End-point Deflection Research Articles

Adaptive neural network independent joint-based control for an ODE-PDE rigid-flexible manipulator with multiple constraints

This paper deals with the adaptive neural network control of a nonlinear rigid-flexible manipulator subject to external disturbances and multiple constraints. The system dynamic is modeled by ordinary and partial differential equation (ODE and PDE) based on Hamilton’s Principle. An adaptive neural network sliding mode control strategy is designed to estimate the unknown disturbances and uncertain parameter. The sliding surface consisting of angular error, angular velocity error, and end-point vibration information is proposed based on the energy analysis of the flexible beam. The tangent barrier Lyapunov function is used to ensure the angle errors and end-point deflection within the restrictions. It is shown that the joint motion and vibration of the flexible beam can be adjusted only with an independent joint control input, and no boundary force input is required for vibration suppression. The stability is obtained by semi-group theory and LaSalle’s Invariance Principle. Simulation results demonstrate the effectiveness of the control strategy.

Designing Custom Mechanics in Running-Specific Prosthetic Feet via Shape Optimization.

Running-specific prosthetic feet are curved cantilever springs, distinguished from ordinary prosthetic feet by their size, shape, and greater ability to store and return elastic potential energy. Finite element analyses show how modifications to prosthesis shape alter the multidimensional and nonlinear mechanics, but designers seeking to prescribe custom mechanics are limited by the complex constraints and high dimensionality of possible geometries. We introduce two simple formulations for describing foot mechanics, and use them with a custom spline-based shape optimization to generate new prosthetic foot shapes given desired endpoint mechanics. We then tackle a relevant example problem using this approach, designing and characterizing three running-specific prosthetic feet with similar vertical and angular deflections but varied horizontal deflections, with the expectation that knee extension moments would increase with anterior deflection of the toe. Finally, we compare the prostheses' endpoint mechanics and resulting biomechanics in an athlete with unilateral transfemoral amputation. The shape optimization was able to derive shapes that substantially alter prosthesis mechanics along all dimensions of endpoint behavior, and benchtop testing validated the behavior of two new feet constructed from the optimization. The subject's knee moments increased with horizontal endpoint deflection as expected. We developed and validated a shape optimization tool using a simplified formulation of foot behavior to achieve desired running prosthesis mechanics. With this framework, researchers can begin to elucidate the link between prosthesis mechanics and athlete biomechanics and performance.

Lifetime prediction of linear slide rails based on surface abrasion and rolling contact fatigue-induced damage

The research presented in this paper deals with the development of an integrated numerical model for the estimation of the incremental surface wear and damage accumulation in linear slide rails. The target is the estimation of the progressive increment of the end-point deflection of the last member of the slide rail during the operational lifetime. The surface abrasion is accounted for by utilizing a modified Archard equation with the aim of estimating the amount of wear along the vertical direction of the slide rails members. In addition to that, the Lemaitre damage model is utilized for the estimation rolling contact fatigue (pitting), considering the total strain and not only the plastic strain. Experiments have been carried out on a small-scale slide rail testing machine in order to define the wear increment on the slide rail inner groove for increasing number of cycles and, accordingly, estimate the modified Archard model constants. In addition to that, the wear parameters for the Lemaitre damage model have been inversely calibrated from the results of tensile tests. A numerical model has been implemented in ABAQUS/Explicit and an external geometry-update subroutine has been employed to update the geometry of the slide rail groove for increasing number of cycles as a consequence of wear and roll contact fatigue. The comparison between numerical and experimental results on real rails have shown a maximum deviation equal to 12.9%, supporting the reliability of the proposed approach.

Open-Loop Vibration Control of an Underwater System: Application to Refueling Machine

This paper addresses a residual vibration control problem of the refueling machine (RM) that transports fuel rods in water to their desired locations in the nuclear reactor. A hybrid lumped-mass and distributed-parameter model of the RM is considered for investigation of the transverse vibrations (caused by trolley movement) of a fuel rod in water. Simulations and experiments reveal that the hydrodynamic force causes a large deflection of the rod in water as compared with in air, which must be suppressed to avoid damage to the rod's fissile material. A new command-shaping method for suppression of the flexible rod's residual vibrations in water is developed, which considers both a similitude law relating the maximum endpoint deflection of the rod in water to the maximum trolley velocity and a constraint on the rod's maximum endpoint deflection during its transport. The simulation and experimental results show that the proposed underwater-command-shaping method can effectively suppress the vibrations of the flexible rod operating in water.

Wear-caused deflection evolution of a slide rail, considering linear and non-linear wear models

The research presented in this paper details an experimental-numerical approach for the quantitative correlation between wear and end-point deflection in a slide rail. Focusing the attention on slide rail utilized in white-goods applications, the aim is to evaluate the number of cycles the slide rail can operate, under different load conditions, before it should be replaced due to unacceptable end-point deflection. In this paper, two formulations are utilized to describe the wear: Archard model for the linear wear and Lemaitre damage model for the nonlinear wear. The linear wear gradually reduces the surface of the slide rail whereas the nonlinear one accounts for the surface element deletion (i.e. due to pitting). To determine the constants to use in the wear models, simple tension test and sliding wear test, by utilizing a designed and developed experiment machine, have been carried out. A full slide rail model simulation has been implemented in ABAQUS including both linear and non-linear wear models and the results have been compared with those of the real rails under different load condition, provided by the rail manufacturer. The comparison between numerically estimated and real rail results proved the reliability of the developed numerical model, limiting the error in a ±10% range. The proposed approach allows predicting the displacement vs cycle curves, parametrized for different loads and, based on a chosen failure criterion, to predict the lifetime of the rail.

Computer Aided Modelling and Static Analysis of an Inspection Robot

This paper describes the method for computer aided modelling of the newly designed robot with the aid of 3D modelling software. The static analysis of the designed robot also done by using the analysis software. The conventional design procedures of the elements of the mechanical configurations of the robot base and arm explained in exhaustive manner. Nuclear waste storage steel canisters are often required regular maintenance and surface inspection in order to ensure the goodness of the canisters. In this research work also the designed robot is doing the same task with the help of NDT system available at the end of the arm. However, these types of robot manipulators suffer from different payload capacity and relatively some amount of end point deflections. Through the static analysis the stability of the robot manipulator is proved. This paper features the optimized new design of mechanical configuration of the robot suitable for inspection of outer surface welds present in the steel storage canister at nuclear industry with the help of NDT equipment. The effective utilization of knuckle joints and screw jack mechanisms at the base gives the higher order of degree of freedom when compare with currently available robots.

Linear matrix inequality-based robust proportional derivative control of a two-link flexible manipulator

This paper presents the design and development of a robust proportional derivative (PD) controller based on linear matrix inequality (LMI) for the control of a hub angular position and end-point deflection of a planar two-link flexible manipulator. The dynamics of the manipulator is uncertain and time varying due to the variation of payloads that result in large variations in the excitation of flexible modes. Practical design steps are presented in which the LMI-based conditions are formulated to obtain a robust PD gains to control the flexible manipulator. The robust controller has an advantage as compared to the Ziegler-Nichols tuned PD controller as the identified PD gains can be used to control the system under various loading conditions. The performances of the proposed controller are evaluated in terms of input tracking capability of the hub angular position response and level of deflection of both links of the flexible manipulator. Experimental results show that despite using the same sets of PD gains, LMI-PD control provides better robustness and system performance.

Cascade fuzzy logic control of a single-link flexible-joint manipulator

This paper presents the design and control of a single-link flexible-joint robot manipulator. A cascade fuzzy logic controller (FLC) was used to remove link vibrations and to obtain fast trajectory tracking performance. The cascade FLC structure includes 3 different FLCs. The input variables of the first and the second FLCs are the motor rotation angle error, its derivative, and the end-point deflection error its derivative, respectively. The outputs of these controllers are the inputs of the third FLC, which yields the control signal to the flexible robot arm. All of the FLCs were embedded in a DS1103 real-time control board. Several experiments were conducted to verify the controller performance. In the step-response experiments, the error of motor rotation angle was obtained as less than 0.12° and there was no steady-state error in the end-point deflection. In trajectory tracking experiments with the same FLC structure, small errors and phase shifts in the system variables occurred. Model parameters of the flexible arm such as link length and spring stiffness were changed to test the robustness of the FLC. It was seen that the FLCs were very robust to internal and external disturbances. Considering the results of the experiments, the proposed FLC structure shows efficient control performance in flexible robot arms.

Modeling and performance of two types of piston-like out-of-plane motion micromechanical structures

We have modeled and analyzed the performance of two types of piston-like out-of-plane motion micromechanical structures: a conventional microstructure, which has a single bimorph region, and a flip-over-bimaterial (FOB) microstructure, which has two bimorph regions respectively located on the top and bottom sides of the structure. For both structures, simple analytical expressions of their end-point deflections have been established to facilitate parametric studies in sensor or actuator designs. These structures can be used in several applications such as temperature and chemical sensors, or as actuators for micromirrors. The derived analytical deflection predictions are in good agreement with those made using finite element (FE) models. For a micro-opto-mechanical sensor using interconnected FOB microstructures, these analytical and FE predictions agree with the experimental results within about 25%. Discrepancies can be attributed to uncertainties in the material properties of the specimen being tested. Both the analytically derived deflection expressions and the FE models predict that the FOB microstructures are capable of achieving up to two times higher deflection than conventional microstructures that have a single bimorph region. When compared to a cantilever design, a sensor design having interconnected FOB structures has a higher signal-to-noise ratio for the same device footprint. The analytical modeling and performance analysis presented in this paper can be useful to predict the device performance as well as optimize design parameters.

Walking and Climbing Service Robots for Safety Inspection of Nuclear Reactor Pressure Vessels

Nuclear reactor pressure vessels are often required regular inspection and maintenance in order to ensure the safety of the reactors. Failing to carry out proper maintenance could cause severe casualty. The usual way of carrying out inspection in these hazardous environments is using long reach fixed base manipulators. However, these manipulators suffer from low payload capacity and relatively large end point deflections. Also, the installation and the storage of these long manipulators could be costly. An alternative solution is to use walking-climbing robots, which overcome the problems encountered by the long reach manipulators. In this paper, two robots, NERO (Nuclear Electric Robot Operator) and SADIE (Sizewell A Duct Inspection Equipment) which have been applied successfully to inspect two Magnox reactors in the UK are described. The deployment and operational experience of these robots are also explained. Finally the applications and the usefulness of these robots for improving safety inspection of nuclear reactors in general are discussed in this paper.

Experimental Study on Active Vibration Control of a Single-Link Flexible Manipulator Using Tools of Fuzzy Logic and Neural Networks

This paper is concerned with the design and implementation of active vibration control based on fuzzy logic and neural networks (NNs). The controller is used to dampen the end-point vibration in a single-link flexible manipulator mounted on a two degrees-of-freedom platform. The inputs to the fuzzy logic controller (FLC) are the angular position of the hub and the end point deflection of the flexible beam. A NN predicting the deflection was obtained using a set of three strain gauge pairs mounted on the beam and an linear-variable differential transformer placed at the tip. This paper discusses how to build the rule base for the flexible beam based on the relation between the angular displacement of the hub and the end-point deflection, as well as the approach that was used to develop the NN model. Several experimental results showing the effectiveness of the FLC in reducing the end-point vibration of the flexible beam are presented.

Fuzzy Logic Control of the End-Point Vibration in an Experimental Flexible Beam

This paper is concerned with the design and implementation of a fuzzy logic controller (FLC) to control the end-point vibration in a single flexible beam mounted on a two-degrees-of-freedom platform. The angular position of the hub and the signal from a strain gage mounted on the beam are used as the two inputs to the FLC. In order to add more damping, the strain gage signal is combined with the hub angular velocity represented by the output of a tachometer attached to the motor shaft. We discuss how to build the rule base for the flexible beam based on the relation between the angular displacement of the hub and the end-point deflection, as well as the effect of different scaling gains on the performance of the FLC. We present several experimental results showing the effectiveness of the FLC in reducing the end-point vibration of the flexible beam.

Fuzzy Logic Control of the End-Point Vibration in an Experimental Flexible Beam

This paper is concerned with the design and implementation of a fuzzy logic controller (FLC) to control the end-point vibration in a single flexible beam mounted on a two-degrees-of-freedom platform. The angular position of the hub and the signal from a strain gage mounted on the beam are used as the two inputs to the FLC. In order to add more damping, the strain gage signal is combined with the hub angular velocity represented by the output of a tachometer attached to the motor shaft. We discuss how to build the rule base for the flexible beam based on the relation between the angular displacement of the hub and the end-point deflection, as well as the effect of different scaling gains on the performance of the FLC. We present several experimental results showing the effectiveness of the FLC in reducing the end-point vibration of the flexible beam.

Deflection characteristics of some special configurations of snake-type robots

The redundant robots analyzed here have large numbers of degrees of freedom. Such robots are analogous to snake or tentacles and are useful for operation in highly constrained environments and novel forms of locomotion — here it has been defined as critical manipulation. In this paper the end-point deflection of hyper-redundant robots have been studied by parameterization of the flexible links of the robot manipulator. A number of planar configurations of the redundant manipulator were taken into consideration for the present study and the configuration which gives minimum end-point deflection has been recommended for the critical manipulation. This work is significant for some of the research activities recently going on in NASA's Kennedy Space Center towards the application of hyper-redundant robots for manipulation inside the space Shuttle Cargo Bay.

Branch breakage under snow and ice loads.

Measurements were made on branches and trunks of Picea sitchensis (Bong.) Carr. to determine the relationship between (i) the bending moment at the bases of branches that cause breakage, and (ii) midpoint diameter cubed. The theory for cantilever beams was then used to calculate the basal bending moments and midpoint diameters of branches with different numbers of laterals and endpoint deflections, given previously measured values of Young's modulus, taper and weights of foliage and wood. Snow and ice loads (equal to 2 and 4 g cm(-1) of shoot, respectively) were then included in the calculation to determine whether the basal bending moments exceeded the breakage values. The likelihood of breakage increased with an increase in (i) number of laterals, and (ii) endpoint deflection under self weight (without snow or ice)-features that had previously been shown to lessen the amount of branch wood required to support a unit of foliage. However, branches which deflected moderately (> 10% of their length) under their own weight deflected greatly under snow or ice loads and might shed powdery snow before breakage occurs.

Support costs of different branch designs: effects of position, number, angle and deflection of laterals.

The structural theory for cantilever beams was used to calculate the dry weight of wood that a branch of Picea sitchensis (Bong.) Carr. must produce to support its own weight plus that of laterals in different positions and numbers, and with different angles and deflections. The endpoint of the branch was maintained at 2% of its length, and constant values or functions (measured on real branches) were assumed for Young's modulus, taper and self weights of wood and foliage. Support costs (branch wood dry weights) were minimized when laterals were positioned so that the center of gravity was close to the base of the branch, and when the branch was angled upward from the horizontal. Small savings in support costs also resulted when laterals were not forward pointing, were angled upward and had endpoint deflections of at least 20% of their length.

Diameters and dry weights of tree shoots: effects of Young's modulus, taper, deflection and angle.

The structural theory for cantilever beams was used to calculate the diameters and dry weights of wood that unbranched shoots must produce to support their own weights. The study was done on Picea sitchensis (Bong.) Carr., Pinus contorta Dougl., Larix decidua Mill. and Betula pendula Roth. syn. verrucosa Ehrh. The weights of wood increased in a non-linear fashion with increase in shoot length. A large investment in wood (as measured by diameter and dry weight) was required to maintain a small endpoint deflection (1-5% of the length). By contrast, the degree of linear taper had only a small effect on support costs, as did the Young's modulus of the wood (over the range 1-4 GPa) and the angle of the shoot from the horizontal (over the range 0-45 degrees ). Current year's shoots on young trees of P. sitchensis and P. contorta incur a high support cost in order to maintain small (1-5%) deflections throughout the year: similar shoots of L. decidua and B. pendula have smaller support costs because they deflect by about 20% after leaf expansion in spring.