Showing papers on "Stiffness published in 2012"

Independent regulation of tumor cell migration by matrix stiffness and confinement

Abstract: Tumor invasion and metastasis are strongly regulated by biophysical interactions between tumor cells and the extracellular matrix (ECM). While the influence of ECM stiffness on cell migration, adhesion, and contractility has been extensively studied in 2D culture, extension of this concept to 3D cultures that more closely resemble tissue has proven challenging, because perturbations that change matrix stiffness often concurrently change cellular confinement. This coupling is particularly problematic given that matrix-imposed steric barriers can regulate invasion speed independent of mechanics. Here we introduce a matrix platform based on microfabrication of channels of defined wall stiffness and geometry that allows independent variation of ECM stiffness and channel width. For a given ECM stiffness, cells confined to narrow channels surprisingly migrate faster than cells in wide channels or on unconstrained 2D surfaces, which we attribute to increased polarization of cell-ECM traction forces. Confinement also enables cells to migrate increasingly rapidly as ECM stiffness rises, in contrast with the biphasic relationship observed on unconfined ECMs. Inhibition of nonmuscle myosin II dissipates this traction polarization and renders the relationship between migration speed and ECM stiffness comparatively insensitive to matrix confinement. We test these hypotheses in silico by devising a multiscale mathematical model that relates cellular force generation to ECM stiffness and geometry, which we show is capable of recapitulating key experimental trends. These studies represent a paradigm for investigating matrix regulation of invasion and demonstrate that matrix confinement alters the relationship between cell migration speed and ECM stiffness.

Elastin in large artery stiffness and hypertension

Abstract: Large artery stiffness, as measured by pulse wave velocity, is correlated with high blood pressure and may be a causative factor in essential hypertension. The extracellular matrix components, specifically the mix of elastin and collagen in the vessel wall, determine the passive mechanical properties of the large arteries. Elastin is organized into elastic fibers in the wall during arterial development in a complex process that requires spatial and temporal coordination of numerous proteins. The elastic fibers last the lifetime of the organism but are subject to proteolytic degradation and chemical alterations that change their mechanical properties. This review discusses how alterations in the amount, assembly, organization, or chemical properties of the elastic fibers affect arterial stiffness and blood pressure. Strategies for encouraging or reversing alterations to the elastic fibers are addressed. Methods for determining the efficacy of these strategies, by measuring elastin amounts and arterial stiffness, are summarized. Therapies that have a direct effect on arterial stiffness through alterations to the elastic fibers in the wall may be an effective treatment for essential hypertension.

Lateral Stability Control of In-Wheel-Motor-Driven Electric Vehicles Based on Sideslip Angle Estimation Using Lateral Tire Force Sensors

Abstract: This paper presents a method for using lateral tire force sensors to estimate vehicle sideslip angle and to improve vehicle stability of in-wheel-motor-driven electric vehicles (IWM-EVs) Considering that the vehicle motion is governed by tire forces, lateral tire force measurements give practical benefits in estimation and motion control To estimate the vehicle sideslip angle, a state observer derived from the extended-Kalman-filtering (EKF) method is proposed and evaluated through field tests on an experimental IWM-EV Experimental results show the ability of a proposed observer to provide accurate estimation Moreover, using the estimated sideslip angle and tire cornering stiffness, the vehicle stability control system, making best use of the advantages of IMW-EVs with a steer-by-wire system, is proposed Computer simulation using Matlab/Simulink-Carsim and experiments are carried out to demonstrate the effectiveness of the proposed stability control system Practical application of lateral tire force sensors to vehicle control systems is discussed for future personal electric vehicles

Static, free vibration, and buckling analysis of laminated composite Reissner-Mindlin plates using NURBS-based isogeometric approach

Abstract: SUMMARY This paper presents a novel numerical procedure based on the framework of isogeometric analysis for static, free vibration, and buckling analysis of laminated composite plates using the first-order shear deformation theory. The isogeometric approach utilizes non-uniform rational B-splines to implement for the quadratic, cubic, and quartic elements. Shear locking problem still exists in the stiffness formulation, and hence, it can be significantly alleviated by a stabilization technique. Several numerical examples are presented to show the performance of the method, and the results obtained are compared with other available ones. Copyright © 2012 John Wiley & Sons, Ltd.

Fabrication of Hydrogels with Steep Stiffness Gradients for Studying Cell Mechanical Response

Abstract: Many fundamental cell processes, such as angiogenesis, neurogenesis and cancer metastasis, are thought to be modulated by extracellular matrix stiffness. Thus, the availability of matrix substrates having well-defined stiffness profiles can be of great importance in biophysical studies of cell-substrate interaction. Here, we present a method to fabricate biocompatible hydrogels with a well defined and linear stiffness gradient. This method, involving the photopolymerization of films by progressively uncovering an acrylamide/bis-acrylamide solution initially covered with an opaque mask, can be easily implemented with common lab equipment. It produces linear stiffness gradients of at least 115 kPa/mm, extending from ∼1 kPa to 240 kPa (in units of Young's modulus). Hydrogels with less steep gradients and narrower stiffness ranges can easily be produced. The hydrogels can be covalently functionalized with uniform coatings of proteins that promote cell adhesion. Cell spreading on these hydrogels linearly correlates with hydrogel stiffness, indicating that this technique effectively modifies the mechanical environment of living cells. This technique provides a simple approach that produces steeper gradients, wider rigidity ranges, and more accurate profiles than current methods.

Extended graphynes: simple scaling laws for stiffness, strength and fracture

Abstract: The mono-atomistic structure and chemical stability of graphene provides a promising platform to design a host of novel graphene-like materials. Using full atomistic first-principles based ReaxFF molecular dynamics, here we perform a systematic comparative study of the stability, structural and mechanical properties of graphynes – a variation of the sp2 carbon motif wherein the characteristic hexagons of graphene are linked by sp1 acetylene (single- and triple-bond) carbyne-like chains. The introduction of acetylene links introduces an effective penalty in terms of stability, elastic modulus (i.e., stiffness), and failure strength, which can be predicted as a function of acetylene repeats, or, equivalently, lattice spacing. We quantify the mechanical properties of experimental accessible graphdiyne, with a modulus on the order of 470 to 580 GPa and a ultimate strength on the order of 36 GPa to 46 GPa (direction dependent). We derive general scaling laws for the cumulative effects of additional acetylene repeats, formulated through a simple discrete spring-network framework, allowing extrapolation of mechanical performance to highly extended graphyne structures. Onset of local tensile buckling results in a transitional regime characterized by a severe reduction of strength (ultimate stress), providing a new basis for scaling extended structures. Simple fracture simulations support the scaling functions, while uncovering a “two-tier” failure mode for extended graphynes, wherein structural realignment facilitates stress transfer beyond initial failure. Finally, the specific modulus and strength (normalized by areal density) is found to be near-constant, suggesting applications for light-weight, yet structurally robust molecular components.

Bond characteristics between ultra high modulus CFRP laminates and steel

Abstract: The use of high modulus CFRP laminates in strengthening steel members has the advantage of increasing the strength and stiffness of such members. In this paper, the bond characteristics between ultra high modulus (UHM) CFRP laminates with a modulus of 460 GPa and steel were studied. A series of experiments with double strap steel joints bonded with UHM CFRP laminates were conducted. Experimental results presented in this paper include failure modes, bond strength, effective bond length, CFRP strain distribution, adhesive layer shear stress distribution and bond slip relationship. Comparison was made with previous research on CFRP sheet–steel and normal modulus CFRP laminate–steel systems and different aspects of bond characteristics were discussed. Theoretical models were employed for the prediction of the specimen bond strength and effective bond length, and their applicability for UHM CFRP–steel joints was verified by comparisons with experimental results. Nonlinear finite element analysis was carried out to simulate the experimental specimens. The FEA results agreed well with those from experiments.

Design of a variable stiffness flexible manipulator with composite granular jamming and membrane coupling

Abstract: Robotic manipulators for minimally invasive surgeries have traditionally been rigid, with a steerable end effector. While the rigidity of manipulators improve precision and controllability, it limits reachability and dexterity in constrained environments. Soft manipulators with controllable stiffness on the other hand, can be deployed in single port or natural orifice surgical applications to reach a wide range of areas inside the body, while being able to passively adapt to uncertain external forces, adapt the stiffness distribution to suit the kinematic and dynamic requirements of the task, and provide flexibility for configuration control. Here, we present the design of a snake-like laboratory made soft robot manipulator of 20 mm in average diameter, which can actuate, soften, or stiffen joints independently along the length of the manipulator by combining granular jamming with McKibben actuators. It presents a comprehensive study on the relative contributions of the granule size, material type, and membrane coupling on the range, profile, and variability of stiffness.

Coordinate Measuring Machine

Abstract: The invention relates to a coordinate measurement machine for determination of at least one space coordinate of a measurement point on an measured object, with a first frame element (11), a second frame element (4), a linear drive unit (7) with a motor for moving the second frame element (4) relative to the first frame element (11) in a direction of movement and a position measurement instrument, for determining a drive position of the second frame element relative to the first frame element. Therein the drive unit has limited stiffness and dynamic deflections on movement. The machine comprises a mechanical coupler (3) from the drive unit (12) to the second frame element (4), which coupler (3) comprises a first part (3A) fixed to the drive unit (12) and a second part (3B) fixed to the second frame element (4), which parts (3A,3B) are movable relative to each other by an active compensation actuator (5). The active compensation actuator (5) is built in such a way to shift the second frame element (4) against the drive unit (12) to introduce a counter-displacement in such a way that the dynamic deflections are at least partially compensated. Fig. 2a

Normal Contact Stiffness of Elastic Solids with Fractal Rough Surfaces

Abstract: Using the boundary element method, we calculate the normal interfacial stiffness and constriction resistance of two elastic bodies with randomly rough surfaces and varying fractal dimensions. The contact stiffness as a function of the applied normal force can be approximated by a power law, with an exponent varying from 0.51 to 0.77 for fractal dimensions varying from 2 to 3.

Mechanical property evaluation of single-walled carbon nanotubes by finite element modeling

Abstract: Computational simulation for predicting mechanical properties of carbon nanotubes (CNTs) has been adopted as a powerful tool relative to the experimental difficulty. Based on molecular mechanics, an improved 3D finite element (FE) model for armchair, zigzag and chiral single-walled carbon nanotubes (SWNTs) has been developed. The bending stiffness of the graphene layer has been considered. The potentials associated with the atomic interactions within a SWNT were evaluated by the strain energies of beam elements which serve as structural substitutions of covalent bonds. The out-of-plane deformation of the bonds was distinguished from the in-plane deformation by considering an elliptical cross-section for the beam elements. The elastic stiffness of graphene has been studied and the rolling energy per atom has been calculated through the analysis of rolling a graphene sheet into a SWNT to validate the proposed FE model. The effects of diameters and helicity on Young’s modulus and the shear modulus of SWNTs were investigated. The simulation results from this work are comparable to both experimental tests and theoretical studies from the literatures.

Depth-Dependent Transverse Shear Properties of the Human Corneal Stroma

Abstract: Thorough characterization of the mechanical properties of connective tissue, including the cornea, presents significant theoretical and experimental challenges. To date, mechanical testing of the cornea has been almost exclusively focused on estimating the tensile modulus of the stroma using techniques such as strip tensile tests or cornea pressure-inflation tests.1–4 However, even in the most simple of material models there are at a minimum two elastic constants that must be measured to characterize the three-dimensional elastic behavior of the material. This most simple case is called isotropic elasticity5 and occurs when the material properties under investigation exhibit no dependence on direction during testing. In this case, the material is fully characterized by the Young's modulus and the shear modulus. The shear modulus naturally measures the resistance of the tissue to shearing strains. In fact, the microstructure of the corneal stroma suggests that its elasticity cannot be isotropic. The parallel arrays of collagen fibrils within each lamella and the layering of lamellae one on another imply that the transverse (anterior-posterior) properties of the tissue will be different from the in-plane properties. To address this anisotropy and other considerations, increasingly complex elasticity models have been introduced with the goal of achieving greater fidelity to the full three-dimensional behavior of the tissue.6–8 More complex models always have more than two intrinsic elastic constants that need to be measured. When such models are extended to nonlinear behavior, yet more constants must necessarily be introduced (Petsche SJ, et al., manuscript submitted, 2012).6,8 Experimental measurement of elastic constants must be interpreted against an assumed elasticity model (i.e., material symmetry). Transversely isotropic linear elasticity5 is the simplest possible model that can reasonably be applied to the corneal stroma. Materials exhibiting transverse isotropy have a single plane of material isotropy (the corneal tangent plane) and properties in this plane will be different from properties measured orthogonally (through the corneal thickness). In this case, characterization of the material elasticity requires the measurement of five independent elastic constants: the in-plane Young's modulus (related to the tensile modulus) and transverse Young's modulus, the in-plane and transverse Poisson's ratios, and the transverse shear modulus, denoted G.5 To appreciate the role of the transverse shear modulus, consider the anterior and posterior surfaces of a circular stromal button subjected to relative torsional twisting about an axis perpendicular to the surfaces (see Fig. 4). The tissue will become deformed in a state of pure transverse shear strain and the resistance of the tissue will be dependent only on the transverse shear modulus G. Experimental measurement of the shear properties of human corneas are missing from the extant literature. A thesis by Nickerson9 discusses the use of torsional rheometry to measure shear properties of porcine cornea. Standard inflation and strip testing1–4 do not introduce shearing deformations and these tests therefore give no information about shear stiffness. Figure 4. Typical stress/strain curve from a final load cycle used for calculating the magnitude of the complex shear modulus. The inset cartoon shows the applied torque and resulting shear strain (γ) on a cornea button, which is maximum at the perimeter. ... Because the corneal stroma makes up 90% of the tissue's thickness and contains almost all the cornea's collagen and proteoglycan content, it is the crucial layer for explaining corneal stiffness. The stroma consists of 200 to 500 sheet-like lamellae, each made up of collagen fibrils maintained at quasi-uniform spacing for transparency by the glycosaminoglycan (GAG) chains of the stromal proteoglycans. Evidence of lamellar interweaving that varies with depth through the cornea is provided by imaging that uses polarized light.10 The interweaving appears maximal at the anterior surface and significantly reduces toward the posterior. Recent images by Jester et al.11,12 using second harmonic generated imaging confirm this assessment. Figure 1 shows the central part of a full human cornea cross-section created from many second harmonic generated images and in which distinct interweaving in the anterior third may be discerned by the through-thickness trajectory of many of the lamellae. It is also noted that scanning electron microscopy and transmission electron microscopy images show that lamellae become wider and thicker toward the posterior of the stroma.13 X-ray scattering studies have demonstrated that the collagen associated with preferred directions measured in the limbal plane also varies with depth through the cornea.14 After using a femtosecond laser to cut the stroma into thirds through the thickness, Abahussin et al.14 showed that lamellae exhibit preferred angular distributions in the posterior third but transition toward a more uniform distribution in the anterior third. Figure 1. Cross-section of a human cornea from second harmonic generated imaging showing the interweaving of lamellae in the anterior third. The complex patterns of the three-dimensional collagen architecture within the stroma can be expected to affect and contribute to the elasticity of the tissue regionally. In particular, the variation of microstructure through the thickness suggests that the mechanical properties of the stroma may have a nonconstant profile through the thickness. Depth dependence of mechanical properties in the stroma, including transverse shear stiffness, has not been considered heretofore and may be important for the biomechanics of the cornea. We hypothesize that the pronounced interweaving of lamellae in the anterior third compared with the central and posterior thirds will provide the anterior third with a relatively larger transverse shear modulus because the collagen in vertically descending lamellae may be engaged during the shearing deformations. This will not be the case in noninterweaving regions. In this work we report direct measurement of the transverse shear modulus of the human corneal stroma through the depth using torsional rheometry.

Analysis of Sandwich Beams With a Compliant Core and With In-Plane Rigidity—Extended High-Order Sandwich Panel Theory Versus Elasticity

Abstract: A new one-dimensional high-order theory for orthotropic elastic sandwich beams is formulated. This new theory is an extension of the high-order sandwich panel theory (HSAPT) and includes the in-plane rigidity of the core. In this theory, in which the compressibility of the soft core in the transverse direction is also considered, the displacement field of the core has the same functional structure as in the high-order sandwich panel theory. Hence, the transverse displacement in the core is of second order in the transverse coordinate and the in-plane displacements are of third order in the transverse coordinate. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases the other available sandwich computational models cannot predict correctly the stress fields involved. Thus, this theory, referred to as the “extended high-order sandwich panel theory” (EHSAPT), can be used with any combinations of core and face sheets and not only the very “soft” cores that the other theories demand. The theory is derived so that all core=face sheet displacement continuity conditions are fulfilled. The governing equations as well as the boundary conditions are derived via a variational principle. The solution procedure is outlined and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model without shear, the first-order shear, and the earlier HSAPT are also presented for completeness. The comparison among these numerical results shows that the solution from the current theory is very close to that of the elasticity in terms of both the displacements and stress or strains, especially the shear stress distributions in the core for a wide range of cores. Finally, it should be noted that the theory is formulated for sandwich panels with a generally asymmetric geometric layout. [DOI: 10.1115/1.4005550]

Parameters controlling stiffness and strength of artificially cemented soils

Abstract: The treatment of soils with cement is an attractive technique when a project requires improvement of the local soil for the construction of subgrades for rail tracks, for roads, as a support layer for shallow foundations, and to prevent sand liquefaction. This paper advances understanding of the key parameters for the control of strength and stiffness of cemented soils by testing two soils with different gradings and quantifying the influence of porosity/cement ratio on both initial shear modulus (G0) and unconfined compressive strength (qu). It is shown that the porosity/cement ratio is an appropriate parameter to assess both the initial stiffness and the unconfined compressive strength of the soil–cement mixtures studied. Each soil matrix has a unique relationship for G0/qu against adjusted porosity/cement ratio, linking initial stiffness and strength.

Model-Based Estimation of Knee Stiffness

Abstract: During natural locomotion, the stiffness of the human knee is modulated continuously and subconsciously according to the demands of activity and terrain. Given modern actuator technology, powered transfemoral prostheses could theoretically provide a similar degree of sophistication and function. However, experimentally quantifying knee stiffness modulation during natural gait is challenging. Alternatively, joint stiffness could be estimated in a less disruptive manner using electromyography (EMG) combined with kinetic and kinematic measurements to estimate muscle force, together with models that relate muscle force to stiffness. Here we present the first step in that process, where we develop such an approach and evaluate it in isometric conditions, where experimental measurements are more feasible. Our EMG-guided modeling approach allows us to consider conditions with antagonistic muscle activation, a phenomenon commonly observed in physiological gait. Our validation shows that model-based estimates of knee joint stiffness coincide well with experimental data obtained using conventional perturbation techniques. We conclude that knee stiffness can be accurately estimated in isometric conditions without applying perturbations, which presents an important step toward our ultimate goal of quantifying knee stiffness during gait.

On the design and characterisation of low-stiffness auxetic yarns and fabrics:

Abstract: An auxetic material is one which exhibits a negative Poisson's ratio; it expands laterally when stretched longitudinally and contracts laterally when compressed longitudinally. The helical auxetic yarn is a novel fibre structure with a diverse range of potential applications. The unusual mechanical properties of the yarn can be determined by particular combinations of geometry and component material properties. This paper reports on the development of low-stiffness auxetic yarns and fabrics which offer a range of applications such as medical devices, particularly bandages, compression hosiery and support garments and fashion apparel. The mechanical performance of the yarns and fabrics is elucidated, with emphasis on the ability to exploit significant changes through a prescribed strain range. A yarn Poisson's ratio as low as −1.5 is demonstrated, and fabrics with in-plane and out-of-plane negative Poisson's ratios are illustrated. Stiffness is shown to be highly dependent upon yarn geometry.

Modeling of Concrete for Nonlinear Analysis using Finite Element Code ABAQUS

Abstract: Concrete is the main constituent material in many structures. The behavior of concrete is nonlinear and complex. Increasing use of computer based methods for designing and simulation have also increased the urge for the exact solution of the problems. This leads to difficulties in simulation and modeling of concrete structures. A good approach is to use the general purpose finite element software ABAQUS. In this paper a 3D model of a concrete cube is prepared using smeared crack model and concrete damage plasticity approach. The validation of the model to the desired behavior under monotonic loading is then discussed. Keywords Finite element, ABAQUS, smeared cracking, concrete damage plasticity, tension stiffening. 1. ultimate INTRODUCTION Since 1970, analyses of reinforced concrete structures using finite element method, have witnessed a remarkable advancement. Many researchers have made valuable contributions in understanding the behavior of concrete and have developed sophisticated methods of analysis. These achievements are well documented and available in various reports and technical papers but still there are many areas in which much remains to be understood and researched. The past decade with the advancement in computing techniques and the computational capabilities of the high end computers has led to a better study of the behavior of concrete. However the complex behavior of concrete sets some limitations in implementing FEM. The complexity is mainly due to non-linear stress-strain relation of the concrete under multi-axial stress conditions, strain softening and anisotropic stiffness reduction, progressive cracking caused by tensile stresses and strains, bond between concrete and reinforcement, aggregation interlocks and dowel action of reinforcement, time dependant behavior as creep and shrinkage [1]. Several researchers have documented about nonlinear analysis of reinforced concrete and prestressed concrete structures. For nonlinear analysis many commercial software are available, such as ANSYS, ABAQUS, NASTARAN, and ADINA. All these softwares are not tailor made applications which can work automatically on just feeding few data and the requirements. An acceptable analysis of any structure as a whole or a part there in, using Finite element software, and the correctness of it totally depends on the input values, especially the material properties used. However when one is working with concrete a sound technical background is required to use them in a proper manner and get the desired results. Concrete used in common engineering structures, basically is a composite material, produced using cement, aggregate and water. Sometimes, as per need some chemicals and mineral admixtures are also added. Experimental tests show that concrete behaves in a highly nonlinear manner in uniaxial compression. Figure.1 shows a typical stress-strain relationship subjected to uniaxial compression. This stress-strain curve is linearly elastic up to 30% of the maximum compressive strength. Above this point tie curve increases gradually up to about 70-90% of the maximum compressive strength. Eventually it reaches the pick value which is the maximum compressive strength

Generating realistic laminate fiber angle distributions for optimal variable stiffness laminates

Abstract: The advent of advanced fiber placement technology has made it possible, through the use of fiber steering, to exploit the anisotropic properties of composite materials to a larger extent than was previously possible. Spatial variation of stiffness can be induced by steering composite fibers in curvilinear paths to give beneficial load and stiffness distribution patterns. Buckling of composite panels is one area where fiber steering has been proven to be very effective. Fiber angles and predefined fiber angle variations are used in most of the research on fiber steered composites reported in the literature, however, from an optimization point of view it is attractive to design such variable stiffness (VS) structures in terms of lamination parameters (LPs). This results in a two-step design approach. In the first step a VS composite is designed in terms of LPs, and in the second step the LPs are converted into fiber angle distributions for each layer in the laminate. A methodology is proposed to convert a known LP distribution for a VS composite laminate into a realistic design in terms of fiber angles, with minimum loss of structural performance, whilst satisfying a constraint on in-plane fiber angle curvature. The proposed conversion process is formulated as an optimization problem and can be used for any number of equi-thickness plies. The methodology was tested by converting a known optimal LP design for a sample structure, a square plate under bi-axial compression into a fiber angle design. The effect of the in-plane curvature constraint, the number of layers in the laminate, and the choice of objective function for the conversion process were studied for a balanced symmetric lay-up.

Design and Control of a Variable Stiffness Actuator Based on Adjustable Moment Arm

Abstract: For tasks that require robot-environment interaction, stiffness control is important to ensure stable contact motion and collision safety. The variable stiffness approach has been used to address this type of control. We propose a hybrid variable stiffness actuator (HVSA), which is a variable stiffness unit design. The proposed HVSA is composed of a hybrid control module based on an adjustable moment-arm mechanism, and a drive module with two motors. By controlling the relative motion of gears in the hybrid control module, position and stiffness of a joint can be simultaneously controlled. The HVSA provides a wide range of joint stiffness due to the nonlinearity provided by the adjustable moment arm. Furthermore, the rigid mode, which behaves as a conventional stiff joint, can be implemented to improve positioning accuracy when a robot handles a heavy object. In this paper, the mechanical design features and related analysis are explained. We show that the HVSA can provide a wide range of stiffness and rapid responses according to changes in the stiffness of a joint under varying loads by experiments. The effectiveness of the rigid mode is verified by some experiments on position tracking under high-load conditions.