pavement in outdoor settings is an unstructured environment with sharp corners, varying widths, and pedestrian activity that poses navigation challenges while cleaning for autonomous systems. In this work, an approach towards navigating without collision in constrained pavement spaces using the optimal instantaneous center of rotation (ICR) is demonstrated using an in-house developed omnidirectional reconfigurable robot named Panthera. The Panthera reconfigurable design results in varying footprints, supported by passive linear joints along the robot width, with locomotion and steering action using four wheels independent steering drive (4WISD). The robot kinematics and perception sensors system are discussed. Further, the ICR selection is carried out using multi-objective optimization, considering functions for steering, varying width, distance, and clearance to avoid a collision. The framework is incorporated in a local navigation planner and demonstrated experimentally in real pavement settings. The results with optimal selection of ICR in two dimensional space within the robot footprint successfully perform smooth navigation in the constraint space. It is experimentally highlighted with four different scenarios, i.e., constraint conditions encountered by a robot during navigation. Moreover, the formulation of optimal selection of ICR while avoiding collision is generic and can be used for other mobile robot architectures.

Nominal geometry and force measures for solids and fluids

AbstractUnderstanding solid‐ and fluid‐inertia forces and their coupling with the gravity potential in complex motion scenarios is necessary for evaluating system stability and identifying root causes of system failure and accidents. Because solids and fluids have an infinite number of degrees of freedom and distributed inertia and elasticity, having meaningful qualitative and quantitative nominal measures of the kinematics and forces will contribute to a better understanding of the system dynamics. This paper proposes developing new continuum‐based nominal measures for the characterization of the oscillations and forces. By using a material‐point approach, these new nominal measures, which have their roots in the continuum‐mechanics partial‐differential equations of equilibrium and Frenet geometry, are independent of the formulation or generalized coordinates used to develop the dynamic equations of motion. The paper proposes a data‐driven‐science approach to define a nominal continuum space‐curve geometry with nominal curvature and torsion; a nominal instantaneous motion plane (IMP), which contains the resultant of all forces including the inertia forces; and a nominal instantaneous zero‐force axis (IZFA) along which the resultant of all forces vanishes. While using the material‐point approach eliminates the need for introducing moment equations associated with orientation coordinates, the IMP and IZFA concepts can be used to define the instantaneous axis of significant moment components, which can lead to accidents such as in the case of vehicle rollovers.

The Role of Instant Centers in Kinematics and Dynamics of Planar Mechanisms: Review of LaMaViP’s Contributions

Theoretical kinematics and dynamics is one of the research fields where LaMaViP (Laboratory of Mechatronics and Virtual Prototyping) operates, which is the lab leaded by the author at the University of Ferrara. In the last two decades, this research activity at LaMaViP has produced, among others, many novel results that highlight how instant centers’ (ICs) locations condition the kinetostatic and dynamic behaviors of planar mechanisms, and that provide tools suitable for design purposes. This paper reviews/summarizes the tools devised at LaMaViP for PM analysis and synthesis through ICs, and shows that they are a complete set of tools, which make the full description of PMs’ kinematics and dynamics possible, and that the new IC features, identified while setting up these tools, are relevant in machine design.

ОПРЕДЕЛЕНИЕ КИНЕМАТИЧЕСКИХ И ДИНАМИЧЕСКИХ ХАРАКТЕРИСТИК ТЕХНОЛОШИЧЕСКИХ МАШИН ПЛАНЕТАРНОГО ТИПА

The article deals with issues related to the study of planetary machines. It is demonstrated that they are able to significantly intensify most of the processes applicable to them. This is due to the complication of the trajectory of the movement of the working body and the increase in inertial forces. In addition, planetary units are energy efficient. The influence of the mutual action of grinding bodies on their power characteristics in a planetary mill with external and internal running of the drums is presented. The dependence of destructive forces on the angular velocity, the degree of filling of the grinding drums, the geometric ratios of the mill itself is shown. Sufficiently simple dependences have been obtained for calculating the total speed at any point of the planetary working body of the smoothing machine. Their use makes it possible to analyze the change in speed over a wide range, depending on a number of design and technological parameters. The proposed method allows to calculate the speeds of the working bodies that make planetary motion. Using the methods of classical mechanics, using the instantaneous center of velocities, a formula is obtained for calculating the speed at any point of the mixing blade. It is established that the speed of the blade changes in time according to a sinusoidal law. The total power gradually increases with increasing angular velocity. The results obtained in this article can be applied in the design and operation of planetary units.

Analytical Derivation and Analysis of Vertical and Lateral Installation Ratios for Swing Axle, McPherson and Double Wishbone Suspension Architectures

In the context of suspension design, the installation ratio (or motion ratio) is a parameter that relates wheel movement with spring deflection, quite an important kinematic property of a suspension. Yet, no study in the literature provides a clear relationship between the installation ratio and the geometrical features of a suspension. This paper employs rigid body kinematics and appropriate geometrical schematics to fill such a gap. Analytical expressions of the installation ratio are derived for three suspension layouts: swing axle, McPherson, double wishbone. Key concepts such as instant center, roll center and camber gain are harnessed to provide insightful analyses for relevant case studies of suspension passenger cars. Among the key results, the typical assumption of a McPherson installation ratio close to 1 is supported by a formal demonstration, and the new concept of “lateral” installation ratio is introduced which, alongside the classical “vertical” installation ratio, further characterizes suspension motion. Numerical results obtained through a multibody software support the findings of this paper. In conclusion, this study provides valuable insights for suspension design engineers.

Design and testing a highly backdrivable and kinematic compatible magneto-rheological knee exoskeleton

Lower limb exoskeletons (LLE) have been successfully used in robotic-assisted rehabilitation to reduce the burden of locomotor impairment of disabled people. However, the design limitations of LLE mechanisms, such as the lack of kinematic compatibility relative to the user’s joints and the use of high stiff or heavy actuators, limit the outcomes of treatment and increase the risk of injury. To address these shortcomings, in this work we present the design of the MRKneeExo, a highly backdrivable and kinematically compatible active knee exoskeleton. The powertrain of the system is composed of a BLDC 70 W motor associated with a harmonic drive gearbox and a customized magneto-rheological (MR) clutch. To improve kinematic compatibility with the user’s knee, a crossed four-bar linkage mechanism (FBLM) was optimally designed to follow the trajectory of the instant center of rotation (ICR) of the knee projected in the parasagittal plane where the joint is placed. The MR clutch is used to decouple the motor-reducer from the FBLM, thus enabling high backdrivability. The results showed a small error (&lt;3 mm) between the FBLM and the knee ICR. Furthermore, the MR clutch allowed for low back-drive torque (1.28 N m) compared to the torque to back-drive the motor-reducer (18.51 N m). This paper is presented in a framework that can be generalized to support the design of other knee exoskeletons.

Floquet Quadrupole Photonic Crystals Protected by Space-Time Symmetry

High-order topological phases, such as those with nontrivial quadrupole moments [1,2], protect edge states that are themselves topological insulators in lower dimensions. So far, most quadrupole phases of light are explored in linear optical systems, which are protected by spatial symmetries [3] or synthetic symmetries [1,2,4--7]. Here we present Floquet quadrupole phases in driven nonlinear photonic crystals that are protected by space-time screw symmetries [8]. We start by illustrating space-time symmetries by tracking the trajectory of instantaneous optical axes of the driven media. Our Floquet quadrupole phase is then confirmed in two independent ways: symmetry indices at high-symmetry momentum points and calculations of the nested Wannier bands. Our Letter presents a general framework to analyze symmetries in driven optical materials and paves the way to further exploring symmetry-protected topological phases in Floquet systems and their optoelectronic applications.

Разработка шаблона мгновенных центров вращения коленного сустава (экспериментальное исследование)

Relevance There are data in the literature describing the trajectory of displaced center of rotation of the knee joint. However, data on the exact location of instantaneous centers of rotation at various angles of the knee flexion are not available. Objective To identify the localization of instantaneous centers of rotation at various angles of the knee flexion and present the results in the form of a template. Material and methods The bench testing was performed using a specially developed device that provides fixation of the anatomic cadaver preparation of the lower extremity. The device made it possible to identify the zero instantaneous center of rotation using a radiographic positive marker. Control radiographs were performed to determine the "movement" of instantaneous centers of rotation at every 10° of flexion to reach an angle of 120°. The exact location of instantaneous centers of rotation at different knee flexion angles were obtained with a graphical editor and tibia internal rotation identified during the knee flexion. Results The identified instantaneous centers of rotation were applied to the contour of the distal femur to form the template and allow scaling. Conclusions The template developed could be useful for computer hexapod assisted orthopaedic surgery in the treatment of knee stiffness, for mechanotherapy and joint replacement.

Research on the varying-displacement-coefficient modification method for automobile steering noncircular sector gears

The local drum shape tooth profile is adopted for automobile steering noncircular sector gears, which can be obtained according to a piecewise linear function modification on CNC gear shaper. In the practical process, the actual amount of drum shape is always smaller than the theoretical amount, and we conclude that overcut of the tooth profile occurred. Because the modification coefficient is variable, we call it varying-displacement-coefficient modification(VDCM). Currently, researches on tooth profile of noncircular sector gears are primarily concerned with constant modification coefficient to improve gear transmission performance, while modification functions, overcut, and methods of reducing or eliminating the overcut are rarely touched upon.This paper focus on the VDCM method of automobile steering noncircular sector gears. On the basis of noncircular sector gear and rack pair meshing theory, the modifying motion mathematical model is first established, including kinematic relations, pith curves, track of relative instantaneous centre point, calculation formula for the modified tooth profile. And then, the reasons for the overcut are analyzed, and the local overlap and separation of the tooth profile are found. To reduce the overcut amount, a cosine function modification method is proposed. Furthermore, an inverse calculation method for the rack tool tooth profile is proposed to eliminate the overcut entirely. The VDCM modification methods are verified by simulation, trial cutting and parts measurement.

A geometric and analytic technique for studying multi-DOF planar mechanisms’ dynamics

Most approaches of analytical mechanics (e.g., D'Alembert principle) build dynamic models of mechanisms that are difficult to relate with clear geometric interpretations. This feature is a drawback that confines their use to the implementation of algorithms in multi-body-dynamics software, whose results must be interpreted by using the designer intuition when the mechanism must be modified to match particular design requirements. Here, starting from D'Alembert principle, the dynamic model of any multi-degrees-of-freedom (multi-DOF) planar mechanism (PM) is obtained by suitably combining the dynamic models of all the single-DOF PMs generated by locking all the actuated joints, but one. The dynamic models of the so-generated single-DOF PMs are written by using an approach, presented in a previous paper, which admits a geometric interpretation through diagrams, named “active-load diagrams”, and fully discloses the role of instant centers (ICs) in the dynamic behavior of single-DOF PMs. Accordingly, the resulting dynamic model of the generating multi-DOF PM admits a geometric interpretation that reveals the role of ICs in multi-DOF PMs’ dynamic behavior. Such geometric interpretation is so effective that, formally, the model could be written starting from it without any analytic consideration the same way as the equilibrium equations can be written from free-body diagrams in the Newton-Euler formulation. The presented model is general and, as far as this author is aware, is novel. The proposed model and the associated algorithms for solving dynamic problems are also illustrated through a case study. The obtained results are of interest in mechanism analysis and design.

Neural-Network-Based Ultrasonic Inspection of Offshore Coated Concrete Specimens

A thin layer of protective coating material is applied on the surface of offshore concrete structures to prevent its degradation, thereby extending the useful life of the structures. The main reasons for the reduction in the protective capability of coating layers are loss of adhesion to concrete and flattening of the coating layer wall. Usually, the state of the coating layer is monitored in the setting of water immersion using ultrasonic inspection methods, and the method of inspection still needs improvement in terms of speed and accuracy. In this study, the ultrasonic pulse echo method was used in a water immersion test of the coated specimens, and continuous wavelet transform (CWT) with complex Morlet wavelets was implemented to define the received waveforms’ time of flight and instantaneous center frequency. These allow one to evaluate the thickness of the coating layer during water immersion. Furthermore, phases of reflected echoes at CWT local peaks were computed using a combination of Hilbert transforms (HT) and wave parameters derived from CWT. In addition, three relative wave parameters of echoes were also used to train deep neural networks (DNN), including instantaneous center frequency ratio, CWT magnitude ratio, and phase difference. With the use of three relative waveform parameters of the DNN, the debonded layer detection accuracy of our method was 100%.

Evaluating Knee Mechanisms for Assistive Devices.

State-of-the-art knee braces use a polycentric mechanism with a predefined locus of the instantaneous center of rotation (centrode) and most exoskeleton devices use a knee mechanism with a single axis of rotation. However, human knees do not share a common centrode nor do they have a single axis. This leads to misalignment between the assistive device's joint axis and the user's knee axis, resulting in device migration and interaction forces, which can lead to sores, pain, and abandonment of the device over time. There has been some research into self-aligning knee mechanisms; however, there is a lack of consensus on the benefit of these mechanisms. There is no research that looked purely at the impact of the knee mechanisms, either. In this article, we compare three different knee brace mechanisms: single axis (SA), polycentric with predefined centrode (PPC), and polycentric with a self-aligning center of rotation (PSC). We designed and conducted an experiment to evaluate different joint mechanisms on device migration and interaction forces. Brace material, weight, size, cuff design, fitment location, and tightness were consistent across trials, making the knee joint mechanism the sole variable. The brace mechanisms had no significant effect on walking kinematics or kinetics. However, the PPC brace had greater interaction forces on the top brace strap than the SA and PSC. The PSC and SA had significantly lower interaction forces on the bottom strap compared to the PPC brace. The PSC had significantly less migration than both the SA and PPC braces. These results show that a PPC mechanism may not be beneficial for a wide range of users. This also shows that the PSC mechanisms may improve mechanism alignment and lessen device migration.

The Dual Expression of Parallel Equidistant Ruled Surfaces in Euclidean 3-Space

In this study, we examine the dual expression of Valeontis’ concept of parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to the Study mapping. Furthermore, we show that the dual part of the dual angle on the unit dual sphere corresponds to the p-distance. We call these ruled surfaces we obtained “dual parallel equidistant ruled surfaces” and we briefly denote them with “DPERS”. Furthermore, we find the Blaschke vectors, the Blaschke invariants and the striction curves of these DPERS and we give the relationships between these elements. Moreover, we show the relationships between the Darboux screws, the instantaneous screw axes, the instantaneous dual Pfaff vectors and dual Steiner rotation vectors of these surfaces. Finally, we give an example, which we reinforce this article, and we explain all of these features with the figures on the example. Furthermore, we see that the corresponding dual curves on the dual unit sphere to these DPERS are such that one of them is symmetric with respect to the imaginary symmetry axis of the other.