AU2010201258B2

AU2010201258B2 - Improved wheeled vehicles

Info

Publication number: AU2010201258B2
Application number: AU2010201258A
Authority: AU
Inventors: Ian James Spark
Original assignee: Appuhamillage Gayan Chanaka Kahandawa
Current assignee: Appuhamillage Gayan Chanaka Kahandawa
Priority date: 2009-03-30
Filing date: 2010-03-30
Publication date: 2015-11-26
Anticipated expiration: 2030-03-30
Also published as: AU2010201258A1

Abstract

The principle of cooperative redundancy between multiple steering systems is extended to six wheeled vehicles where most of the power is delivered to the driven wheels by means of high efficiency shaft drives. Furthermore because power can be delivered to steerable wheels capable of turning through 180 degrees, the six wheeled vehicle is capable of rotating about the centre of the non steerable axle. The principle of cooperative redundancy between multiple steering systems has also been extended to articulated trains comprising one tractor and one or more trailers. The invention enables scuffing to be eliminated and off tracking to be minimised. E~IIJ - _ "ii £2 ___ I *q-4 ~Ij I

Description

1 IMPROVED WHEELED VEHICLES Technical Field The invention relates to the extension of the concept of cooperative redundancy to vehicles turning around the midpoint of a driven axle and to articulated trains consisting of at least one tractor and at least one trailer. The problems to be solved The first problem is to extend the concept of cooperative redundancy to vehicles with primary shaft drives which are capable of turning around a centre of curvature located in the middle of a non-steered but driven axle. The second problem is to use the concept of cooperative redundancy to solve all or some of the problems inherent to trains consisting of one or more wheeled tractors coupled to one or more wheeled trailers. The problems to be eliminated are as follows: 1. Scuffing of the wheels, where they are dragged across the ground at right angles to the plane of rotation. 2. Bogging of the train when operating in difficult conditions. 3. Skidding of the driven wheels, where they are dragged across the ground in their direction of rotation. Spinning of the driven wheels can be regarded as negative skidding. 4. Off-tracking of some trailers (or axles), where the radius of curvature of the path of trailing wheels is smaller than that of leading wheels. 5. Jack knifing of tractor/trailer trains. Drawings Fig. 1 shows a vehicle with four non steerable drive wheels and two steerable drive wheels. Fig. 2 shows details of the drive system of the zero turn radius (ZTR) vehicle shown in Fig.1. Fig. 3 shows details of the drive train for a wheel capable of turning through 1800. Fig. 4 shows details of the combined speed reduction gearbox/speed correcting differential. Fig. 5 shows the general hydraulic system for the ZTR vehicle shown in Figs. 1 and 2. Fig. 6 shows a simplified hydraulic system for the ZTR vehicle shown in Figs. 1 and 2. Fig. 7 shows a further simplified hydraulic system for the ZTR vehicle shown in Figs. 1 and 2. Fig. 8 shows the relationship between the centre of curvature and wheel angles and speeds. Fig. 9 shows a semi trailer where all wheels are positively driven at the correct speeds. Fig. 10 shows a traditional 3 axle trailer showing scuffing on turning. Fig. 11 shows an improved 3 axle trailer with zero scuffing. Fig. 12 shows two means of controlling trailer wheel angles Fig. 13 shows a traditional trailer showing off-tracking. Fig. 14 shows an improved trailer with zero off-tracking of the trailer wheels. Fig. 15 shows an improved multi axle trailer with reduced off-tracking and zero scuffing. Fig. 16 shows the relationship between wheel angles and the hitch angle. Fig. 17 shows toe-in required for trailer wheels on fixed axle. Fig. 18 shows a means of positively controlling the hitch angle. The Solutions Proposed The problem of turning a vehicle, with a primary shaft drive to all wheels, about any centre of curvature lying on the axis of the non-steered wheels, including the midpoint of the said axle, is described below: A combined speed correcting and turn correcting differential drives and supports each wheel. The primary input to these differentials is via shafts driven by the engine via the primary gearbox. The secondary input to each said differential is provided by a hydraulic (or electric) motor close coupled to the said differentials. The said hydraulic motors are driven by variable displacement hydraulic pumps which are driven directly by the engine (and not via the primary gearbox). The speed of each wheel is adjusted so that they produce the same centre of 2 curvature as would be produced by the angles of all the wheels. When the driver selects a centre of curvature in the middle of the non-steered axle, all the primary drive shafts (and primary gearbox output shaft) will be stationary and the speed of each wheel will be determined only by the speed of the close-coupled hydraulic motors. Due to the symmetry of the wheels on the non-steered axle, the speed of these wheels could be corrected by a single variable displacement hydraulic pump connected in series to all the hydraulic motors correcting the speed of the said wheels. Note that for the centre of curvature to be able to lie anywhere on the axis of the non-steered wheels, the steered wheels must be able to be turned through a total angle of 180 degrees. If the primary drive to these wheels is via shafts, then vertical shafts must be incorporated to allow such a large range in wheel angles. In this case the speed-correcting differentials also correct for the undesirable effect of turning the steerable wheels. Figure 1 shows a six wheeled vehicle with four coaxial non-steerable front wheels and two steerable rear wheels. The driver determines the path of the vehicle with a steering wheel or joystick, which determines the centre of curvature of the path of the vehicle. This centre of curvature always lies on the axis of the non steerable front wheels. If the steering wheel or joystick is not displaced from its central null position, the vehicle proceeds in a straight line with a radius of curvature of infinity. If the steering wheel or joystick is displaced as far as it will go to the right, the vehicle will turn around the mid point of the front axle with a radius of curvature of zero. When the driver selects the desired centre of curvature, the rear wheels will be turned so that they are at right angles to the line joining the desired centre of curvature to the centre of the contact patch of each wheel. Figure 1(a) shows the six wheeled vehicle proceeding straight ahead. In this case the rear wheels point straight ahead and all six wheels are positively driven at the same speed (as indicated by the arrows). Figure 1(b) shows the six wheeled vehicle turning around a centre of curvature to the right of the front non-steered wheels. In this case the rear wheels are turned to the appropriate angles and all wheels are positively driven at a speed which is proportional to their distance from the desired centre of curvature. The appropriate speeds are indicated by the arrows. Figure 1(c) shows the six wheeled vehicle turning around a centre of curvature located midway between the inner front wheels. Once again the rear wheels are turned to the appropriate angles and all the wheels are positively driven at speeds which are proportional to their distance from the desired centre of curvature. Note that the right hand rear wheel must be turned through an angle greater than 90 degrees and the right hand front wheels must be driven in reverse. The appropriate speeds are indicated by the arrows. Once the driver has selected the desired centre of curvature, an on-board computer calculates the appropriate wheel speeds and wheel angles and an on board controller implements these speeds and angles. Turning the positively driven steerable rear wheels to the appropriate angles is relatively straight forward if they are solely driven and supported by hydraulic motors. This is because power can be transmitted to these motors via flexible hydraulic hoses. Similarly positively driving all wheels at appropriate speeds is relatively straight forward if they are solely driven and supported by hydraulic motors. In this case each hydraulic wheel motor can be driven by a variable displacement hydraulic pump, where all six pumps are driven directly by an internal combustion engine. The speed of each wheel can now be varied by varying the displacement of the associated pump. The disadvantage of hydrostatic drives is that they are less efficient than mechanical drives. However the disadvantage of mechanical drives is that it is difficult to positively drive each wheel at a different speed and to turn the driven wheels through an angle range of 180 degrees. Means of overcoming the problems of mechanical drives are described below.

3 Figure 2 shows a six wheeled vehicle where most of the power is provided to the wheels by means of shafts 1 and 2. The essential feature of the invention is that each wheel is driven and supported by a combined speed correcting (and turn correcting) differential and speed reducing gear box 3 to 8. The output from these differential/gearboxes 3 to 8 is the axle shaft of each wheel 9 to 14. The primary input to the combined speed correcting (and turn correcting) differential and speed reducing gear box is the shaft drive from the engine 15 via the primary gearbox 16. The secondary input to each combined speed correcting (and turn correcting) differential and speed reducing gearbox 3 to 8 is provided by a hydraulic motor 17 to 22. The speed of each hydraulic motor is controlled by varying the displacement of the associated variable displacement pump. All variable displacement pumps 23 to 28 are directly driven by the engine 15. Details of the combined speed correcting (and turn correcting) differential and speed reducing gearbox are shown in Figure 4. The input shaft 29 is driven by the engine 15 via the primary gearbox 16. The input shaft 29 drives sun gear 30 which in turn drives planet gear 31 which is also driven by annular gear 32 which in turn is driven by hydraulic motor 33. Planet gear 31 drives cage 34, which in turn drives the sun gear of the second stage of the three-stage speed reduction gearbox. The annular gears of the second and third stages are fixed to the housing and are therefore stationary. The cage of the third stage drives the wheel 35. Details of the drive to the steerable rear wheels are shown in Figure 3. In this case the horizontal drive shaft 36 drives a vertical shaft 37 which is coincident with the vertical turning axis of the steerable wheel 38 via two bevel gears 39 and 40. The said vertical shaft 37 drives a parallel vertical shaft 41 via a pair of spur gears 42 and 43. The second vertical shaft 41 drives the primary input shaft 43 of the combined speed correcting (and turn correcting) differential and speed reducing gear box via a pair of bevel gears 45 and 46. The secondary input to the combined speed correcting (and turn correcting) differential and speed reducing gear box is provided by a hydraulic motor 47. In this case the hydraulic motor must not only correct the speed of the wheel, it must also cancel out the undesirable linkage between the turning of the wheel (about its vertical axis) and the rotation of the wheel (about its horizontal axis). Figure 5 shows the most general hydraulic circuit for connecting the six speed (and) correcting hydraulic motors 17 to 22 and the associated variable displacement hydraulic pumps 23 to 28 which are all directly driven by the engine 15. In this case the speed of the primary input shaft 48 does not have to correspond to the average speed of the front wheels 9 to 12. Figure 6 shows the special case where the primary drive shaft speed corresponds to the average of the appropriate speeds of the four front wheels. In this case the speed of the outer left speed correcting hydraulic motor needs to be equal but opposite to the speed of the outer right speed correcting hydraulic motor. In this case the outer hydraulic motors 17 and 20 can be connected in series and driven by a single variable displacement pump 49. Similarly the inner speed correcting hydraulic motors 18 and 19 can be connected in series and driven by a single variable displacement pump 50. Figure 7 shows a further simplification for the special case where the primary drive shaft speed corresponds to the average of the appropriate speeds of the four front wheels. In this case the displacement of the front hydraulic motors is made inversely proportional to the distance of the wheel contact patches from the midpoint of the front axis. In this case all the speed correcting hydraulic motors 17 to 20 can be connected in series and driven by a single variable displacement hydraulic pump 50.

4 The advantage of mounting the combined speed correcting (and turn correcting) differential and speed reducing gear box adjacent to the positively driven wheel is that it enables the driven wheel assembly to be turned through an angle range up to 180 degrees. The disadvantage of this arrangement is that it tends to increase the unsprung weight of the wheel assembly. If reducing the unsprung weight of the wheel assembly is more important than maintaining a wheel angle range of 180 degrees, then the combined speed correcting (and turn correcting) differential and speed reducing gear box can be mounted in the drive train just after the point where it divides in order to drive each wheel. A second advantage of locating the combined speed correcting (and turn correcting) differential and speed reducing gear box adjacent to the positively driven wheel is that a smaller reduction ratio is required for any right angle drive that is used to split the drive train from the primary gearbox. This means that the diameter of this right angle drive can be reduced, thus increasing the ground clearance. The problems inherent to trains consisting of one or more tractors and one or more trailers can be solved as follows: 1. Skidding of the driven wheels: Skidding of the driven wheels can be avoided by either allowing them to free wheel or driving them at speeds that would produce the same centre of curvature as the wheel angles. The appropriate wheel speeds Wn are given by the equations: on = RMSWS (Rn/ RMSR where RMSWS = ((Wn2+ Wn ... .+ Wn2 )/n)1 and RMSR = ((R 1 2 + R 2 2 ...... + Rn2)/n)1 Where RMSWS is the desired Root Mean Square Wheel Speed, RMSR is the desired Root Mean Square Radius, and Rn is the radius pertaining to the wheel in question. When the tractor or trailers are turning the wheels on a given axle must rotate at different speeds. Ideally each wheel of a double wheel should rotate at slightly different speeds. Consequently double wheels connected to a single hub should be avoided. 2. Bogging of the Train Bogging of the train will occur if the total resistive force acting on all wheels is greater than the total traction force provided by the driven wheels. If any of the driven wheels are connected via differentials then the maximum traction force provided by connected wheels is the lowest maximum traction force of all the connected wheels multiplied by the number of wheels connected by the differential. One way of increasing the resistance to bogging is to prevent the operation of one or more differentials by means of one or more differential locks. Another is to impede the operation of one or more differentials by replacing them with limited slip differentials. Yet another is to reduce the number of non-driven wheels. A better method is to positively drive all the driven wheels at speeds which will produce the same radius of curvature as all the wheel angles, where the later is selected by the driver by means of a steering wheel. This is an example of cooperative redundancy between two steering systems. Trains operating on steep or slippery slopes would maximise their resistance to bogging by positively driving all wheels.

5 Trains that have to snake around obstacles so that one part of the train is turning left while another part is turning right would tend to "straighten out" unless the majority of the wheels were positively driven at appropriate speeds. Figure 9(a) shows a traditional tractor 60 and trailer 61 where the rear wheels of the tractor are the only driven wheels. The traction force of the left and right wheels are equalised by the presence of a differential 62. Figures 9(b) and 9(c) show a modified tractor 63 and trailer 64 where the differential is replaced with a simple right angle drive 65 and two speed-correcting differentials located adjacent to the driven wheels of the tractor. The second input to each of the speed correcting differentials is provided by two hydraulic motors 66 and 67, where the speed of the latter is controlled by driving them with variable displacement pumps. In this case an on-board computer calculates the appropriate speeds of the speed correcting hydraulic motors 66 and 67 from the angle of the front wheels of the tractor. Resistance to bogging can be further increased by replacing all the free wheels with driven wheels. In this case each driven wheel is mounted on the output shaft of a speed correcting differential where the primary input to the differential is provided by the engine 68 via the primary gearbox 69 and drive shaft 70. The secondary input to the speed correcting differential is provided by a hydraulic motor whose speed is controlled by varying the displacement of an associated variable displacement pump. Once again an on-board computer calculates the appropriate speed of each of the hydraulic motors from the relative positions of the tractor and trailer. The wheels of the trailer 71 and 72 can also be driven by means of speed correcting differentials 73 and 74. The primary drive to these speed correcting differentials is provided by the engine 68 via the primary gearbox 69 and drive shafts 75 and 76 and right angle drive 77. 3. Scuffing of the wheels: Scuffing of the tractor or trailer wheels can be avoided by ensuring that the wheels on all axles (with the possible exception of one axle) can be steered to some extent. An on-board computer is used to control the wheel angles (for each trailer) so that they all tend to produce the same centre of curvature (or instant centre) even when the tractor and trailer have different centres of curvature (or instant centres). The appropriate wheel angles On are given by the equation: Tan On = Yn/Xn Where Rn is the displacement of the desired centre of curvature relative to the wheel and where Xn and Yn are the components of this displacement in the lateral and transverse directions respectively. Figure 8 shows the relationship between the centre of curvature selected by the driver and the appropriate wheel angles and wheel speeds. Figure 10 shows a traditional tractor 51 and trailer 52 where the latter has three rear axles. The trailer is in transition since it has a different centre of curvature (COC') than the tractor (COC). Eventually a steady state would be attained where the tractor and trailer have almost the same centre of curvature. With the above configuration scuffing of the trailer tyres is inevitable. If the middle trailer axle aligns with the trailer centre of curvature, then the wheels on the forward axle will point to the outside of the curve while the wheels on the rearward axle will point to the inside of the curve.

6 In order to avoid scuffing of the trailer wheels, their axes of rotation should all intersect a single vertical line. If all the axes lie on a single plane, then they must all intersect at a single point. The COC of the tractor is given by the intersection of the axis of the rear wheels and the axes of the steerable front wheels. The COC' of a trailer with one axle is given by the intersection of a line parallel to the axis of the rear tractor wheels which passes through the hitch point and the axis of the trailer wheels. In general the COC' of the trailer with non-steerable wheels will be different from the COC of the tractor. If the path of the tractor changes from a straight line to a circle then the COC 'of the trailer will asymptotically approach the constant COC of the tractor. If the trailer has more than one non-steerable axle, the steering system so formed it will tend to make it roll in a straight line. This steering system is in conflict with the steering systems formed by the movement of the hitch point and the trailer axles when the trailer is turning. This conflict between the steering systems will cause the trailer to take a path which is a compromise between the opposing paths. The above conflict will cause scuffing of the trailer tyres, resulting in increased tyre wear and road damage. This conflict will also cause a braking effect, resulting in increased fuel consumption by the tractor. Since this increased fuel consumption is avoidable it can be regarded as fuel wastage. Figure 11 shows a modified trailer 53 where the forward and rearward wheels are allowed to turn so that they are always perpendicular to a line through their contact patch and the centre of curvature of the trailer. The on-board computer calculates the correct angle for the four steerable trailer wheels from the relative positions of the tractor and the trailer. Each of the four steerable wheels can be steered independently by means of a steering arm and a hydraulic (or electric) actuator. Note that the forward trailer wheels are turned outwards and the rearward trailer wheels are turned inwards. One way of ensuring that all trailer wheels have a single centre of curvature is as follows: * The hitch angle Lp of the trailer is measured as the angle between the projected longitudinal axis of the tractor and the longitudinal axis of the trailer where clockwise angles are positive. * The radius of curvature R of the second trailer axle (with non steerable wheels) is calculated from the equation: R = L/cosqi Where L is the distance between the hitch point to the midpoint of the second trailer axle, where R is positive if the centre of curvature is to the right of the vehicle path. * The appropriate angles for the wheels on the first and third axles are given by the equations: Tan 01R = b 1 /(L/(cos Lp+ a/2) Tan 01L = b 1 /(L/(cos Lp - a/2) Tan 03R = b 3 /(L/(cos Lp+ a/2) Tan 03L = b 3 /(L/(cos Lp - a/2) Where b 1 is the distance between the first and second axle and b 3 is the distance between the third and second axle and a is the track of trailer axles.

7 * Linear Actuators linking the steering arms and the trailer chassis are activated to achieve the appropriate wheel angles. These actuators could be hydraulic cylinders or electrically driven screw actuators. Figure 12(a) shows a possible configuration for the steerable trailer wheels. In this case a leaf spring rigidly connected to a beam axle is used to resist braking and cornering forces and braking and rolling torques, while being elastically compliant to vertical forces. Figure 12(b) shows a second possible configuration for the steerable trailer wheels. In this case a trailing link rigidly connected to a beam axle is used to resist braking and cornering forces and braking and rolling torques, Vertical forces are carried by an air spring (or coil spring)superimposed between the projected trailing link and the chassis of the trailer. The ends of the links will incorporate "elastomer" bushes which will allow limited rotation and twisting. 3 Off Tracking. The performance of the tractor/ trailer train can be improved if off tracking is eliminated or reduced. If one set of wheels on the trailer is made to follow in the tracks of the rear wheels of the tractor then off tracking will be zero for these nominated wheels. Off tracking of the other trailer wheels will still occur, being maximum for wheels located midway between the nominated wheels and the hitch point. Zero off tracking of the nominated wheels can be achieved by turning them in the opposite direction to the steerable front wheels of the tractor. To a first approximation the turning required for the other trailer wheels to ensure that they have the same centre of curvature as the nominated wheels will be proportional to their distance from the midpoint between the nominated wheels and the hitch point. This means that trailer wheels located at this midpoint need not be turned and wheels located between the midpoint and the hitch point need to be turned in the opposite direction to wheels located between the midpoint and the nominated wheels. However this only applies for steady state turns where both the trailer and the tractor have the same instant centre, as depicted in Figure 15. If the path of the tractor changes from a straight line to a circular path, the path of the trailer will undergo a transition. With normal off tracking (where the trailer has no steerable wheels), this transition will be long, as the COC' of the trailer will asymptotically approach the COC of the tractor. If off tracking of the nominated trailer wheels is eliminated a much shorter transition is required. Indeed steady state will be achieved in this case when the train travels a distance which is equal to the distance between the hitch point and the nominated (or slave) reference point, as shown in Figure 14 and Figures 16(a) to 16(c). In this case the COC' of the trailer will coincide with the COC of the tractor when the nominated wheels of the trailer coincide with the position of the rear wheels of the tractor when the latter commenced the circular path. After this point the tractor/trailer train will be in a steady state (with constant hitch angle and wheel angles) until another COC is selected by the driver by changing the steering wheel angle. Figure 13 shows three positions of a normal tractor/trailer train. The first (1) position shows the position when the front wheels of the tractor are turned and the tractor commences its circular path. The second position (2) shows the position when the tractor is in the circular Steady state) path and the trailer is in transition. The third position (3) shows the tractor further along the circular path while the trailer is still in transition so that the degree of off tracking continues to increase. For the sake of simplicity only the rear wheels of the trailer are shown. Also the hitch point is assumed to coincide with the midpoint of the rear axle of the tractor. In practice the hitch point is often located slightly ahead of the said rear axle. Figure 14 shows three positions of tractor/trailer train where off tracking of the nominated trailer wheels are eliminated. Note that as the tractor proceeds along the circular path the nominated trailer wheels must be turned in the opposite direction to the front wheels of the tractor. Once the midpoint of the nominated trailer axle reaches the point occupied by the 8 midpoint of the rear tractor axle when the tractor began to turn, a steady state is achieved and the hitch angle and trailer wheel angle should be kept constant. Figure 15 shows a tractor/trailer train where off tracking of the nominated wheels are eliminated and the train has attained a steady state circular turn. In this case extra axles are added with steerable wheels. The exception is an axle is located at the midpoint between the nominated axle and the hitch point. In this case the wheels do not need to be steerable. However these midpoint wheels would still need to be steered to eliminate off tracking in a non steady state turn. Note that wheels can also be located between the hitch point and the midpoint between the hitch point and the nominated axle (axle G in Figure 15. In this case the wheels must turn in the same direction as the front tractor wheels. Also note that wheels can be added behind the nominated axle C without substantially increasing the width of the swept path of the train. These extra steerable wheels are attached to axle D. In general the radius of curvature of the path of the non- steered wheels will be less than that for the steered wheels. This increases the width of road required by turning vehicle trains. If all the trailer wheels are steerable they can be made to follow the path of the rear tractor wheels. This reduces the width of the road required by turning vehicle trains. The appropriate angles for each wheel can be calculated and controlled by an on-board computer to produce a "virtual railway" effect. It should be borne in mind that if the radius of curvature of the path of the tractor is changed rapidly, then the radius of curvature of the following trailers will go through a transition until a new steady state radius of curvature is established. Figure 13 shows a traditional tractor 51 and trailer 52 in the transitional phase of a turn. It is inevitable that the trailer wheels will track inside the trailer wheels. Figure 5) shows a modified trailer 55 where all the trailer wheels are steerable so that they follow as closely as possible to the rear wheels of the tractor. In this case an on-board computer calculates the appropriate trailer wheel angles from the relative position of the tractor and trailer and the angle of the front wheels of the tractor. Note that trailer wheels located before and after the midpoint of the trailer toe out and toe in respectively. One method of achieving the above, that should be obvious to a person skilled in the art (of control) is as follows: 1. The driver selects the desired path for the vehicle (and thereby the path of the master reference point) with the steering wheel. Note that this path does not need to be described by an equation. 2. An on-board computer samples the angle of the front wheels of the tractor and the speed of the master reference point every 0.005 seconds. 3. The computer determines the position of the master reference point for each sample time. 4. The computer calculates the required instant centre of the trailer which enables it to follow the desired path. 5. From the instant centre, the computer calculates the angles of the trailer wheels required to follow the desired path. 6. Control systems are used to implement the required trailer wheel angles. 7. A new sample is taken and the process repeated. Note that at no stage is the hitch angle measured in this process Figure 16 shows a tractor/trailer train transitioning from a straight line path to a circular path of radius R. In the interest of simplicity only notional wheels on the centre line of the tractor and trailer are shown.

9 Figure 16(a) shows the train at the start of the transition from a straight line to a circular path. The turn is initiated by suddenly turning the notional wheel at the front of the tractor to angle e' where 0' is given by the equation: Tan 0' = L'/R' where L' and R' are the wheel base of the tractor and the radius of the path of the rear tractor wheel. Figure 16(b) shows the configuration of the tractor and the trailer when the tractor has rotated an angle e relative to the original straight line path, and where the nominated trailer wheel is steered so that it follows the rear wheel of the tractor.. It can be shown that: G = Lp + 0 = vt/R' where Lp is the hitch angle and 0 is the angle required for the nominated trailer wheel, v is the velocity of the rear tractor wheel and t is the time elapsed since the commencement of the turn. It can be shown that: Tan 0 = (1 - cos 0)1//2 = 2-12 sin (0/2) Therefore L = e - (1 - cos 0)"/2 = 0 - 2-12 sin (0/2) Figure 16(c) shows the configuration of the tractor/trailer train when the nominated wheel of the trailer reaches the end of the straight line path of the rear tractor wheel and the beginning of the circular path. Beyond this point the tractor/trailer train will be in a steady state configuration. It can be shown that sin (0,,/2) = L/2R providing L/2R < 1 Furthermore '.s = 0,, = (0,,/2) Where 0,, is the steady state rotation, and Lp, and 0,, are the steady state hitch angle and required nominated wheel angle respectively. Figure 16(d) shows the steady state condition where the hitch angle and nominated wheel angle are independent of the total angle of rotation. The angles of the left hand and right hand wheel relative to the angle of the notional wheel are given by: tan AOL = ((a/2) sin 0)/(R - (a/2) cos 0) And tan AOR = ((a/2) sin 0)/(R + (a/2) cos 0) Where AOL is the turn out of the left wheel and AOR is the turn in of the right hand wheel. 4. Jack-knifing: Jack-knifing of one or more trailers can be prevented by the use of active hitch points wherein the hitch angle is positively controlled by means of one or more hydraulic cylinders or linear actuators, so that the steering effect of the positively controlled hitch angle is identical to the steering effect of all the wheel angles. If the wheel angle steering effect starts to fail (as it inevitably must as ground conditions worsen) it is backed up by the steering effect of the hitch angle. This is an example of cooperative redundancy of two steering systems. Note that in articulated loaders controlled "jack knifing" is the only enabled steering system. Figure 18 shows a means of controlling jack knifing. Here two hydraulic cylinders 56 and 57 are connected between the rear of the tractor and the spine 58 of the trailer 59.

10 In this case the on-board computer determines the appropriate hitch angle from the angle of the front wheels of the tractor and the relative positions of the tractor and the trailer. Note that this active hitch point system needs to be very reliable. If the hitch angle jammed in the straight ahead position it would be very difficult to turn the trailer. Conversely if the active hitch point jammed while turning it would be very difficult to straighten the trailer. Cooperative redundancy between the steering effect of the tractor front wheel angles and the positively controlled hitch angle is most easily achieved if off tracking of a nominated pair of trailer wheels is eliminated. The equations for the transition and steady state hitch angles are given in the previous section. . One method of achieving the above, that should be obvious to a person skilled in the art (of control) is as follows: 1. The driver selects the desired path for the vehicle (and thereby the path of the master reference point) with the steering wheel. Note that this path does not need to be described by an equation. 2. An on-board computer samples the angle of the front wheels of the tractor and the speed of the master reference point every 0.005 seconds. 3. The computer determines the position of the master reference point for each sample time. 4. The computer calculates the required instant centre of the trailer which enables it to follow the desired path. 5. From the instant centre, the computer calculates the hitch angle required to to make the trailer follow the desired path. 6. A control system is used to implement the required hitch angle. 7. A new sample is taken and the process repeated.

Claims

1. A train consisting of a tractor with two or more driven non steerable wheels mounted at the extremities of one or more rear axles and two steerable wheels mounted at the extremities of the front axle, where the angle of the steerable wheels is determined by a driver by means of a steering wheel (or joystick), where a trailer with one axle with two or more steerable wheels at the extremities of the trailer axle, is rotatably connected to the tractor at a hitch point (referred to as the first hitch point) adjacent to the midpoint of the one or more rear tractor axles, where the angle of the trailer wheels is controlled so that a nominated point on the axis of the trailer follows a path identical to the path of the said first hitch point regardless of whether or not the tractor and trailer have identical instant centres.

2. A train according to claim 1 where the correct angles for all trailer wheels are calculated by numerical means and then implemented.

3. A train according to claims 1 or 2 where the correct angles for the trailer wheels are calculated when the train is transitioning from one steady state (with a single centre of curvature), to another steady state (with a different centre of curvature), where such transitions are characterized by the tractor and the trailer or trailers having different centres of curvature at any instant of time.

4. A train according to claims 1, 2 or 3 where the angles of the front wheels of the tractor and the speed of the tractor are sampled at regular intervals and used to determine discrete points on the path of the hitch point, from which the required position of the nominated point on the axis of the trailer is determined, and from the latter the instant centre of the trailer, and the required angles for the trailer wheels can be calculated trigonometrically at the same time intervals.

5. A train according to claims 1 to 4 where further trailers are added, where the path of a nominated point on each trailer is also identical to the path of the first hitch point.

6. A train according to claims 1 to 4 where more axles with steerable wheels are added to the trailer where the angle of these wheels are also controlled so that the path of the midpoint of each added axle, if that axle if that axle where acting alone, has the same instant centre (or centre of curvature) as the nominated point on the trailer.

7. A train according to claims 1 to 4 where more axles with steerable wheels are added to the trailer where the angle of these wheels are also controlled so that the axes of rotation of each wheel on the trailer intersect at the centre of curvature of the path of the nominated point on the trailer.

8. A train according to claims 1 to 5 where more axles with steerable wheels are added to the trailers where the angle of these wheels are also controlled so that the path of the midpoint of each axle if that axle were acting alone has the same centre of curvature as the nominated point on the trailer on which the axle is located.

9. A train according to claims 1 to 5 where more axles with steerable wheels are added to each trailer where the angle of these wheels are also controlled so that the axes of rotation of each wheel on each trailer intersect at the centre of curvature of the path of the nominated point on each trailer.

10. A train according to any one of claims 1 to 9 , where the angle of the hitch point is positively controlled by one or more hydraulic or electric actuators so that the path of a nominated point on the axis of the trailer that would result if the hitch angle was the only steering effect is identical to the path that would result if the trailer wheel angles were the only steering effect. 12

11. A train according to claim 10 where further trailers are added, where the hitch angle of each trailer is positively controlled by one or more hydraulic or electric actuators so that the path of a nominated point on the axis of each trailer that would result if the hitch angle was the only steering effect, is identical to the path that would result if the trailer wheel angles of each trailer were the only steering effect.

12. A train according to claims 1 to 11 where the left and right hand wheels of each trailer are turned (i.e. steered) with separate hydraulic or electric actuators.