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The development of a dynamics simulator with identification capabilities will contribute to the trafficability, maneuverability and terrainability of these rovers, hence enhancing their adaptability and autonomy. These algorithms should enable the rover to investigate unknown environment and difficult terrains. The successful candidate will be joining our robotics research group, which includes staff and other PhD students with expertise in mobile robots ground, and aerial , control systems, soft robotics, medical robotics, image processing, IoT and communications, and human-robot interaction.

Moreover, you will be part of the School of Engineering and Informatics with research groups in areas such as sensors, dynamics and control, image processing, data science, evolutionary and adaptive systems, and software systems amongst others. Experience in control systems and systems modelling is essential, and experience in designing and implementing mechatronic systems is desirable. In the 'Finance information' section of the application form clearly state you are applying for the " PhD Studentship: Development of a dynamics simulator for an exploration robot.

Application deadline: 15 July GMT the deadline has now expired. Open navigation menu Close navigation menu. International students Meet us at an event Information by country Visiting and exchange University preparation courses International Summer School English language courses Visas and immigration Brexit information. In this process, another compressive shear failure may occur due to the develop- ment of lateral plastic flow. If this happens, then the penetration pressure p will increase dramatically.

As shown in the Table, penetration resistance under a constant penetration depth of the plate increases with increasing age of sintering. The fundamental failure pattern of the sintered snow can be explained in a similar way to that already mentioned in Figure 1. After that, the failure pattern shows a complex behaviour as the snow changes its rheology and goes from an elasto-plastic to a rigid-plastic material as the penetration depth reaches some value. Yong et al. In their tests they used a shear box and established that the mechanism of shear in snow can be explained by consideration of the mutual adhesion and the mutual frictional forces that exist between the individual snow particles.

They also hypothesised that the Coulomb frictional relationship that connects normal stress and shear resistance could be used for artificially crushed snow particles but then the rule would not apply to sintered snows because the snow particles are bonded tightly due to sintering action. Now, let us consider a test method for prediction of snow shear resistance based on the idea of use of a vane cone.

Photo 1. The test procedure involves making a sample by filling up a snow box. The vane or a vane cone as shown in Photo 1. After measuring the relationship between the penetration force F and the penetration depth, another relationship between the torque T and the rotational deformation X can be determined. These factors can be measured as the vane or vane cone rotates and shears the snow sample.

The test conditions are set at a peripheral speed of 1. Vane cone test apparatus.

## Land Locomotion on the Surface of Planets

The calculated results can then be developed by use of the following equations. As an example, Figure 1. This data confirms that the Mohr-Coulomb failure criterion operates for the whole range of initial density, threshold density and final density of the fresh snow and for sintered snow samples. These results arise because the soil samples are tested in a state of normal compression as a consequence of the collapse of the structure of snow particles during the cone penetration.

Next let us consider the shear deformation characteristics of wet snow. The experimental study showed the existence of an initial elasto-plastic behaviour. Portable vane cone apparatus. In this case, the slip line in the snow that developed during the vane cone shear test developed along a logarithmic spiral line.

This spiral failure line is clearly visible in Photo 1. The shear stress and deformation characteristics for the same wet snow were measured using the same portable shear test apparatus as shown in Figure 1. In this case, the study showed that the material behaves, phenomenologically, as an elasto-plastic material.

Characteristic results for the tests are shown in Figure 1. The angle of inter- nal friction measured in this ring shear test is generally larger than that derived from the vane cone shear test for remolded snow samples. We have also reviewed some traditional matters of soil mechanics as a precursor to apply- ing them to machinery-terrain interaction problems.

Relationship between shear stress and shear deformation. Having studied this chapter, the reader should be able to describe the mechanical pro- cesses typically employed to, objectively and quantitatively, characterise specific terrains. The reader should also be able to appreciate and comment upon the degree to which the various terrain metrics can be used as inputs to engineering prediction models. The Japanese Geotechnical Society Soil Testing Methods.

In Japanese. Yamaguchi, H. Soil Mechanics. Gihoudou Press. Akai, K. Asakura Press. Oda, M. Tsuchi-to-Kiso, Vol. Toriumi, I. Geotechnical Engineering. Morikita Press. Bearing Capacity and Depression of Soil. Sankaido Press. Advanced Soil Mechanics. Terzaghi, K. Soil Mechanics in Engineering Practice. Handbook of Soil Engineering. Bekker, M. Off-the-Road Engineering. The University of Michigan Press. Sugiyama, N.

Several Problems between Construction Machinery and Soil. Kashima Press. Taylor, D. Fundamentals of Soil Mechanics. Wong, J. Terramechanics and Off-road Vehicles. Reece, A. Principles of Soil-Vehicle Mechanics. Instn Mech. Leonards, G. Foundation Engineering. McGraw-Hill and Kogakusha. Kondo, H. Trial Production of Dynamic Direct Shear. Terramechanics, 6, 98— Bjerrum, L. Richardson, A.

In-situ Determination of Anisotropy of a Soft Clay. ASCE, Vol. Shibata, T. Study on Vane Shear Strength of Clay. JSCE, No.

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Muro, T. Yonezu, H. Tsuchi-to-kiso, Vol. Umeda, T. The Japanese Geotechnical Society. Wechselbeziehungen zwischen fahrzeuglaufwerk und boden beim fahren auf unbefestigter fahrbahn. Grundlagen der Landtechnik, Heft 13, 21— Tanaka, T. Journal of Agricultural Machinery, 27, 3, — Introduction to Terrain-Vehicle Systems. Golob, T. Development of a Terrain Strength Measuring System.

Journal of Terramechanics, 18, 2, — Journal of Terramechanics, 17, 1, 13— Desai, C. Mogami, T. Gihoudo Press. Skempton, A. Soils pp. Chapter 10 of Building Materials. Amsterdam: North Holland. Muromachi, T. Report on RailRoad Engineering, No. Hata, S. Yong, R. Journal of Terramechanics, Vol. Cohron, G. A New Trafficability Prediction System. Kashima Press, In Japanese. Tire Society Considerations on Tire for Construction Machinery.

Komatsu Technical Report, Vol. Yoshida, Z. Japanese Construction Machinery Association New Handbook of Snow Prevention Engineering. Kinoshita, S. Hardness of Snow Covered Terrain. Tanuma Snow and Construction Works pp. Journal of the Japanese Society of Snow and Ice. Compaction Properties of Wet Snow. Compression of Snow at Constant Speed. Mechanical properties 1 , Vol. Kawada, K. Physics, Vol. Performance of Snow in Confined Compression. Snow Mechanics — Machine Snow Interaction. Shallow Snow Performance of Tracked Vehicle. Soils And Foundations, Vol. Suppose then, that the initial weight of a moist soil sample plus container was measured to be Also, suppose that the total weight of the sample plus container — after oven drying for a period of 24 hours — was If the self weight of the container was The dimensions of the rectangular plate were: length 50 cm, width 20 cm and depth 5 cm.

Using this data, calculate the static amount of sinkage s0 of a bulldozer of track length 1. Calculate the cohesion c of the clay, neglecting any adhesion between the rod of the vane and the clay. The terrain-track system constants as given in Eq. After joining both the vessels, the container was shaken until the temperature of the hot water assumed a constant value.

Assume a water equivalent of g for vessel A and g for vessel B. The mass of the falling weight is m, and the base area of the disc is S and its mass is M. Assuming that the total energy, when the falling weight falls n times from a constant height h equals the energy of penetration of the disc into the snow covered terrain, develop an equation to calculate the hardness H of the snow covered terrain.

Chapter 2. For the compaction of subgrade materials, asphalt pavement materials and roller compacted concrete, several forms of compaction machines equipped with single steel drum rollers and tandem rollers are in everyday use in civil engineering — for example the macadam and steam rollers of old. Al-Hussaini et al. These researchers concluded that a network of stress lines corresponding to those of an equivalent normal and shear stress developed within the ground under a rigid wheel.

In other research work, Ito et al. They showed that the distribution of contact pressure could be divided into two parts; one is a compression zone which develops as a result of the thrust of wheel and the other is a bulldozing zone which produces increased land locomotion resistance with increasing vehicle sinkage. Relative to the distribution of contact pressure of a rigid wheel running on a weak terrain, Wong et al. They also showed that the distribution of shear resistance could be calculated from the slip ratio and that the normal stress distribution could be assumed to be symmetrical around the maximum-value application point.

They also developed a method for predicting the continuous behaviour of a rigid wheel by use of the principle of energy conservation and equilibrium. They also attempted to analyse the stress response under a rigid running wheel using the finite element method FEM. However, despite this research there are many unresolved problems which still need to be addressed in the future. These arise because it is still difficult to estimate the stress—strain relationship under a rigid wheel from the results of the plate loading test. The trafficability of a rigid wheel running on a shallow snow covered terrain may be calculated from the total of the compaction energy — which is necessary to collapse the unremolded fresh snow under the roller — and the slippage energy which is required to give thrust to the wheel supplemented by the local melting of snow due to an excessive slip of wheel.

Using this broad method, Harrison [6] developed a relationship between the effective tractive effort, amount of sinkage and the compaction resistance of a rigid wheel running over snow materials. In the following sections of this Chapter, we will consider the various modes of behaviour of a rigid wheel running on weak ground during driving or braking action.

We will then investigate the fundamental mechanics of land locomotion in relation to driving or braking force, thrust or drag, land locomotion resistance, effective driving or braking force, amount of sinkage and distribution of contact pressure.

The ground bearing capacity of a rigid wheel at rest Qw can be calculated by use of the following formula for bearing capacity [7]. The formula assumes that the contact shape of the roller can be modelled as a rectangular plate of wheel width B and contact length L. The factors may be determined from the cohesion and the angle of internal friction of the soil. A zero summation is required since no net torque on the wheel may be present. Rigid Wheel Systems The general situation is as shown in Figure 2.

For the amount of sinkage s0 of the bottom-dead-center of the wheel, the amount of sinkage z at the arbitrary point X can be calculated from geometry to be:. This interface tangential force develops by virtue of a relative motion i. In this situation:. The numerical value of these factors depends on the material that comprises the surface of the wheel, its surface roughness and the soil properties. The slippage function f j for a loose sandy soil and a weak clayey soil was given by Janosi-Hanamoto [10] as follows:. For a hard compacted sandy soil and for a hard terrain, Bekker [11] and Kacigin [12] have proposed another function.

Figure 2.

As a further comment, it is noted that a horizontal force does not occur on a static rigid wheel, because the horizontal component of the resultant stress p is symmetrical on both the left and right hand sides. It is defined as positive for a counter clockwise direction. The amount of slippage jd is positive for the whole range of the contact part AE. Typically, two slip lines emerge from the point N on the contact interface between the rigid wheel and the terrain. When the slip line is in the region of the logarithmic spiral portion, the slip zone is referred to as the transient state zone.

Similarly, the slip zone surrounding the straight slip line is called the passive state zone. As shown in Figure 2. Within both slipping soil masses, there are a lot of conjugate slip lines s1 and s2 which introduce the occurrence of plastic flow within the soil. In addition, it should be noticed that the circumferential surface of the wheel is coincident directly with the slip line s1 at the bottom-dead-center M. In relation to this, Wong et al. With reference to Figure 2. The resultant velocity vectors of all the soil particles on the contact part of the rigid wheel are always rotating around the instantaneous center I.

The position of the center I is located between the axis O and the bottom-dead-center M for the driving state and the length OI can be given as follows, using the symbols of Figure 2. This relationship between position of I and slip ratio id has been validated experimentally by Wong [15]. Suppose that we now consider the locus of an arbitrary point on the peripheral surface of a rigid wheel when the wheel is running during driving action.

Next, consider the problem of tracking the locus of an arbitrary point on the peripheral surface of a rigid wheel when the wheel is rolling at a slip ratio id during driving action. Moving locus of a soil particle under rigid wheel during driving action [17] where x represents horizontal displacement and z represents vertical displacement. From Figure 2. The moving locus of the soil particle show an elliptical path for each slip ratio.

Each soil particle moves forward and slightly upward during the progression of the wheel. It goes downward to a minimum position and then returns upward to a final position during the procession of the wheel. With increasing slip ratio id , the vertical distance of the final position of the soil particle i. The three operating regimes or modes of action are as shown in Figure 2. The effective driving force Td balances with the horizontal ground reaction Bd which acts reversely to the moving direction of the wheel.

The axle load W balances with the vertical ground reaction N. The direction of the resultant ground reaction, which is composed of N and Bd , does not go through the wheel axle, but deviates a little bit to the front-side of the wheel axle. The position of the point of application of the ground reaction on the peripheral surface of the rigid wheel has a horizontal position equal to the amount of eccentricity ed and is located at a vertical distance from the axle of ld. In this case, the effective driving force Td and the horizontal ground reaction Bd decrease with an increase in driving torque Qd.

When Td and Bd become zero, only the vertical ground reaction acts on the wheel.

## Muro & O'Brien Terramechanics - Land Locomotion Mechanics

At this time, the force and moment balances and the horizontal amount of eccentricity ed can be established as follows:. Sufficient effective tractive effort to be able to draw another wheel say will develop when the driving force can overcome the land locomotion resistance of the wheel. The direction of the horizontal ground reaction Bd is coincident with the moving direction of the wheel.

The direction of the resultant ground reaction composed of N and Bd deviates to a large extent to the front-side of the wheel axle. The force and moment balances and the horizontal amount of eccentricity ed in this case can be established as follows:. In interpreting this expression, it can be seen firstly that the actual horizontal ground reaction Bd and its direction depends on the slip ratio id and secondly that Bd equals the difference between the driving force and the land locomotion resistance. The rolling locus of an arbitrary point X on the peripheral surface of the rigid wheel can be determined using Eq.

Component of a rolling locus in the direction of applied stress during driving action. The Eq. The apparent effective driving force Td0 as shown in the above equation can be expressed as a difference between thrust Thd and compaction resistance Rcd in the following equation:. In this case, the amount of slip sinkage ss is not considered. It acts in the moving direction of the rigid wheel. This force acts reversely to the moving direction of the wheel and manifests as the land locomotion resistance associated with the static amount of sinkage s0. As shown in the diagram, the point Y on the peripheral surface of the rigid wheel is determined when the direction of the resultant applied stress p becomes vertical.

Hence it can be seen that the horizontal ground reaction acting on the section AY of the contact part to the terrain develops as the land locomotion resistance, whilst the horizontal ground reaction acting on the section YE develops as the thrust of the rigid wheel. These values have to be determined experimentally for a given steel plate and terrain. To calculate the amount of slip sinkage ss at the point X , it is necessary to determine the amount of slippage js at the point X. If we now recall, from the previous Section 2.

Then, by substituting these values into Eq. Also, the amount of rebound u0 given in Eq. In the expression, Lcd is the value of the total land locomotion resistance of the rigid wheel. From force balance and horizontal and vertical equilibrium considerations, the effective driving force Td and the axle load W must equal the horizontal reaction force Bd and the vertical component N respectively.

The amount of eccentricity ed0 for the no slip sinkage state can be worked out from consid- erations of the moment equilibrium of the vertical stress applied to the peripheral contact surface taken around the axle of the rigid wheel. These components are the sinkage deformation energy E2 required to make a rut under the rigid wheel, the slippage energy E3 which develops at the peripheral contact part of the wheel and the effective drawbar pull energy E4 which is required to develop an effective driving force.

Thence, the following equation is obtained. The slip lines are largely divided into two parts for left and right hand sides from the point N on the peripheral contact area. Similarly section NE of the rim has a relatively fast forward movement while the soil particles along the rim move forward slowly and therefore the shear resistance acts in the direction of wheel revolution. Wong et al. The resultant velocity vector of all the soil particles on the peripheral contact part of the rigid wheel always rotates around the instantaneous center I.

The position of I lies below the bottom-dead-center M at a distance OI from the axle of the wheel. These ground reactions to the rigid wheel apply reversely to the moving direction, and they will make the rigid wheel brake. The land locomotion resistance acts as a form of bulldozing resistance to the rigid wheel. Next, the trajectories i. Wong [15] observed the trajectories of the soil particles in a soil bin, filled with clay, when a rigid wheel was rotating during braking action. As to his results, it was observed that the final horizontal amount of movement of a soil particle to the moving direction of the wheel decreased with depth.

Then, the soil particle moved downward along a circular trajectory. After the pass of the wheel, the soil particle moved upward and reached its initial position due to a rebound action in the non-compressible saturated clay.

### Kundrecensioner

In this case, i. In this case, the effective braking force Tb which is directed in the moving direction of the wheel increases when a braking torque Qb is applied. Tb can also do external work as an actual braking force to another wheel. The horizontal ground reaction Bb acts oppositely to the moving direction of the wheel. The direction of the resultant ground reaction composed of N and Bb deviates to the left hand side of the wheel axle.

Ground reaction acting on rigid wheel during braking action. Contact pressure distributions applied on peripheral surface of rigid wheel during braking action. The amount of sinkage z at an arbitrary point X on the peripheral surface, the amount of sinkage s0 at the bottom-dead-center M and the amount of rebound u0 at the point E can all be expressed as shown in Eqs. The above equations can be applied for loose sandy soil or weak clayey soft ground, but another equation [12] is better used in the case of hard compacted sandy ground.

To calculate the amount of slip sinkage ss of a wheel at a point X on the ground surface, it is necessary to determine the amount of slippage js at a point X. Rolling motion of a towed rigid wheel for point X on ground surface. Then, substituting this into Eq. Likewise, the horizontal ground reaction Bb and the vertical reaction N act on a point deviated from the bottom-dead-center by an eccentricity amount eb and by a vertical distance lb from the wheel axle.

From force balance considerations, Tb and W equal Bb and N respectively. The amount of eccentricity eb0 for the no slip sinkage state is given as follows, considering the moment equilibrium of vertical stress applied to the peripheral contact surface around the axle of the rigid wheel. These components are the sinkage deformation energy E2 required to make a rut under the rigid wheel, the slippage energy E3 which develops on the peripheral contact part of the wheel and the effective braking force energy E4.

Tdopt, idopt, Tbopt, ibopt, Tdmax, idmax, Tbmax, ibmax.

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Further to this, the total amount of sinkage si may be calculated from Eq. Then, the driving or braking torque Qdi or Qbi can be calculated from Eq. Additionally, the optimum slip ratio idopt or the optimum skid ibopt and the optimum effective driving or braking force Tdopt or Tbopt can be determined.

The analytical simulation results have then been contrasted and verified by comparison with detailed experimental test data. All the terrain-wheel system constants for the experimental situation are given in Table 2. The size of soil bin was cm in length, 10 cm in width and 35 cm in depth. The sandy soil was filled uniformly into the two dimensional soil bin by means of a free fall method that employed a 35 cm drop height. The initial density of the sandy. The actual traction test on the rigid wheel was executed under conditions of plane strain with the driving torque Qd , the effective driving force Td , and the total amount of sinkage s being measured directly.

As a consequence, the rigid wheel cannot move any more — without external pushing — at this slip ratio. In this case, the optimum effective driving force Tdopt is calculated as 0. After this the sinkage increases rapidly.

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Relationship between total amount of sinkage S and slip ratio id during driving action. Relationship between amount of eccentricity ed and slip ratio id during driving action. The sinkage deformation energy E2 increases parabol- ically with id from an initial value of 0. After that, E4 decreases almost parabolically till it develops negative values. Relationship between energy values E1 , E2 , E3 , E4 , and slip ratio id during driving action. Hiroma et al. Likewise the mathematical simulation results have been verified by comparison with exper- imental test data.

All the terrain-wheel system constants and the soil properties are the same as given in the previous session 2. The experimental towing test of the rigid wheel was executed under conditions of plane strain and the braking torque Qb , the effective braking force Tb and the total amount of sinkage s were measured directly. Afterwards, Tb increases parabolically with ib.

Relationships between amount of eccentricity eb of vertical reaction and skid ib during braking action. After that, E1 decreases gradually to zero. Afterwards, E4 increases rapidly with ib. Relationships among energy values E1 , E2 , E3 , E4 and skid ib during braking action. The shape of these stress distribution agrees well with experimental results published by Onafeko et al.

This tendency can be compared to the experimental test data presented by Oida et al. In this case, it is clearly shown that the position showing the maximum normal stress shifts forward In this chapter, we have studied the simplest of the machine-terrain interaction problems namely that of predicting the behaviour of a, loaded, rigid cylindrical drum operating upon a compressible, and potentially yielding, medium. The prediction is made by developing mathematical models of the system.

The cylindrical drum used in the modelling process can be thought of as the drum of an earthworks compactor or of an old fashioned steam-roller. Alternately it may be the steel tire or rigid wheel of a truck or trailer. While the use of rigid wheels may seem somewhat artificial to many, the assumption of rigidity makes the problem more mathematically tractable and gives experimentally testable results. The analyses presented here are generally two-dimensional only and the end effects of the drum and other three-dimensional effects have been typically ignored in the interests of mathematical tractability.

The chapter also continues the ideas developed in Chapter 1, namely that of the use of metrics to characterise a terrain and a particular load state. In this chapter, the ideas have been systematised by use of a matrix of terrain-wheel system constants. Al-Hussaini, M. Ito, N. Soil Failure beneath Rigid Wheels. Harrison, W. Shallow Snow Performance of Wheeled Vehicles. Theoretical Soil Mechanics. Janosi, Z.

Off-the-Road Locomotion. Kacigin, V. The Basis of Tractor Performance Theory. Prediction of rigid wheel performance based on the analysis of soil-wheel stresses — Part I. Performance of driven rigid wheels. Behaviour of soil beneath rigid wheels. Prediction of wheel-soil interaction and performance using the finite element method. Performance of Towed Rigid Wheels. From Wikipedia, the free encyclopedia. This article needs additional citations for verification.

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