Pantograph Mechanism Research Articles

Detecting early damages in the railway pantograph mechanism: a multiple excitation approach for the frequency domain

In this work, we address the problem of damage diagnosis on the railway pantograph mechanism including nonlinear behaviour and sample-induced uncertainties. In particular, we discuss an experimental campaign in which investigation pursued the analysis of frequency response functions estimated by a dedicated inspection robot that we intentionally developed for vibration tests on pantographs. Special focus is pointed to the inherent nonlinear behaviour of the pantograph for which we estimated the damage index for different levels of the input excitation. The investigation is carried out on a population of pantographs of the same type and studying three kinds of damages. Results highlight the relevance of including several excitation levels and encourage investigation in a real operational scenario.

Fully mechanical motion-scaling instrument for microsurgery assistance: design improvement for enhancing the dynamic performance

Abstract Robot assistance can improve the outcome of microsurgery by scaling down the surgeon’s hand motions. However, the high cost of surgical robots has prevented their use in small hospitals or medical facilities in several developing countries. As a novel alternative, a fully mechanical motion-scaling instrument, which can be operated without computers and motors, was proposed based on the pantograph mechanism. However, it had several problems owing to the cumbersome and heavy structures during the prototype test. This study aims solving the problems found in the first design and proving the advantages of the improvement, based on the design and performance criteria. The pantograph structure was simplified, and the gravity compensation method was modified to reduce inertia by using a constant force spring instead of a counter-mass. The improvement was computationally predicted using a mathematical model, and the results were verified through trajectory measurements in a micropositioning task. Finally, the evaluation of dynamic performance is quantitatively presented through iterative positioning tasks.

Разработка математической модели робототехнического комплекса для неразрушающего контроля стальных тросов

In order to improve the safety of lifting equipment, the task was set to create a new robotic complex for automated research of the technical condition and bearing capacity of steel cables in places that are difficult to access and dangerous for personnel. A new mathematical model of a robotic complex has been developed that describes the controlled movement of a magnetic flaw detector for performing technological procedures for non-destructive testing of steel cables. A mathematical model of the dynamics of the system is obtained using the Lagrange formalism. An algorithm for evaluating the control moments necessary for the implementation of programmed motion has been developed. Numerical simulation of the motion corresponding to the mode of approaching the magnetic flaw detector heads to the steel rope has been carried out. The graphs of the traction-speed characteristics and load diagrams of the drives providing the programmed movement of the links of the pantograph mechanism are presented. The results presented in this paper can be used to calculate the parameters of the power section of the electro-hydraulic drives included in the robotic device. The accuracy of performing flaw detection tasks is studied, taking into account the dynamics of the executive and measuring systems of the complex.

Reliability modeling for dependent competing failure processes based on planar mechanism

Considering the influence of external random shock on the kinematic accuracy of mechanism, a new reliability model of dependent competing failure processes (DCFP) is proposed in this paper. The kinematic accuracy of the mechanism is limited by the original errors such as the dimension error and joint clearance error, and it is also affected by aging and wear-out during service life, thus eventually leading to functional failure. Meanwhile, according to the magnitude of the external random shock, the random shock has different effects on the degradation process of the mechanism. In this study, a DCFP model with accuracy degradation process and multi-type mixed shock is considered. The time-dependent kinematic accuracy reliability model of the planar mechanism is established based on the Gamma degradation theory, effective length model, mechanism kinematic error theory and the fourth moment technique. Moreover, the magnitude of random shock is divided into different regions when the extreme shock, cumulative shock, and δ-shock on mechanism reliability are considered. Finally, a numerical example of the pantograph mechanism is conducted to demonstrate the feasibility and effectiveness of the proposed model. The results show that the kinematic accuracy reliability of the pantograph mechanism reduces with the increasing of wearing capacity and external shocks. According to sensitivity analysis, an effective way to improve the reliability of the planar mechanism is to optimize its strength of the mechanism. The proposed method can be used to evaluate the reliability of planar mechanisms with dependent competing failure modes.

Controllability of a generalized multi-pantograph system of non-integer order with state delay

<abstract><p>This paper presents the dynamical aspects of a nonlinear multi-term pantograph-type system of fractional order. Pantograph equations are special differential equations with proportional delays that are employed in many scientific disciplines. The pantograph mechanism, for instance, has been applied in numerous scientific disciplines like electrodynamics, engineering, and control theory. Because of its key rule in diverse fields, the current study establishes some necessary criteria for its controllability. The main idea of the proof is based on converting the system into a fixed point problem and introducing a suitable controllability Gramian matrix $ \mathcal{G}_{c} $. The Gramian matrix $ \mathcal{G}_{c} $ is used to demonstrate the linear system's controllability. Controllability criteria for the associated nonlinear system have been established in the sections that follow using the Schaefer fixed-point theorem and the Arzela-Ascoli theorem, as well as the controllability of the linear system and a few key assumptions. Finally, a computational example is listed.</p></abstract>

Performance Comparison of Se formance Comparison of Several Contr al Control Algorithms for ol Algorithms for Tracking Contr acking Control of P ol of Pantograph Mechanism aph Mechanism

A sort of parallel manipulator known as a pantograph robot mechanism was created primarily for industrial requests that required high precision and satisfied speed. While tracking a chosen trajectory profile requires a powerful controller. Because it has four active robot links and one robot passive link in place of just two links like the open chain does, it can carry more loads than the open chain robot mechanism while maintaining accuracy and stability. The calculated model for a closed chain pantograph robot mechanism presented in this paper takes into account the boundary conditions. For the purpose of simulating the dynamics of the pantograph robot mechanism, an entire MATLAB Simulink has been created. The related Simscape model had been created to verify the pantograph mathematical model that had been provided. Five alternative tracking controllers were also created and improved using the Flower Pollination (FP) algorithm. The PID controller, which is used in many engineering applications, is the first control. An enriched Fractional Order PID (FOPID) controller is the second control. The third control considers an improved Nonlinear conventional PID (NLPID) controller, and the parameters for this controller were likewise determined using (FP) optimization using the useful objective function. Model Reference Adaptive Control (MRAC) with PID Compensator is the fourth control. The Fuzzy PD+I Control is the last and final controller. A comparison of the different control methods was completed. A rectangular trajectory was chosen as the end effector of the pantograph robot's position reference because it displays performance during sharp edges and provides a more accurate study. The proposed controllers were used for this task to analyse the performance. The outcomes demonstrate that the Fuzzy PD+I control outperforms the PID, FOPID, NLPID, and MRAC with PID Compensator controllers in terms of performance. In the case of the Fuzzy PD+I control, the angles end effector has a lower rise time, a satisfied settling time, and low overshoot with good precision.

Analytical spectral design of mechanical metamaterials with inertia amplification

Functional metamaterials offering superior dynamic performances can be conceived by introducing local mechanisms of inertia amplification in the periodic microstructure of cellular composite media. The minimal physical realization of an inertially amplified metamaterial is represented by a one-dimensional crystal lattice, characterized by an intracellular pantograph mechanism. The microstructural dynamics of the periodic tetra-atomic cell is synthetically described by a low-dimension lagrangian model. The lagrangian coordinates account for the longitudinal motion of a pair of elastically coupled principal atoms, rigidly connected by the pantograph arms to a pair of transversely-oscillating secondary atoms, serving as inertial amplifiers. Within the range of small-oscillations, the free propagation of undamped harmonic waves is described by a linear difference equation, governed by a symplectic transfer matrix. First, the band structure of the complex-valued dispersion spectrum is determined analytically, by properly exploiting the formal (time-to-space) analogy with the Floquet Theory for the stability of non-autonomous dynamic systems (direct problem). Second, a spectral design problem is stated and solved by inverting analytically the functions expressing parametrically the boundaries separating attenuation (stop) and propagation (pass) bands in the frequency spectrum (inverse problem). Specifically, the inverse problem solution has the merit of providing simple formulas for parametric design. Such formulas explicitly and exactly identify the mechanical parameters of the inertially amplified metamaterial possessing a desired pass-stop-pass band structure, assigned according to functional design requirements. The existence and uniqueness of the solution in the admissible range of mechanical parameters is discussed. The discussion provides (i) mathematical demonstration for the existence of feasible design solutions or multi-solutions, (ii) complete definition of the physically realizable band structures in the frequency domain, and (iii) alternative criteria to design iso-band structured metamaterials within the admissible domain of mechanical parameters. The extra-customization possibilities offered by iso-band structured metamaterials are analyzed in terms of static and dynamic performances. As feasible limit cases of the analytical spectral design, extreme mechanical metamaterials working as phononic superfilters and/or superpropagators are realizable.

Paper-Based Piezoresistive Force Encoder for Soft Robotic Applications

This work demonstrates the design, implementation, and experimental results of a low-cost disposable flexible sensor system capable of both impact localization and measurement. The proposed flexible sensor structure utilizes a special series of Bristol paper as the main fabrication material, which is coated with electric paint graphite paste and silver paste. The implemented sensor system uses a planar absolute encoder-like sensing topology to locate the impact and has a low-cost and quick manufacturing process. The size of the structure is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${210}\times {18}.{56}$ </tex-math></inline-formula> mm with a thickness of approximately 340 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> . It has an electronic read-out consisting of three identical Wheatstone bridge circuits and instrumentation amplifiers for each bit. It can detect the external forces in the range of 0.6N to 12N with a spatial resolution of 2.4 cm and 0.55 cm in horizontal and vertical axes, respectively. The proposed sensor structure is tested in a series of experiments using a robotic setup consisted of a pantograph mechanism and a direct drive linear motor. The experiments illustrate the results with measurement sensitivity as small as 1N and proper fatigue resilience against repetitive loads.

Stiffness Modeling of a Double Pantograph Transmission System: Comparison of VJM and MSA Approaches

This paper deals with the stiffness modeling of the double pantograph transmission system. The main focus is on the comparison analysis of different stiffness modeling approaches: virtual joint modeling (VJM) and matrix structural analysis (MSA). The aim of this work is to investigate the limitations of the considered approaches. To address this issue, corresponding MSA-based and VJM-based stiffness models were derived. To evaluate the deflections of the end effector, the external loads were applied in different directions at multiple points in the robot workspace. The computational cost and the difference in end-effector deflections were studied and compared. MSA was found to be 2 times faster than VJM for this structure. The results obtained showed that the MSA approach is more appropriate for the double pantograph mechanism.

Development of a wire-storage pantograph mechanism to amplify both the strain and force of the twisted and coiled polymer fiber

Development of a wire-storage pantograph mechanism to amplify both the strain and force of the twisted and coiled polymer fiber

A Modified Model Reference Adaptive Control for High-Performance Pantograph Robot Mechanism

Pantograph Robot Mechanism is considered a type of parallel manipulator which has been developed largely for industrial applications that need high accuracy and speed. Whereas, it needs a high-performance controller to track preselected trajectory planning. It is also able to carry higher weights than the open-chain mechanism with suitable accuracy and stability; this is because it consists of four active links and one passive link, instead of two links as in the open chain. This study presents a mathematical model for a closed chain pantograph mechanism, where the boundary conditions are taken into account. A complete MATLAB Simulink has been developed to simulate the dynamics of the pantograph robot mechanism. To validate the proposed mathematical model of the pantograph, the corresponding Simscape model had been developed. Also, three different tracking controllers were designed. The first control is the PID controller which had optimized by Flower Pollination (FP) optimization. The second control is an enhanced Nonlinear PID (NLPID) controller where its parameters were obtained by Flower Pollination (FP) optimization based on the effective objective function. The third control is the model reference adaptive control. A comparative study between the control techniques was accomplished. A rectangular trajectory was selected to be a position reference of the end effector of the pantograph robot. This task was done using the proposed controllers to investigate the performance. The results show that the model reference adaptive control has a better performance compared to the NLPID and PID controllers. The end effector has a less rise time and settling time with high accuracy in the case of the model reference adaptive control.

Nonlinear dispersion properties of one-dimensional mechanical metamaterials with inertia amplification

Architected metamaterials offering superior dynamic performances can be conceived by inducing local mechanisms of inertia amplification in the periodic microstructure. A one-dimensional cellular lattice characterized by a pantograph mechanism in the tetra-atomic cell is proposed as minimal physical realization of inertially amplified metamaterial. A discrete model is formulated to describe the undamped free dynamics of the cell microstructure. The ordinary differential equations of motion feature quadratic and cubic inertial nonlinearities, induced by the indeformability of the pantograph arms connecting the principal atoms with the secondary atoms, serving as inertial amplifiers. An asymptotic approach is employed to analytically determine the dispersion properties governing the free propagation of harmonic waves in the pantographic metamaterial. First, the linear wavefrequencies and waveforms are obtained by solving the eigenproblem governing the lowest asymptotic order. An invariant parametric form is achieved for the pass and stop band structure, corresponding to propagation and attenuation branches of the dispersion spectrum in the plane of complex wavenumbers. The major effects due to the mass ratio of the inertial amplifiers are discussed. Particularly, the existence conditions, amplitude and centerfrequency of the band gap separating the acoustic and optical pass bands are determined analytically. Second, the nonlinear wavefrequencies and waveforms are obtained by solving the hierarchical linear problems governing the higher asymptotic orders. Analytical, although asymptotically approximate, functions are achieved for the nonlinear wavefrequencies and waveforms, which show quadratic dependence on the oscillation amplitudes. The mechanical conditions for the softening/hardening behaviour of the nonlinear wavefrequencies and the different topological properties of the invariant manifolds associated to the nonlinear waveforms are discussed. Finally, numerical simulations are provided to validate the analytical results.

Topological solitons and bulk polarization switch in collinear type-II multiferroics

We introduce a microscopic model for collinear multiferroics capable to reproduce, as a consequence of magnetic frustration and easy-axis anisotropy, the so-called "uudd" (or antiphase) magnetic ordering observed in several type II multiferroic materials. The crucial role of lattice distortions in the multiferroic character of these materials is entered into the model via an indirect magnetoelectric coupling, mediated by elastic degrees of freedom through a pantograph mechanism. Long range dipolar interactions set electric dipoles in the antiferroelectric order. We investigate this model by means of extensive DMRG computations and complementary analytical methods. We show that a lattice dimerization induces a spontaneous Z2 ferrielectric bulk polarization, with a sharp switch off produced by a magnetic field above a critical value. The topological character of the magnetic excitations makes this mechanism robust.

MATHEMATICAL MODEL OF TWO-DOF FIVE LINKS CLOSED-CHAIN MECHANISM (PANTOGRAPH)

Parallel manipulators have been developed largely for applications that need high accuracy and speed, which make them useful in important fields. This paper presents a detailed mathematical model for a closed chain pantograph mechanism. This task was done by defining its differential equation of motion and implements it using the Matlab Simulink. The mathematical model describes the forward and inverse kinematics, in addition, the dynamic behavior. The mathematical model advantage is studying the parameters variation using different advanced control techniques. This model can be implemented using the Simscape model, which considers a black-box model. To validate the proposed mathematical model for the pantograph, the corresponding model mechanism using the Simscape had been implemented. A comparative study was executed between the mathematical model and the outputs of the Simscape. The results indicated a perfect match for output extracted from Simscape and Simulink. This is evidence for the validity of the inferred equations and Simulink model.

Robotic device for automation of the control of the status of cables in the mining industry

In this work, we propose a design of a robotic device designed to automate the process of nondestructive testing of wire rope equipment. A schematic hydraulic diagram of a robotic device with a description of the logic of work of the system is given. A mathematical model of the dynamics of the system is obtained using the Lagrange formalism. An algorithm for evaluating the control moments necessary for the implementation of programmed motion has been developed. Numerical simulation of the motion corresponding to the mode of approaching the magnetic flaw detector heads to the steel rope has been carried out. The graphs of the traction-speed characteristics and load diagrams of the drives providing the programmed movement of the links of the pantograph mechanism are presented. The results presented in this paper can be used to calculate the parameters of the power section of the electro-hydraulic drives included in the robotic device.

Effect of combination of flexure joints and material used on performance of compliant pantograph mechanism

Compliant mechanism transfers motion or force using the elastic deflection of flexures or the whole mechanism (distributed). Pantograph is a widely proven mechanism which can imitate motion. The compliant pantograph models proposed by earlier researcher are limited to use of all circular flexure hinges; with some reporting geometric amplification (GA) around 2. Thus the present research work is an attempt towards using different combinations of flexures viz. circular, elliptical and parabolic deployed (for proposed six models), while developing the compliant pantograph (CP) in order to improve the GA. Also the effect of material Stainless Steel (SS) and Mild Steel (MS) on the performance of CP is presented. The finite element analysis is undertaken and output displacement is estimated for pre-decided range of input motion The maximum GA achieved for one of the combinations (combination no. 4) using SS is 2.57 wherein the flexures considered consist of two Elliptical and four circular flexures. Depending on desirable output range any of the above models can be used in micro stages/slides and many more precision applications.

Study of Effect of Friction on the Pin of Pantograph Mechanism

Study of Effect of Friction on the Pin of Pantograph Mechanism

Prediction of the Pantograph/Catenary Wear Using Nonlinear Multibody System Dynamic Algorithms

In this investigation, computational multibody system (MBS) algorithms are used to develop detailed railroad vehicle models for the prediction of the wear resulting from the pantograph/catenary dynamic interaction. The wear is predicted using MBS algorithms for different motion scenarios that include constant-speed curve negotiation and acceleration and deceleration on a tangent (straight) track. The effect of the vehicle vibration in these different motion scenarios on the contact force is further used to study the wear rates of the contact wire. The wear model used in this investigation accounts for the electrical and the mechanical effects. The nonlinear finite element (FE) absolute nodal coordinate formulation (ANCF), which is suitable for implementation in MBS algorithms, is used to model the flexible catenary system, thereby eliminating the need for using incremental-rotation procedures and co-simulation techniques. In order to obtain efficient solutions, both the overhead contact line and the messenger wire are modeled using the gradient-deficient ANCF cable element. The pantograph/catenary elastic contact formulation employed in this study allows for separation between the pantograph panhead and the contact wire, and accounts for the effect of friction due to the sliding between the pantograph panhead and the catenary cable. The approach proposed in this investigation can be used to evaluate the electrical contact resistance, contribution of the arcing resulting from the panhead/catenary separation, mechanical and electrical wear contributions, and the effect of the pantograph mechanism uplift force on the wear rate. Numerical results are presented and analyzed to examine the wear rates for different motion scenarios.

Multibody modeling and nonlinear control of the pantograph/catenary system

In this paper, a closed-chain multibody model of a pantograph/catenary system is developed and used for the optimal design of a nonlinear controller based on an open-loop control architecture. The goal of the nonlinear controller is the reduction of the contact force arising from the pantograph/catenary interaction and, at the same time, the suppression of the mechanical vibrations of the pantograph mechanism. The analytical formulation employed in this paper for describing the nonlinear dynamics of the pantograph/catenary multibody system considers a Lagrangian approach and is based on a redundant set of generalized coordinates. The contact forces generated by the pantograph/catenary interaction are modeled in this work employing an elastic force element collocated between the pantograph pan-head and a moving support. The external support follows a prescribed motion law that simulates the periodic deployment of the catenary system. On the other hand, in this investigation, the algebraic constraints arising from the closed-loop topology of the pantograph multibody system are enforced employing a method based on the Udwadia–Kalaba equations recently developed in the field of analytical dynamics. Furthermore, the problem of the determination of an effective feedforward controller for reducing the pantograph/catenary contact force is formulated in this work as a nonlinear optimal control problem. For this purpose, the solution of the control optimization problem is carried out by using an adjoint-based computational procedure. Numerical simulations demonstrate the effectiveness of the nonlinear controller obtained in this investigation for the pantograph/catenary multibody system.

Design and Experimental Verification of a Pantograph-Based Mechanism for Lower Limb Load Reduction by Compensating for Upper Body Weight

Several extant studies examine the design of power assist systems that support leg motion of the wearer. However, in most cases, actuators are always required to support the upper body weight of a wearer. This support reduces power efficiency, and thus, a new mechanism is required to effectively support upper body weight. This paper proposes a design of a lower limb load reduction device that uses a pantograph mechanism. In the mechanism, leg motion can be separated into horizontal and vertical motions, and only the lower limb load that is caused by vertical motion and the wearer’s own weight is compensated by the actuators. Additionally, the design enables support of upper body weight only in the support leg phase, and actuators are not used in the lifted leg phase. The design principle is described, and experimental results subsequently demonstrate the effectiveness of the proposed design.