Unknown Forces Research Articles

Principles of Classical Mechanics Describe Gyroscopic Effects

The unexplainable motions of the simple spinning top toy, boomerang, and other spinning objects attracted people since the time of ancient civilizations. The intricated motions of the rotating objects and the action of the unknown forces were named gyroscopic effects. The physicists and mathematicians tried to solve them beginning from the Industrial Revolution until our time. One gyroscopic effect which is the side motion of the spinning disc was described by L. Euler and presented in the world encyclopaedias as the fundamental principle of gyroscope theory. The origin of gyroscopic effects is more sophisticated than in published and simplified theories. Analytical solutions to other gyroscopic effects were described only in our times. The system of the interrelated inertial torques generated by the rotating mass acts on the spinning object based on the principle of mechanical energy conservation. This system presents the fundamental principles of gyroscope theory.

Judgment method of grasping stability for dexterous hand based on force balance theorem and Monte Carlo method

PurposeMulti-sensor fusion in robotic dexterous hands is a hot research field. However, there is little research on multi-sensor fusion rules. This study aims to introduce a multi-sensor fusion algorithm using a motor force sensor, film pressure sensor, temperature sensor and angle sensor, which can form a consistent interpretation of grasp stability by sensor fusion without multi-dimensional force/torque sensors.Design/methodology/approachThis algorithm is based on the three-finger force balance theorem, which provides a judgment method for the unknown force direction. Moreover, the Monte Carlo method calculates the grasping ability and judges the grasping stability under a certain confidence interval using probability and statistics. Based on three fingers, the situation of four- and five-fingered dexterous hand has been expanded. Moreover, an experimental platform was built using dexterous hands, and a grasping experiment was conducted to confirm the proposed algorithm. The grasping experiment uses three fingers and five fingers to grasp different objects, use the introduced method to judge the grasping stability and calculate the accuracy of the judgment according to the actual grasping situation.FindingsThe multi-sensor fusion algorithms are universal and can perform multi-sensor fusion for multi-finger rigid, flexible and rigid-soft coupled dexterous hands. The three-finger balance theorem and Monte Carlo method can better replace the discrimination method using multi-dimensional force/torque sensors.Originality/valueA new multi-sensor fusion algorithm is proposed and verified. According to the experiments, the accuracy of grasping judgment is more than 85%, which proves that the method is feasible.

Forceful interaction of the casing string with the walls of a curvilinear well

Purpose. Developing a method for determining the axial forces and the walls reactions along a casing string, which bend it and make it follow a curved wellbore shape. Methodology. The casing string is represented as a long elastic rod in the curved well. An inhomogeneous system of four differential equations is developed to describe the rods deformations. It was reduced to a first-order differential equation with respect to axial force. Its solution was found by the Bernoulli method. The numerical integration of the differential equation is applied. Findings. The axial force distribution along the casing string was found, taking into account the well curvature and the friction, as well as the reaction forces of the well walls. A method of the tables numerical integration of the wells inclinometric measurements has been developed. The calculating formulas for the reaction forces, axial forces, bending moments and stresses acting in the casing pipes in the well deep are obtained. Originality. The solved problem takes into account the walls reaction and the friction forces that create longitudinal bend during the columns movement. The system of differential equations of equilibrium was supplemented by Eulers kinematic equation. The function of zenith angle, which is known due to the table of the directional survey data, was taken as the integration variable. The inverse problem is solved all unknown internal forces, also such the external distributed reaction, which causes the column to repeat the wells shape, was been determined by the angular deformations of casing string, which are given by the wells shape in the inclinometric table. Practical value. The developed method allows detecting the areas with a significant local increase in the wells curvature, which indicate their obstructed passability. This allows for accurate determination of depth intervals to increase the borehole diameter, which is necessary before lowering the column. According to the analysis results, it is possible to determine the parameters of the stress-strain state of the casing string, which can be used to predict its working capacity and operating life.

Смешанный метод в расчетах пластинок со сложными граничными условиями

The paper presents new possibilities of using a mixed method for calculating bendable plates with complex boundary conditions. When composing resolving equations, it is sufficient to have an expression to determine the deflections of a plate with a normal pinched at the origin. Such solutions are given in the authors’ previously published works for plates of various shapes. On the basis of these solutions, the canonical equations of the mixed method are compiled, where the unknown forces of the method are the forces in the support links, the displacement method is linear and angular displacement of the pinching introduced at the origin. After determining the unknown forces of the method, according to the generally accepted formulas of the mixed method, the deflections of the plate are determined, according to which, in turn, internal forces are determined. Two examples of calculating plates in Cartesian and polar coordinates are given. Numerical implementation of the proposed methodology and algorithm for elastic calculation of bendable plates with complex boundary conditions is carried out using the Wolfram Mathematica 11.3 computer program.

Entanglement based tomography to probe new macroscopic forces

Quantum entanglement provides a novel way to test short distance physics in the non-relativistic regime. We will provide a protocol to {\it potentially} test new physics by bringing two charged massive particle interferometers adjacent to each other. Being charged, the two superpositions will be entangled via electromagnetic interactions mediated by the photons, including the Coulomb and the Casimir-Polder potential. We will bring a method of {\it entanglement based tomography} to seek time evolution of very small entanglement phases to probe new physical effects mediated by {\it hitherto unknown macroscopic force} which might be responsible for entangling the two charged superpositions modelled by the Yukawa type potential. We will be able to constrain the Yukawa couplings $\alpha \geq 10^{-35}$ for $r\geq 10^{-6}$m for new physics occurring in the electromagnetic sector, and in the gravitational potential $\alpha_g \geq 10^{-8}$ for $r \geq 10^{-6}$m. Furthermore, our protocol can also constrain the axion like particle mass and coupling, which is complimentary to the existing experimental bounds.

Seismic Damage Assessment for Isolated Buildings with a Substructure Method

A seismic damage detection method for isolated buildings is proposed based on substructure identification with incomplete contaminated measurements. A concept of a pseudo substructure with virtual conditions is constructed for the proof of the proposed substructure identification method. This identification method is implemented in a two-stage procedure. The interface forces of the target substructure are identified in the first stage and the parameter of the target substructure is updated in the second stage, which can enable the parameter identification of substructures with unknown input. Two computational methods are also proposed to improve the two-stage identification algorithm. A sub-time zone identification method is utilized to reduce the computation effort and the simultaneous identification of the unknown force and initial structural responses is presented in the first-stage identification for a general case in practical engineering. Numerical studies of a shear frame with nonlinear base isolation subject to earthquake ground motion are investigated to validate the proposed seismic damage detection method. A fourteen-storey concrete shear wall building with a two-storey steel frame on top connected by isolation is studied experimentally with shaking table tests to further validate the proposed method. The shear wall structure is taken as the target substructure for damage assessment. The interface force and parameter of the concrete shear wall building are estimated with the proposed method. Results from both the numerical simulations and laboratory tests indicate that the proposed method can estimate seismic isolated structures and detect damage effectively based on only a few accelerometers. It is also demonstrated that the parameter identification results based on the structure response measurement during the earthquake are more accurate than the identification with post-earthquake structural response measurement.

A learning-based model predictive control scheme and its application in biped locomotion

This paper proposes a learning-based model predictive control scheme. This scheme divides the predictive model into a known nominal model and an unknown model residual. Model residual is learned using Gaussian process regression. The learned stochastic model is solved quickly using differential dynamic programming, taking into account control input constraints. The simulation results show that compared with state of art optimal control methods, this scheme has good robustness to model residual, accelerates the solution of high-dimensional problems, and can strictly constrain the control inputs according to the actual situation. Based on this learning-based model predictive control scheme, this paper also proposes an online learning gait generator for the uncertainty problem in the locomotion control of biped robots. The zero moment point is strictly constrained during training to ensure safety. The simulation results show that the gait generator is robust to unknown load and unknown external force.

Hierarchical estimation of vehicle state and tire forces for distributed in-wheel motor drive electric vehicle without previously established tire model

In this paper, a hierarchical estimator combined with the nonlinear observer and particle filter (PF) is proposed to accurately estimate the vehicle state and tire forces of distributed in-wheel motor drive electric vehicles (DIMDEVs) when the traditional tire models are not available. The proposed estimator consists of lower and upper layers. The lower layer, i.e. longitudinal tire force nonlinear observer (LTFNO) aims at estimating the longitudinal force based on the available drive/brake torques and rotational speed of wheels. The convergence of LTFNO is proved by the invariant set principle. The upper layer receives these estimated longitudinal tire forces from LTFNO and estimates the vehicle state including lateral tire forces based on an expert model (EM). The designed EM utilizes basic knowledge and rules about tire characteristics to approximate the unknown lateral tire force. The upper estimator combines with EM (EEM) to further improve the accuracy. The EEM takes the modeling errors and disturbances into account and avoids the usage of complex established tire models. Then PF is applied in the upper layer to complete the estimation, which only needs measurable longitudinal/lateral accelerations and yaw rate signals. Finally, the effectiveness of the designed hierarchical estimator is verified by Carsim and Simulink co-simulations. The results show the proposed strategy can accurately estimate the vehicle state and tire forces in real-time.

Development of a High-Precision Optical Force Sensor With μN-Level Resolution

Unknown micro-contact forces may affect operation accuracy in micro-operation technology and high-precision contact measurement. Existing micro force sensors are unable to meet the demand for high resolution, large range, and low cost. Therefore, a more economical solution for high-precision force measurement is needed. A high-precision optical force sensor (OPFS) with a simple sensing principle is proposed in this study. The OPFS is mainly composed of a laser diode, a force-sensitive structure, and a four-quadrant photodetector (QPD). When force is applied to the measuring platform, the force-sensitive structure produces the corresponding elastic deformation, which is sensed by the QPD. The multi-range and customized resolution of the OPFS can be achieved by adjusting the stiffness of the force-sensitive structure. The design and optimization of the OPFS are completed via theoretical modeling and simulation analysis. The performance of the OPFS is examined experimentally. The OPFS is found to have a sensitivity of 0.27 mV/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{N}$ </tex-math></inline-formula> , a measuring range of 0–2.71 mN, and a resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$32\mu \text{N}$ </tex-math></inline-formula> . The measurement uncertainty of the OPFS due to nonlinearity, resolution, repeatability, and drift is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$82\mu \text{N}$ </tex-math></inline-formula> . The effectiveness of the OPFS in the measurement of micro-forces is verified. Finally, the OPFS is used to measure the contact force of a micro/nano contact probe. The results show that OPFS can be used for force calibration in micro/nano contact measurement instruments.

Analysis of the Internal Force and Deformation Characteristics of Double-Layer Lining Structure of Water Conveyance Tunnel

Shield double-layer lining structure is used to bear large internal water pressure in water conveyance tunnel engineering, but the mechanism of joint stress of structure and force transmission between linings is still unclear. In this paper, a stress calculation model of the double-layer lining structure of shield water conveyance tunnel considering the influence of transition layer between the inner lining and the outer lining is presented. By analyzing the inner lining and outer lining separately, the calculation formulas of radial displacement and circumferential stress are obtained. Then, according to the deformation coordination condition, the relationship between the inner and outer lining radial displacements is established. Thus, the magnitude of the unknown interaction force among the structures is calculated. Finally, through the stress analysis of the lining structure, the axial force, shear force, and bending moment acted on the structure are obtained. By comparing finite element calculation results with analytical calculation results, the rationality of analytical solutions is verified. Based on the proposed analytical method, the influence of inner lining thickness and material parameters of transition layer on the internal force and deformation of lining structure is analyzed. The results show that with the increase of the thickness of the inner lining, the axial force and bending moment increase, while the internal pressure shared by the outer lining decreases. The larger the elastic modulus of the transition material, the smaller the difference between the internal force and deformation of the inner and outer linings.

Determination of an unknown shear force in cantilever Kirchhoff–Love plate from measured final data with application to atomic force microscope

We present a new and feasible formulation for the inverse problem of identifying the unknown shear force acting on the inaccessible tip of the nonhomogeneous micro-cantilever plate which is a key component in most atomic force microscopes. The mathematical modelling of this phenomena leads to the inverse problem of determining the shear force g(x 2, t) acting on the inaccessible boundary x 1 = ℓ 1 in a system governed by the variable coefficient damped Kirchhoff–Love plate equation , where (x, t) ∈ Ω T ≔ Ω × (0, T), x ≔ (x 1, x 2) and , subject to clamped-free boundary conditions, from final time measured output (displacement) u T (x) ≔ u(x, T). We prove that under appropriate conditions, this inverse problem has a unique solution. We introduce the input–output operator and prove that it is a linear compact and Lipschitz continuous operator. Based on these results, the existence of a quasi-solution of the inverse problem, as a solution of the minimization problem for the Tikhonov functional, is proved. Furthermore, an explicit gradient formula for the Fréchet derivative of the Tikhonov functional is derived. Moreover, it is proved that the Fréchet derivative is Lipschitz continuous. These results provide a mathematical basis for gradient based computational algorithm.

The energy release rate for non-penetrating crack in poroelastic body by fluid-driven fracture

A new class of constrained variational problems, which describe fluid-driven cracks (that are pressurized fractures created by pumping fracturing fluids), is considered within the nonlinear theory of coupled poroelastic models stated in the incremental form. The two-phase medium is constituted by solid particles and fluid-saturated pores; it contains a crack subjected to non-penetration condition between the opposite crack faces. The inequality-constrained optimization is expressed as a saddle-point problem with respect to the unknown solid phase displacement, pore pressure, and contact force. Applying the Lagrange multiplier approach and the Delfour–Zolésio theorem, the shape derivative for the corresponding Lagrangian function is derived using rigorous asymptotic methods. The resulting formula describes the energy release rate under irreversible crack perturbations, which is useful for application of the Griffith criterion of quasi-static fracture.

The localized method of fundamental solutions for 2D and 3D second-order nonlinear boundary value problems

In this paper, a new framework for the numerical solutions of general nonlinear problems is presented. By employing the analog equation method, the actual problem governed by a nonlinear differential operator is converted into an equivalent problem described by a simple linear equation with unknown fictitious body forces. The solution of the substitute problem is then obtained by using the localized method of fundamental solutions, where the fictitious nonhomogeneous term is approximated using the dual reciprocity method using the radial basis functions. The main difference between the classical and the present localized method of fundamental solutions is that the latter produces sparse and banded stiffness matrix which makes the method very suitable for large-scale nonlinear simulations, since sparse matrices are much cheaper to inverse at each iterative step of the Newton's method. The present method is simple in derivation, efficient in calculation, and may be viewed as a completive alternative for nonlinear analysis, especially for large-scale problems with complex-shape geometries. Preliminary numerical experiments involving second-order nonlinear boundary value problems in both two- and three-dimensions are presented to demonstrate the accuracy and efficiency of the present method.

Unified Method for Task-Space Motion/Force/Impedance Control of Manipulator With Unknown Contact Reaction Strategy

Nowadays, higher requirements are placed on the design of the controller when robots enter the factory and co-operate with human. In this letter, we propose a unified task space control method combined with the contact reaction strategy in null space of redundant manipulator, which can not only conveniently switch between different control objectives according to specific tasks, but also react to the unknown contact with compliance. Specifically, the unknown contact force applied on the manipulator’s body is online estimated based on recursive least square estimation law in joint space. Then, the closed-loop dynamics of different control objectives are unified in task space by a generalized target model, and a model-reaching law based on adaptive robust control is proposed to achieve the target model even if there exists an unknown contact. Meanwhile, the estimated contact force is not only compensated in the model-reaching control law to guarantee the correct task execution but also used for the null space impedance control design to ensure compliant behavior. The performance and stability of the proposed scheme are guaranteed and proved in theory. Experiments are conducted on a 7-DoF manipulator for the validation.

Non-linear vibration of delaminated composite beam with two overlapping delaminations

The main aim of this paper is to study the non-linear vibration of a delaminated cross-ply composite beam with two overlapping delaminations. The effect of geometrical non-linearity and large deflection on the axial forces due to the existence of two overlapping delaminations are considered. The unknown axial forces created due to the delaminations are obtained by changing the length of the delaminated segments during the vibration behavior. The homotopy perturbation method (HPM) is utilized to obtain the frequency ratio of the delaminated cross-ply composite beam with two overlapping delaminations. This study describes the effects of different parameters such as two delaminations total length, overlap distance, and the distance between center points of two delaminations in axial and thickness directions on the frequency ratio of the delaminated composite beam in detail.

Interaction of circular cavity and crack near anisotropic bi-material interface under SH-waves incidence

AbstractAn anisotropic bi-material interface with a circular hollow and a crack was used to explore the scattering of SH waves using complex variables and Green's function techniques. A horizontal interface in a bi-material media forms an elastic anisotropic half-space with a circular cavity and a linear crack, whereas the other half-space is an elastic isotropic half-space. The Green's function approach is used to derive the relevant Green's functions, which are then used in the “crack division” procedure to create a crack. During the joining of the two pieces, unknown anti-plane forces are applied to the horizontal surfaces to ensure the interface maintains its continuity criteria. For weakly singular integral equations, Fredholm integral equations are inferred and solved using the direct discrete technique. The simulation results were represented graphically to show how different parameters affect the influence of dynamic stress concentration factors around the cavity and dynamic stress intensity factors toward the crack tip. For example, a cavity's wave number and angle of incidence, as well as the distance between the cavity's center and its horizontal interface and its radius, are all elements that must be taken into consideration.

Flatness‐based disturbance observer for exoskeleton robots under time‐delayed contact forces

AbstractThe article proposes flatness‐based control and a Kalman filter‐based disturbance observer for solving the control problem of a robotic exoskeleton under time‐delayed exogenous disturbances. A two‐link lower‐limb robotic exoskeleton is used as a case study. It is proven that this robotic system is differentially flat. The robot is considered to be subject to unknown contact forces at its free‐end which in turn generate unknown disturbance torques at its joints. It is shown that the dynamic model of the robotic exoskeleton can be transformed into the input–output linearized form and equivalently into the linear canonical Brunovsky form. This linearized description of the exoskeleton's dynamics is both controllable and observable. It allows for designing a stabilizing feedback controller with the use of the pole‐placement (eigenvalues assignment) method. Moreover, it allows for solving the state estimation problem with the use of Kalman Filtering (the use of the Kalman filter on the flatness‐based linearized model of nonlinear dynamical systems is also known as derivative‐free nonlinear Kalman filtering). Furthermore, (i) by extending the state vector of the exoskeleton after considering as additional state variables the additive disturbance torques which affect its joints and (ii) by redesigning the Kalman filter as a disturbance observer, one can achieve the real‐time estimation of the perturbations that affect this robotic system. Finally, by including in the controller of the exoskeleton additional terms that compensate for the estimated disturbance torques, the perturbations' effects can be eliminated and the precise tracking of reference trajectories by the joints of this robot can be ensured.

The neural network terminal sliding mode control for the 3-RRC parallel robot

In this paper, the 3 degrees of freedom (3-DOF) parallel robot (3-RRC) is taken as the research object. The Lagrange method is used to establish the reduced order dynamic equations of three branch chains. On the basis of the U-K (Udwadia-Kalaba) equation, the analytical expressions of ideal and non-ideal constrained forces are obtained. Then the complete dynamic model of 3-RRC parallel robot is established. In order to achieve high precision control of 3-RRC parallel robot, and fully considering the uncertainty of non-ideal constrained force and chattering problem in terminal sliding mode control algorithm, the neural network is used to adaptively adjust the gain of switching function and achieve universal approximation of the unknown non-ideal constrained force. The neural network terminal sliding mode control algorithm is proposed for the complete dynamic model of 3-RRC parallel robot, and the stability of the control system is proved by Lyapunov theorem. Finally, the simulation research is conducted on the 3-RRC parallel robot. Simulation results show that the tracking precision of angle positions and non-ideal constrained forces are all reached 10−2 order, which realize the high precision control of the 3-RRC parallel robot, weaken the chattering phenomenon, and verify the correctness and effectiveness of the proposed dynamic model and control algorithm.

Force of lifelong crystalline lens growth: chronic traumatic mechanical insult to the choroid.

To calculate the forces applied to the uvea and retina as a result of lifelong crystalline lens growth. Retrospective study. MRI Research, Inc., Middleburg Heights, Ohio; Institute of Ophthalmology and Visual Science UMDNJ-New Jersey Medical School, Newark, New Jersey; USC Psychology University of Southern California, Los Angeles. Magnetic resonance images were acquired from 15 phakic/pseudophakic eye pairs in patients with cataract (ages 46 to 83 years). Choroidal lengths were measured. The forces required to produce differences between phakic/pseudophakic choroidal lengths were calculated. The length of the choroid is greater in the phakic eye compared with the corresponding pseudophakic eye (n = 15), and this difference increases with age (P = .00006; power = 0.99). The corresponding choroidal strain also increases with age (P = .00003, power = 0.99) as do the forces required to produce such a change in choroidal length (P = .000008, power = 0.99). The authors theorize that lifelong crystalline lens growth applies a chronic, traumatic, mechanical insult to the uvea and retina. This previously unknown, ever-increasing, force appears to stretch the choroidal tissue and may be an intraocular pressure-independent modifiable risk factor for retinal disease. Implications exist for understanding the pathophysiology of retinal diseases in the aging eye that are often comorbid with cataracts, for example, glaucoma, macular degeneration, and diabetic retinopathy.

КОНТАКТНАЯ ЗАДАЧА ДЛЯ ПЛАСТИНКИ ПРИ УСЛОВИИ ОГРАНИЧЕНИЙ НА ЕЕ НЕКОТОРЫЕ ПЕРЕМЕЩЕНИЯ

Porpose. Calculation of the plate on flexible base where one part of the points of the plate base are in the same inclined plane during bending. The concrete foundation where a base plate is located is an flexible semi-infinite foundation. Method. To determine a contact voltage between the plate and the foundation the Zhemochkin method is used. The system of canonical equations includes the equations of the Zhemochkin method and the equation to find single points of the slab in the inclined plane. The result of solving the system determines the forces in the method of Zhemochkin and unknown forces causing the displacement of the base plate of the foundation in the same inclined plane. Then the displacement of the base plate and the forces in it are found. Results. Calculation of the metal foundation of an eccentrically compressed metal column with an I-beam cross-section based on a concrete surfacing. Isolines of equal contact voltages and displacements, graphs of voltage and displacement with the typical sections of the foundation are shown.