Nonlinear Compliance Research Articles

Robust coordination control of a pneumatic deburring tool

AbstractAn efficient robotic deburring method was developed based on an active pneumatic tool. The developed method considers the interaction among the tool, the manipulator, and the workpiece and couples the tool dynamics and a control design that considers deburring process information. The active pneumatic tool was developed based on a single pneumatic actuator, with a passive chamber to provide compliance and reduce chattering caused by air compressibility. A coordination control method was developed for the efficient control of the system, which adopts two‐level hierarchical control structure based on a coordination scheme. Robust feedback linearization was utilized to minimize the undesirable effect of the disturbances, such as static and Coulomb frictions and the nonlinear compliance of the pneumatic cylinder stemming from air compressibility. The developed coordination control method demonstrated its efficacy in terms of deburring accuracy and speed. © 2006 Wiley Periodicals, Inc.

Simulation of impact, based on an approach to detect interference

This paper describes a method for simulating impacts which occur during the motion of planar mechanisms. An interference detection method is proposed. Using this, distance between bodies can be determined during simulation, without having to solve a system of nonlinear equations. The approach is illustrated by simulating a cam–follower mechanism. Impact is modelled using nonlinear compliance at the point of contact, and friction is modelled as Coulomb’s friction. Numerical integration is partially validated using energy balance.

The influence of friction on contouring accuracy of a Cartesian guided tripod machine tool

This paper is focused on the friction-induced contouring errors of a three-axis parallel kinematic machine (PKM) called a Cartesian-guided tripod (CGT). A dynamic model of the CGT including the nonlinear dynamic, mechanical compliance and mechanical friction has been formulated. Servo control characteristics of the formulated CGT dynamic model are analyzed based on the conventional P-PI controller and feedforward friction compensation implemented in the joint level control scheme. Quantitative analysis and comparison of the various friction sources from the actuated joints (ballscrew/nut) and passive joints (balljoint and guideway) have been conducted. Analysis results show that the ballscrew/nut friction produces the most significant friction-induced contouring errors. The ball-joint friction and linear-guide friction induced contouring errors are two-order and one-order, respectively, lower than the errors by the ballscrew friction. The main reason is that the equivalent friction torques of these two friction sources coupled into the servo drive loop are reduced by the leverage effect of the driving leg length. It was also found that the conventional feedforward friction compensation can effectively reduce the ballscrew-friction-induced contouring errors. However, if not properly compensated, ballscrew friction could excite significant platform-leg structural vibration because the tripod-based PKM usually has a high compliance vibration mode in the horizontal platform-leg direction. The friction-excited structural vibration can be reduced by putting vibration absorbers on the guideways of the passive leg to damp out the platform-leg vibration. From the primary analysis results, it can be seen that the proposed tripod based PKM has high potential for high-speed 5-axis machining applications.

Effects of the Number of Actin-Bound S1 and Axial Force on X-Ray Patterns of Intact Skeletal Muscle

Effects of the number of actin-bound S1 and of axial tension on x-ray patterns from tetanized, intact skeletal muscle fibers were investigated. The muscle relaxant, BDM, reduced tetanic M3 meridional x-ray reflection intensity (IM3), M3 spacing (dM3), and the equatorial I11/I10 ratio in a manner consistent with a reduction in the fraction of S1 bound to actin rather than by generation of low-force S1-actin isomers. At complete force suppression, IM3 was 78% of its relaxed value. BDM distorted dynamic IM3 responses to sinusoidal length oscillations in a manner consistent with an increased cross-bridge contribution to total sarcomere compliance, rather than a changed S1 lever orientation in BDM. When the number of actin-bound S1 was varied by altering myofilament overlap, tetanic IM3 at low overlap was similar to that in high [BDM] (79% of relaxed IM3). Tetanic dM3 dependence on active tension in overlap experiments differed from that observed with BDM. At high BDM, tetanic dM3 approached its relaxed value (14.34nm), whereas tetanic dM3 at low overlap was 14.50nm, close to its value at full overlap (14.56nm). This difference in tetanic dM3 behavior was explicable by a nonlinear thick filament compliance which is extended by both active and passive tension.

Modeling of elastic nonlinearities in ferroelectric materials including nonlinear losses: application to nonlinear resonance mode of relaxors single crystals

(1-x)Pb(Mg1/3Nb2/3)O3-xPbTiO3 (PMN-PT) and (1-x)Pb(Zn1/3Nb2/3)O3-xPbTiO3 (PZN-PT) single crystals are considered to behave like soft Pb(Zr,Ti)O3 (PZT) ceramics because of their small mechanical quality factor Qm and poor stability under external disturbances (Qm > 500-1000 for hard PZT ceramic, and Qm < 100 for soft PZT and PMN-PT and PZN-PT single crystals). At weak signal excitation of the first resonance mode, the displacement at the end of a lateral bar is proportional to the Q31d31 figure of merit that is very close to that found for hard PZT. Indeed the very large piezoelectric coefficient compensates the low Qm. But increasing alternating current (AC) field results in the appearance of strong non-linearities through a shift of the resonance frequency and jumps phenomenon observed on increasing and decreasing frequency sweep. It is shown in this paper that these nonlinearities are due to the nonlinear elastic compliance that can be modeled by a third order development of the constitutive piezoelectric equations. Experiments on PMN-PT and PZN-PT single crystals are used for comparison with the model to show the viability of the approach. Both the frequency shift and jumps phenomenon are simulated with a very good agreement with experimental results. The importance is also shown of losses associated with the third order term responsible for the large decrease of the mechanical quality factor for high strain levels. Thus, the nonlinear losses are related to the hysteresis of domain wall motion when subjected to large displacements.

Modeling time effects of recruitment and P–V curve characteristics: a simulation study

In a multicenter study on respiratory mechanics in ALI and ARDS [1] we observed phenomena most probably related to time effects: change in compliance after a recruitment maneuver, transient end-expiratory volume (Fig. ​(Fig.1)1) after changing PEEP, and a transient change in shape of the P–V curve after a change in tidal volume (Fig. ​(Fig.2).2). To gain a better understanding of temporal effects we developed a mathematical model of the respiratory system to investigate these phenomena. Figure 1 Observed transient volume after switching from ZEEP to PEEP 18 in an ARDS patient. End expiratory volume at ZEEP was defined as 0. Figure 2 Transient in the shape of the P–V curve after an increase in tidal volume. Methods We extended the model of recruitment proposed by Hickling [2] to include chest wall characteristics, FRC, and an initial opening volume of alveolar units once recruited. Alveolar units had a nonlinear compliance and were organized in a bronchial tree structure. Depending on the position in the tree each lung unit was exposed to a gravitational superimposed pressure from 0 in the ventral compartment to a maximal value in the dorsal compartment. Opening and closing pressures of lung units were normally distributed with a modifiable mean and standard deviation. Time dependency was modeled by including timing parameters for recruitment and derecruitment of alveolar units similar to the approach of Bates and colleagues [3].

The Effect of Incorporating Vessel Compliance in a Computational Model of Blood Flow in a Total Cavopulmonary Connection (TCPC) with Caval Centerline Offset

The total cavopulmonary connection (TCPC), a palliative correction for congenital defects of the right heart, is based on the corrective technique developed by Fontan and Baudet. Research into the TCPC has primarily focused on reducing power loss through the connection as a means to improve patient longevity and quality of life. The goal of our study is to investigate the efficacy of including a caval offset on the hemodynamics and, ultimately, power loss of a connection. As well, we will quantify the effect of vessel wall compliance on these factors and, in addition, the distribution of hepatic blood to the lungs. We employed a computational fluid dynamic model of blood flow in the TCPC that includes both the non-Newtonian shear thinning characteristics of blood and the nonlinear compliance of vessel tissue. Power loss in the rigid-walled simulations decayed exponentially as caval offset increased. The compliant-walled results, however, showed that after an initial substantial decrease in power loss for offsets up to half the caval diameter, power loss increased slightly again. We also found only minimal mixing in both simulations of all offset models. The increase in power loss beyond an offset of half the caval diameter was due to an increase in the kinetic contribution. Reduced caval flow mixing, on the other hand, was due to the formation of a pressure head in the offset region which acts as a barrier to flow.

Near-simultaneous impacts

This work considers a three-mass collision model with compliant contacts. If the masses are initially separated by a sufficient distance, the collision sequence is pairwise, that is, comprised of a series of pairwise impacts. The final velocities of each mass are then independent of the specific initial spacing. In contrast, if the initial spacing between the masses is small the three masses interact simultaneously and the final velocity state depends not only on the initial velocities, but also on the initial configuration of the system. Given the impact duration and coefficient of restitution for a pairwise collision, which can be determined from appropriate differential collision models, a two-dimensional map is derived to describe those initial conditions that lead to pairwise sequences in the three mass system. Finally, for a specific nonlinear compliance model the variation in the final velocities are characterized in terms of the initial configuration of the system.

THE ARCHITECTURAL DESIGN FOR DYNAMIC ARTERIAL COMPLIANCE-MEASURING INSTRUMENT

Arterial compliance is defined as the variation of arterial vessel diameter under the blood pressure. This paper introduces the architecture of a brand-new compliance measurement. Two techniques are used: one is to use pressure feedback control and then obtain the variation of arterial vessel diameter at wrist; the other is to detect the delay time between two adjacent pressures and then calculate the downstream blood pressure according to the upstream blood pressure and delay time. The above information can easily compute the dynamic nonlinear arterial compliance. Therefore, the instrument comprises of two pressure sensors: one is fixed and the other is sliding upward and downward by a peizo-actuator. The piezo-actuator is imposed a strain gauge which senses the displacement of the actuator, or the variation of arterial vessel diameter. The design philosophy and fabrication of this instrument are present.

Mathematical study of the role of non-linear venous compliance in the cranial volume-pressure test.

The role of the cerebral venous bed in the cranial volume-pressure test was examined by means of a mathematical model. The cerebral vascular bed was represented by a single arterial compartment and two venous compartments in series. The lumped-parameter formulation for the vascular compartments was derived from a one-dimensional theory of flow in collapsible tubes. It was assumed in the model that the cranial volume is constant. The results show that most of the additional volume of cerebrospinal fluid (deltaV(CSF)) was accommodated by collapse of the cerebral venous bed. This profoundly altered the venous haemodynamics and was reflected in the cranial pressure P(CSF). The cranial volume-pressure curve obtained from the model was consistent with experimental data; the curve was flat for 0 < or = deltaV(CSF) < or = 20 ml and 35 < or = deltaV(CSF) < or = 40 ml, and steep for 20 < or = deltaV(CSF) < or = 35 ml and deltaV(CSF) > or = 40 ml. For deltaV(CSF) > 25 ml and P(CSF) > 5.3 kPa (40 mmHg), cerebral blood flow dropped. When P(CSF) was greater than the mean arterial pressure, all the veins collapsed. The conclusion of the study was that the shape of the cranial volume-pressure curve can be explained by changes in the venous bed caused by various degrees of collapse and/or distension.

A MATHEMATICAL MODEL OF NEONATAL TIDAL LIQUID VENTILATION FOR THE OPTIMIZATION OF AIRWAY MECHANICS AND GAS TRANSFER

Tidal Liquid Ventilation (TLV) was demonstrated to improve lung mechanics and ventilation/perfusion matching in neonatal animal models with respiratory distress. Benefits derive from removing the liquid-gas interface in alveoli, by filling the lungs with liquid perfluorocarbon (PFC). The effects of ventilator settings on blood arterialization and lung mechanics have been scarcely studied quantitatively up to now. We developed a mathematical model describing the course of a neonatal TLV treatment as a function of the ventilator settings (breathing frequency (f), tidal volume (TV), inspiration-to-expiration ratio, PFC flow waveform and PFC pO2). In the overall model, a morphometric lumped-parameter model of airway mechanics (M1) and a model describing O2 and CO2 transport in PFC (M2) are coupled. M1 outputs the pressure and wall shear stress acting at all airway generations, accounting for nonlinear hydraulic airway resistance, inertance, and non-linear compliance, the latter allowing prediction of possible airway collapse phenomena. M2 calculates the diffusive and convective gas transfer through the PFC-filled lungs and the alveolus-capillary gas transfer by describing transport and kinetics of respiratory gases in pulmonary blood. Through the results of model simulations, strategies were defined to increase gas transfer taking the mechanical stresses into account. The model predicts that improving gas exchange without increasing maximum airway pressure is possible by increasing f and decreasing TV. Different strategies were also drawn to limit airway collapse danger or maximum airway shear stress.

Numerical simulation of the influence of gravity and posture on cardiac performance.

A numerical model of the cardiovascular system was used to quantify the influences on cardiac function of intrathoracic pressure and intravascular and intraventricular hydrostatic pressure, which are fundamental biomechanical stimuli for orthostatic response. The model included a detailed arterial circulation with lumped parameter models of the atria, ventricles, pulmonary circulation, and venous circulation. The venous circulation was divided into cranial, central, and caudal regions with nonlinear compliance. Changes in intrathoracic pressure and the effects of hydrostatic pressure were simulated in supine, launch, sitting, and standing postures for 0, 1, and 1.8 G. Increasing intrathoracic pressure experienced with increasing gravity caused 12% and 14% decreases in cardiac output for 1 and 1.8 G supine, respectively, compared to 0 G. Similar results were obtained for launch posture, in which the effects of changing intrathoracic pressure dominated those of hydrostatic pressure. Compared to 0 G, cardiac output decreased 0.9% for 1 G launch and 15% for 1.8 G launch. In sitting and standing, the position of the heart above the hydrostatic indifference level caused the effects of changing hydrostatic pressure to dominate those of intrathoracic pressure. Compared to 0 G, cardiac output decreased 13% for 1 G sitting and 23% for 1.8 G sitting, and decreased 17% for 1 G standing and 31% for 1.8 G standing. For a posture change from supine to standing in 1 G, cardiac output decreased, consistent with the trend necessary to explain orthostatic intolerance in some astronauts during postflight stand tests. Simulated lower body negative pressure (LBNP) in 0 G reduced cardiac output and mean aortic pressure similar to I G standing, suggesting that LBNP provides at least some cardiovascular stimuli that may be useful in preventing postflight orthostatic intolerance. A unifying concept, consistent with the Frank-Starling mechanism of the heart, was that cardiac output was proportional to cardiac diastolic transmural pressure for all postures and gravitational accelerations.

Reduction of oscillatory pressure along the endotracheal tube is indicative for maximal respiratory compliance during high‐frequency oscillatory ventilation: A mathematical model study

We hypothesized that during high-frequency oscillatory ventilation (HFOV), a reduction of peak-to-peak oscillatory pressure along the endotracheal tube is maximal when respiratory system compliance is maximal. We made a mathematical model of the endotracheal tube and the respiratory system of a neonate suffering from idiopathic respiratory distress syndrome (IRDS). The model consisted of linear viscous and inertive elements, a non-linear endotracheal tube resistance, and a non-linear compliance allowing for alveolar recruitment and overdistention. Respiratory compliance was maximal at the transition between maximal recruitment and minimal overdistention. A new variable, the oscillatory pressure ratio (OPR), was defined as the ratio between peak-to-peak oscillatory pressures at the distal end and the proximal opening of the endotracheal tube, respectively. The respiratory variables of four patients were fed into the model, and the relationship between respiratory system compliance and OPR was determined. OPR decreased as compliance increased, except for very low compliances below where 0.08 mL. cm H2O(-1), and OPR increased with increasing compliance. The relationship between mean airway pressure P(aw) and OPR revealed that the minimal OPR (range, 0.37-0.78) and maximal respiratory compliance coincided at the same P(aw). However, the relationship did depend on oscillation frequency, applied oscillatory pressure, and endotracheal tube resistance, parameters that may change during clinical application of HFOV. When 81 permutations of nominal and extreme respiratory variables were used in the model, the minimum OPR (0.60 +/- 0.23) and maximum compliance coincided in all cases. These model experiments support our hypothesis. The results indicate that the OPR may be a useful index to optimize lung expansion, where lung recruitment is maximal and overdistention minimal. In vivo tests will be needed to reveal the feasibility and reliability of such an index for biomedical and clinical application.

Pressure-Dependent and Frequency Domain Characteristics of the Systemic Arterial System

Pressure–volume relations in different arteries have been observed to be nonlinear. This gives rise to the pressure-dependent behavior of the overall arterial system compliance. Using a nonlinear pressure-dependent compliance arterial system model, we have shown that this compliance varies continuously throughout the cardiac cycle. However, the overall significance of this nonlinear compliance under different vasoactive conditions has been examined only to a limited extent. In addition, its frequency domain characteristics have not been investigated. We studied these aspects under varied physiological conditions. Systemic arterial compliance of the nonlinear compliance model was expressed as C(P) = a · exp(−bP). It is determined, through optimization, from the following equations: Pao(ti) = Qao(ti)Z0 + P(ti) and P(ti + 1) = P(ti) +Δt (Qao(ti) − P(ti)/Rs)/C(Pti), where Pao and Qao are aortic pressure and flow respectively, Z0 is aortic characteristic impedance, and Rs is the peripheral resistance. Results showed that C(P) increased during vasodilation and decreased during vasoconstriction, as expected. Frequency domain analysis of C(P) revealed a rapid and significant reduction in magnitude with increasing frequency, with a dominant presence at low frequencies, and a near absence at high frequencies, and its mean value approximates that of the windkessel. Thus, the systemic arterial system compliance varies continuously throughout the cardiac cycle with its predominant effect occurring at low frequencies. These features are not observed in the classical windkessel model.

The Traveling Shutter Wave analyses non-linear compliance during mechanical ventilation

Mechanical ventilation is an important, often life-saving component of modern intensive care medicine. However, it may further aggravate pulmonary pathology by endinspiratory overdistension of the alveoli or by their endexpiratory collapse. To prevent both the ventilator may be adjusted based on the slope of the pressure-volume curve, named as compliance, which is often determined by a stepwise inflation of the lungs. This maneuver gained no widespread clinical acceptance because of being cumbersome and invasive. Therefore, we developed a modification of the well known interrupter technique - the Traveling Shutter Wave. A wave of short-term (300 ms) occlusions "travels" over the tidal volume range. Differential compliance is calculated by division of volume and pressure differences between two adjacent occlusion maneuvers. The technique is well suited for the clinical setting because the ventilatory pattern does not need to be changed. This manuscript describes the realization of the Traveling Shutter Wave as well as its application in two patients.

Non-linear surface crack analysis by three dimensional boundary element with mixed boundary conditions

In this paper, an effective three dimensional boundary element method with mixed boundary conditions is prescribed for nonlinear surface crack analyses. The line spring model originally proposed by Rice and Levy is used to form the non-linear mixed boundary conditions of the 3D crack problem in a continuum manner, which is then combined with the three dimensional boundary element method to compute the fracture parameter J integral of non-linear surface crack. A predictor–corrector method is presented for the nonlinear compliance matrix of the mixed boundary so that a more accurate result can be reached. Two numerical examples are discussed to show the effectiveness of the method. Especially, the surface crack problem is addressed in which the non-linear region only happens at the mixed boundary condition area, and most of the remaining area is still elastic.

A Methodology for the Calibration of Spherical Indenters

AbstractSpherical indentation with continuous load and depth measurement is a useful technique for characterizing thin film mechanical properties. With this technique, the initial loading is in the elastic range. Therefore the elastic-plastic transition can be observed. However, the calibration of spherical indenters presents special problems. First, the radius of the indenter at the point of contact must be determined, and any deviation from a spherical radius must be evaluated. The shape of the indenter also causes mounting difficulties that can create a relatively large and nonlinear compliance in the testing machine. The calibration of spherical indenters is further complicated, because asperities on the indenter and surface roughness add to the uncertainty in locating the surface of the sample. In addition, spherical indenters are generally made of anisotropic single crystals, and the calculation of their elastic responses must include this anisotropy. To address these issues, a methodology has been developed for the calibration of spherical indenters, whereby indentation experiments are conducted on multiple ceramic materials in the elastic range. The method was used to determine the local radius of synthetic sapphire spherical indenters. The accuracy of this measurement was verified using confocal microscopy. The method was successfully applied to an indenter with a nonlinear machine compliance. Further results involving indentation in the plastic regime are also presented.

冗長けんを持つけん駆動ロボット機構の剛性調節

Tendon-driven mechanisms have been used mainly in articulated-finger hands because of the small size and the light weight. Recently, for the necessity of forcecontrolled robot arms, several researchers developed tendon driven robot arms. In the case, since robot arms are much heavier and longer than robot hand fingers, tendons increase in the length significantly and also must run through very complicated paths. Therefore usual N+1 type or 2N type tendon-driven mechanisms are not enough to move robot arms and a number of redundant tendons are used to divide the total load into each of tendons and reduce the individual burden. For example, due to the gravity force, if the load in the clockwise direction is different significantly from the one in the counter-clockwise direction, we can use different number of tendons for each direction, respectively. There are additional advantages in a redundant tendon mechanism. For example, we can move the robot arm with the other tendons when some tendons have been broken and we can also adjust the mechanical joint impedance using non-linear elasticity of tendons.In this paper, several basic issues on the joint compliance adjustability for a robot arm controlled with redundant tendons are discussed. Namely, local maximum sets of stiffness elements which are adjustable simultaneously, and conditions under which the joint impedance can be adjusted using non-linear compliance tendons are discussed.

Nonlinear and Adaptive Control of Force and Compliance in Manipulators

This paper presents new position-based force and compliance con trol schemes for robot manipulators using nonlinear and adaptive controllers. The proposed controllers are simple and can easily be implemented in the outer feedback loop that encloses the inner Cartesian position control system supplied by the robot manufac turer. In the position-based force control approach, adaptive PID and nonlinear PI controllers are proposed for setpoint tracking in which the controller gains are adjusted on-line as functions of the force error. In the position-based compliance control approach, nonlinear and adaptive PD controllers are developed to achieve a desired behavior at contact, where the controller gains are func tions of the contact force. Dynamic simulation results for a 7-DOF Robotics Research Corporation (RRC) arm are presented to demon strate the efficacy of the adaptive compliance control scheme in executing contact tasks. Experimental results are also presented to illustrate nonlinear force control of the RRC arm. The results demonstrate that the proposed nonlinear PI controller, where the integral gain is a sigmoidal function of the force error, yields supe rior performance compared to afixed-gain PI controller by produc ing a fast force response with a small settling time while preventing oscillations. Finally, the nonlinear PD compliance controller is im plemented on the RRC arm and experimental results are presented. These results demonstrate that the nonlinear PD controller, where the proportional gain is a hyperbolic function of the contact force, exhibits less sensitivity to the surface stiffness than afixed-gain PD controller.

Accurate characterization of machine compliance for simple compression testing

Correction for machine compliance is an important step in analyzing the data obtained in many mechanical testing procedures. The difficulties associated with compliance correction, as they apply to the simple compression mode of testing, are explored in this paper. The commonly employed approach is to extend the procedure suggested in the ASTM standards for testing high modulus, single-filament materials, which implicitly assumes that the machine behaves as a linear spring with a constant compliance factor. It is shown in this paper that this approach results in different values for the machine compliance factor for different materials. The nonuniqueness of the machine compliance factor is attributed to the inherent nonlinearity of the machine compliance, i.e., the nonlinear dependence of the nonsample displacement on the applied load. Through a set of mechanical tests on a range of materials, it has been demonstrated that it is necessary to characterize this nonlinear compliance relationship for the machine to obtain accurate and consistent measurements.