WO1997002975A1

WO1997002975A1 - Differential driving system

Info

Publication number: WO1997002975A1
Application number: PCT/GB1996/001600
Authority: WO
Inventors: Peter James Gibson
Original assignee: The Secretary Of State For Defence
Priority date: 1995-07-12
Filing date: 1996-07-05
Publication date: 1997-01-30
Also published as: SE9800045D0; GB9514213D0; SE9800045L; AU6313396A; NO980124D0; NO980124L; NO316065B1

Abstract

A differential driving system capable of operating as a steering system for skid steer vehicles having two differentials, a steering differential (11) dedicated to steering and a propulsion differential (1) having its planet carrier (2) adapted to be driven by a vehicle motor (5) and providing drive shafts (6, 7) for the opposite sides of a vehicle. One of the gears of the steering differential is driven by a variable speed reversible motor (17), which is adapted not to rotate for straight running, and the other two gears are each connected to rotate with one of the drive shafts (6, 7). No rotation of the gear of the steering differential driven by the reversible motor (17) means that the other two gears rotate in the same direction and the drive ratios of the connection means ensure that the angular velocities of the two drive shafts (6, 7) are equal.

Description

Differential Driving System

This invention relates to a differential driving system, in particular a differential driving system capable for use as a steering system for skid steer vehicles. Steering of tracked vehicles is most usually effected by causing one side ofthe vehicle to travel faster than the other, a method known as skid steer. Skid steer systems offer good manoeuvrability with very tight turns being possible and have other advantages such as robust suspension linkages and efficient use of space with no need for wheel arches to allow wheels to steer. Various mechanisms have been produced to enable skid steer but many require complex and expensive systems.

Skid steer can be effected by having twin engines or twin gearboxes driven from a common power source, each driving one side ofthe vehicle but this can be expensive in terms of cost and weight, can occupy a large volume and for all these reasons can be unsuitable for small vehicles. Other systems use a single power source and gearbox with clutch and brake mechanisms where steering is achieved by declutching and applying a brake to one side ofthe vehicle. However, this type of system only works well on slow vehicles and results in large power losses.

Many large tracked vehicles , such as battle tanks, tend to use complex systems of epicyclic gears and differentials in a specialised arrangement to allow different rates of travel for each side ofthe vehicle thus effecting steering. Such differential driving systems offer advantages in terms of efficiency and avoid large power losses but the complex systems used are generally too expensive and occupy too much space for use with smaller, less expensive vehicles.

US-A-5,004,060 discloses a tracked vehicle having a differential skid steer system having two epicyclic trains, each having sun, ring and planet gear elements. The vehicle motor drives elements ofthe first and second trains, the ring gear and planet carrier respectively, whilst the sun gears of both trains are driven by a hydraulic steering motor. The remaining elements, the planet carrier ofthe first train and ring gear ofthe second, drive the track drive wheels. However, systems using such epicyclic trains have the disadvantage that specialist manufacture ofthe epicyclic trains is required, resulting in higher costs and low availability of spare parts.

Note that hereinafter the terms sun gear, annular gear and planet carrier shall be applied to the elements of a differential but that the term annular gear does not in any way restrict a gear to being a ring gear with internal teeth and is used in conjunction with the term sun gear to distinguish between the non planet carrier gears.

Application of skid steer systems to small or inexpensive vehicles can be a problem. Cost constraints often contribute to crude steering mechanisms. Autonomous vehicles are often supplied with tracks and skid steering because ofthe desirability to turn in confined spaces and cope with a variety of terrain. However, such vehicles require precise steering means with good control at high and low speeds because there is no onboard driver capable of compensating for the inherent non-linearities in conventional drive mechanisms. At the same time the system may need to be relatively small and inexpensive. Such vehicles may be used, for example, in a hazardous environment.

Patent application WO 85/01784 discloses a differential system having two differentials which are connected for rotation in the same direction on one side and opposed rotation on the other. The system is capable of operating as a skid steer system with one differential being driven by a vehicle engine and the other differential being driven by some steer means. Similarly European Patent application EP0267983 discloses a track-laying vehicle which has a steering system comprising two differentials connected for opposed rotation on one side and rotation in the same direction on the other with one differential being driven by the vehicle motor and the other by a motor controlled by a steer means. However, systems having one side connected for rotation in the same direction and the other side connected for opposed rotation necessitate the use of an idler gear. Use of an idler gear increases the cost and complexity ofthe system both in terms of having an extra component but also in the required supporting structure to enable the idler gear to resist the considerable loads experienced. The versatility of arrangement of such systems is also correspondingly reduced.

It is an object ofthe present invention to provide a relatively simple and inexpensive differential driving system capable of operating as a steering system for skid steer vehicles which mitigates some ofthe aforementioned disadvantages of known differential driving and skid steer systems.

Thus according to the invention there is provided a differential driving system comprising a variable speed reversible motor, a propulsion differential adapted to be driven by a driving motor and connected to two propulsion shafts to provide left and right drive shafts and a steering differential driven by the variable speed reversible motor wherein each ofthe propulsions shafts is connected, via a shaft connection means, to rotate with a gear of the steering differential such that when the propulsion shafts are rotating in the same direction as one another then the gears ofthe steering differential connected with the propulsion shafts are rotating in the same direction as one another and the propulsion differential, steering differential and shaft connections means are adapted such that when the variable speed reversible motor is not rotating the propulsion shafts have equal angular velocity and rotation ofthe variable speed reversible motor causes an equal and opposite change in the angular velocities ofthe propulsion shafts.

Advantages of this system include the low cost and mechanical simplicity. Also the system can easily incoφorate conventional existing differentials without requiring specialist manufacture of components, resulting in lower costs, good availability of spares and a flexibility of use for a wide range of vehicles. The system also demonstrates desirable control characteristics. The velocity difference between the rates of rotation ofthe two drive shafts is constant for a certain steer input, whatever the input from the driving^'motor, therefore, in use where the left and right drive means provide drive for the two sides of a vehicle the steer rate is the same for a certain steer input irrespective ofthe forward velocity. The steering differential input is driven by the variable speed reversible motor which is usefully adapted not to rotate for no steer input. For straight running the propulsion shafts must have equal angular velocity and so the shaft connection means are selected to introduce predetermined ratios into the rates of rotation ofthe propulsion shafts and the gears ofthe steering differential to ensure that the propulsion shafts are rotating at the same rate when the variable speed reversible motor is not rotating. The propulsion shafts may either be connected for rotation in the same direction as the gears ofthe steering differential or may be connected for opposed rotation. The type of connection is the same for each propulsion shaft however. Having the same type of connection for each shaft means that the driving system is versatile in the way it can- be arranged and it can be easily adapted for a particular application. Further, different types of connection on each side would lead to problems such as the ability to coσectly tension each connection means whereas maintenance and repair is easier with the same type of connection being on both sides.

Each ofthe differentials has a planet carrier, a sun gear and an annular gear and the propulsion differential preferably has its sun and annular gears each connected to rotate with a propulsion shaft and has its planet carrier adapted to be driven by a driving motor, the propulsion differential being such that no rotation ofthe planet carrier ensures that rotation of one ofthe gears connected to a propulsion shaft causes the other gear to rotate in the opposite direction.

In a first arrangement ofthe invention the steering differential is such that with no rotation ofthe planet carrier, rotation ofthe sun gear causes the annular gear to rotate in the opposite direction and the steering differential has its sun and annular gears each connected to rotate with a steering shaft, the planet carrier ofthe steering differential is driven, via a carrier driving means, by one ofthe propulsion shafts, the other propulsion shaft being adapted to drive, via a shaft driving means, one ofthe steering shafts, the other steering shaft being driven by the variable speed reversible motor and the shaft driving means and carrier driving means introduce predetermined drive ratios such that, in use, when the variable speed reversible motor is not rotating then the angular velocities ofthe two propulsion shafts are equal. In this arrangement ofthe invention the steering differential can be ofthe same type as the propulsion differential thus reducing complexity and the potential number of spare parts required. By connecting the steer input to one ofthe steering shafts then any rotation ofthe planet carrier, when there is no steer input and the variable speed reversible motor is not rotating, will cause the other steering shaft to rotate in the same direction as the planet carrier. For straight running the propulsion shafts must have equal angular velocity and so the ratios introduced by the shaft driving means and carrier driving means are selected to ensure that the angular velocity imparted to the steering differential planet carrier, via the carrier driving means, by one propulsion shaft causes the steering differential to drive the steering shaft driven by the shaft driving means at a rotational velocity exactly equal to that imparted, via the shaft driving means, by the other propulsion shaft. Rotation ofthe steering shaft driven by the variable speed reversible motor causes the rotation ofthe other steering shaft to either increase or decrease and the rotation ofthe planet carrier to do the opposite, meaning that a velocity differential is imparted to the propulsion shafts. In a second arrangement ofthe invention the steering differential is such that with no rotation ofthe planet carrier, rotation ofthe sun gear causes the annular gear to rotate in the same direction and the steering differential has its sun and annular gears each connected to rotate with a steering shaft, each steering shaft being driven, via a shaft driving means, by one ofthe propulsion half shafts, the planet carrier being driven, via a carrier driving means, by the variable speed reversible motor and the shaft driving means introduce predetermined drive ratios such that, in use, when the variable speed reversible motor is not rotating then the angular velocities ofthe two propulsion shafts are equal.

In this arrangement ofthe invention the steering differential is of a different type to the propulsion differential which means that the two steering shafts are driven by the two propulsion shafts which allows for non complex and space efficient interconnection ofthe two differentials. No rotation ofthe planet carrier corresponds to no steer input and means that the two steering shafts will be rotating in the same direction. As no steer input corresponds to straight running then the angular velocities ofthe propulsion half shafts need to be equal when the planet carrier of the steering differential is not rotating. Therefore the shaft driving means introduce ratios such that the angular velocity imparted to a propulsion shaft, via a shaft driving means, is the same as the angular velocity imparted to the other propulsion shaft via the other shaft driving means. In order to further reduce the complexity, cost and size ofthe differential driving system the variable speed reversible motor is preferably a hydraulic motor.

Preferably the propulsion differential is a conventional differential having an internal ratio between its sun and annular gears of 1 : 1.

The use of conventional, available differentials allows a choice of differentials, enabling the system to be readily used for a range of vehicles having varying steering requirements, without the need for specialist manufacture of components, thus reducing the cost and increasing the availability of spare parts. Having an internal ratio of 1 : 1 between the sun and annular gears ofthe propulsion differential, i.e. having one rotation ofthe sun gear correspond to one rotation ofthe annular gear when the carrier is not rotating, increases the simplicity ofthe system and allows the steering effect on the propulsion shafts to be equal and opposite giving desirable control characteristics. For no drive from a driving motor the effect of a steer input will be to rotate the propulsion shafts at the same rate in opposite directions which would allow a vehicle to rotate on the spot. Conveniently the steering differential may be a bevel gear differential. In a preferred form ofthe first arrangement ofthe invention the steering differential is a conventional bevel gear differential with an internal ratio between its sun and annular gears of 1 : 1 and where the ratio, introduced by the carrier driving means, ofthe angular velocity ofthe propulsion half shaft which drives the steering differential planet carrier and the angular velocity ofthe steering differential planet carrier itself is 1 :2X when the ratio of the angular velocity ofthe steering half shaft to the propulsion half shaft linked by the shaft driving means is 1:X, where X is some real number.

The system may be used as a steering system by adapting the variable speed reversible motor to be controllable by a vehicle steer means and not to rotate for straight running and to rotate in opposite directions for left and right steer. In order to provide intuitive steering characteristics, even when controlled remotely, the variable speed motor is preferably calibrated to increase linearly with increased steer input, up to a pre-set maximum value.

The steering system may be used in a tracked vehicle comprising two parallel, independently drivable tracks driven by a track drive wheel, a vehicle motor and a steering system as described herein, wherein one propulsion half shaft connects to the track drive wheel of one track and the other propulsion half shaft connects to the track drive wheel of the other track.

The invention will now be further described by way of example only with reference to the accompanying drawings, in which;

Figure 1 shows a schematic representation of a specific embodiment ofthe first arrangement of the invention.

Figure 2 shows a kinematic representation ofthe linking ofthe system shown in Figure 1.

Figure 3 shows a schematic representation of a tracked vehicle incoφorating a steering system according to an embodiment ofthe second arrangement ofthe invention

A particular embodiment ofthe differential driving system is shown in figure 1. The propulsion differential 1 is a conventional bevel gear differential and has a planet carrier 2 driven, via a chain drive mechanism 3, by a drive wheel 4 ofthe driving motor 5. The annular gear ofthe propulsion differential 1 is connected to rotate with a first drive shaft 6 and the sun gear of propulsion differential 1 is connected to rotate with a second drive shaft 7, first and second drive shafts 6, 7 extending along a common axis and providing left and right drive means. Disposed along its length, first drive shaft 6 has a first toothed wheel 8 connected to it, said toothed wheel being aligned in a plane peφendicular the axis ofthe first drive shaft and having said axis at its centre. A second toothed wheel 9 is connected to the second drive shaft 7 along its length, the toothed wheel being aligned peφendicular to the axis ofthe second drive shaft and centred upon said axis.

The steering differential 10 is a bevel gear differential having a planet carrier 11 which is driven, via a chain 12 by the second toothed wheel 9, chain 12 and toothed wheel 9 comprising the carrier driving means. The ratio of rotational velocity ofthe second drive shaft to the rotational velocity ofthe planet carrier is determined by the ratio ofthe number of teeth ofthe planet carrier to the number of teeth ofthe second toothed wheel. The steering differential 10 also has a propulsion input shaft 13 connected to its annular gear and a steer input shaft 14 connected to its sun gear. The propulsion input shaft 13 ends in a third toothed wheel 15 aligned peφendicular to the propulsion input shaft 13 and centred thereon, said toothed wheel 15 also being in the same plane as first toothed wheel 8 and driven thereby via a chain 16, the chain 16 and toothed wheels 8, 15 making up the shaft driving means and introducing a ratio in the rate of rotation ofthe propulsion input shaft to the rate of rotation ofthe first drive shaft equal to the ratio ofthe number of teeth ofthe first toothed wheel 8 to the number of teeth ofthe third toothed wheel 15. The steer input shaft 14 is driven directly by a variable speed reversible hydraulic motor 17 which is in tum driven via a hydraulic pump (not shown) driven by the driving motor 5.

It should be noted that in the above the terms sun gear and annular gear are completely interchangeable and that the first drive shaft 6 could equally well be connected to rotate with the sun gear ofthe propulsion differential with the second drive shaft being connected with the annular gear without altering the character or operation ofthe invention. Also, the steer input shaft could equally as well be connected to the annular gear ofthe steering differential and the propulsion input shaft to the sun gear. The kinematic effects resulting in steering will now be described with reference to figure 2. The propulsion differential is represented by P and the steering differential by S. Each differential has a carrier rotating at an angular velocity c, a sun gear rotating at an angular velocity s and an annular gear rotating at an angular velocity of a. It is known in the art that the following equation can be used to describe all differentials and epicyclics; Ra = (l+R)c - s (1) where the value of R depends upon the rotational rates ofthe annular gear to the sun gear when the rotational velocity ofthe carrier is zero. For a differential where the annular and sun gears rotate in opposite directions when the carrier velocity is zero, as in the first arrangement ofthe invention, it can be seen that the value of R is positive, whereas for a differential in which no rotation ofthe carrier ensures that the rotation ofthe sun and annular gears is in the same direction, such as in the second arrangement ofthe invention, the value of R must be negative. For a conventional bevel gear differential, where R is positive, the value of R is equal to N_s / N_a where N_s is the number of teeth ofthe sun gear and N_a is the number of teeth ofthe annular gear.

The carrier ofthe propulsion differential of figure 1 is driven by the driving motor at some angular velocity M. The half shaft connected to the annular gear provides a first drive shaft with an angular velocity of Vi and the half shaft connected to the sun gear provides a second drive shaft with an angular velocity of V₂. Therefore the propulsion differential, being a conventional bevel gear differential with an intemal ratio of 1 ; 1 and hence of value of R equal to one, satisfies the equation;

The carrier ofthe steering differential S is driven by the rotation ofthe second drive shaft with a ratio in the rates of rotation introduced so that the angular velocity ofthe . carrier equals V₂ la. The propulsion input shaft is connected to the annular gear ofthe steering differential and is driven by the rotation ofthe first drive shaft with a ratio between the rates of rotation introduced so that the angular velocity ofthe propulsion input shaft equals Vi /β. The steer input shaft is connected to the sun gear ofthe steering differential and is driven at an angular velocity of I by the variable speed reversible motor. Therefore the steering differential satisfies the equation;

R_s.Vι /β = (l+R_s).V₂ /α - I (3)

The ratios α and β are set to ensure straight running with no steer input. That is, Vi must equal V₂ when I is equal to zero, setting the ratios as α /β = (1+Rs) Rs. Therefore the equation for the steering differential reduces to;

V₁ = V₂ - I.α /(l+R_s) (4)

Combining the equations for the steering differential and the propulsion differentiaT it can be seen that; V₁ = M - I.α 2(1+R_s) V₂ = M + I.α 2(1+Rs)

Therefore, any steer input I causes the angular velocity of one drive shaft to increase by I.α/2(1+Rs) and the angular velocity ofthe other to decrease by the same amount. It can be seen that the steering effect is dependant upon the intemal ratio ofthe steering differential and the value ofthe ratios α and β. The ratios α and β can be chosen to ensure a sensible steering effect as long as α/β = (1+Rs)/Rs. Note that α and β would have negative values if the steering shafts and propulsion shafts were connected for opposed rotation, in which case the ratio of α to β would remain the same but rotation of the variable speed reversible motor would cause an opposite steer effect. It can now be seen that were the steering differential also to be a conventional bevel gear differential then the value of α/β would equal two, that is, the propulsion input shaft would rotate twice as fast as the steering differential planet carrier for straight running. It can also be seen that if the value of β were equal to one then the steer effect would be ±JV2Rs .

Referring now to figure 3, which shows a tracked vehicle incoφorating a steering system according to an embodiment ofthe second arrangement ofthe invention, the propulsion differential 1 is a bevel gear differential having a bevel gear planet carrier 20. The planet carrier 20 is driven by the vehicle motor 5 via a motor drive shaft 22. The annular and sun gears ofthe propulsion differential are connected to rotate with first and second drive shafts 6 and 7 respectively, drive shafts 6, 7 having spur gears 50, 51 disposed along their axes. Drive shafts 6 and 7 are connected to rotate with track drive wheels 24 and 26 respectively and provide drive for tracks 28 and 30.

The steering differential 32 is a spur gear differential having its annular gear connected to rotate with first steering shaft 34 which terminates in spur gear 38. The sun gear ofthe steering differential 32 is connected to rotate with second steering shaft 36 which ends in spur gear 40. The planet carrier 42 of steering differential 32 is chain driven, via chain 43, by drive wheel 44 ofthe hydraulic motor 17. The hydraulic motor is controlled by a vehicle steer means (not shown) and is adapted not to rotate for straight running and to rotate in opposite directions for left and right steer. Spur gear 50 connects with spur gear 38 so that rotation ofthe first drive shaft 6 causes opposed rotation ofthe first steering shaft 34 Likewise spur gear 51 ofthe second drive shaft connects with spur gear 40 ofthe second steering shaft. As steering differential

32 is such that with no rotation ofthe planet carrier 42 the sun and annular gears can only rotate in the same direction then no steer input means that drive shafts 6 and 7 drive the tracks 28 and 30 at the same speed. Any steer input causes a velocity differential in the rates of rotation ofthe drive shafts 6 and 7 and therefore a velocity differential in the rates of travel ofthe tracks resulting in a turning force on the vehicle.

The kinematics ofthe system shown in figure 3 are very similar to the kinetics of the first arrangement. The propulsion differential is again a conventional bevel gear differential with an intemal ratio of 1 : 1 and has its planet carrier driven at some angular velocity M by the vehicle motor and so satisfies the equation

V, = 2M - V₂ (5) where Vi is the angular velocity ofthe first drive shaft 6 and V₂ is the angular velocity of the second drive shaft 7. The steering differential is such that with no rotation ofthe planet carrier the rotation ofthe sun and annular gears are in the same direction. This means that in the equation given above which describes differentials the value of R is negative. The steering differential therefore satisfies: -Rs.a = (l-Rs)c - s (6) where Rs is a positive dimensionless number that is equal to the rotational rate of sun gear divided by the rotational rate ofthe annular gear when the planet carrier is not rotating.

The annular gear ofthe steering differential 32 is driven by steering shaft 34 which is connected to rotate with first drive shaft 6 which rotates at an angular velocity Vi. The connection means, namely spur gears 50 and 38, introduce a ratio into the rates of rotation such that steering shaft 34 rotates at -Vi/β, where β is positive. The value of rotation of the steering shaft 34 has a negative value as it is connected for opposed rotation with first drive shaft 6. Similarly a ratio is introduced between the rates of rotation of second drive shaft 7 and steering shaft 36 such that steering shaft 36 and therefore the sun gear ofthe steering differential rotate at an angular velocity of -V₂/α where α is positive. The planet carrier 42 ofthe steering differential 32 is driven by the hydraulic 17 motor at some angular velocity I dependant upon the steer input.

The equation for the steering differential therefore becomes; Rs.V, /β = (l-Rs).I + V₂ /α (7)

As the ratios α and β are set to ensure straight running with no steer input i.e. Vi must equal V₂ when I is equal to zero, it can be seen that α β must equal 1 Rs. Therefore the equation for the steering differential reduces to;

V, = I.α.(l-Rs) + V₂ (8) Combining the equations for the steering differential and the propulsion differential it can be seen that;

Vi = M - I.α.(l-Rs)/2 V₂ = M + I.α.(l-Rs)/2

It can therefore be seen that any steer input I results in a change ofthe angular velocity ofthe two drive shafts by an equal and opposite amount. The values of α and β can be chosen to ensure a sensible steering effect. It should be apparent that where steering shafts and drive shafts connected for rotation in the same direction then the steering effect would have the same value but that the steer effect would be added to Vi and taken away from V₂. It can also be seen that the total velocity ofthe track drive wheels is constant for constant motor input M and therefore the forward velocity ofthe vehicle is not changed by steering.

Claims

1. A differential driving system comprising a variable speed reversible motor, a propulsion differential adapted to be driven by a driving motor and connected to two propulsion shafts to provide left and right drive shafts and a steering differential driven by the variable speed reversible motor wherein each ofthe propulsion shafts is connected, via a shaft connection means, to rotate with a gear ofthe steering differential such that when the propulsion shafts are rotating in the same direction as one another then the gears ofthe steering differential connected with the propulsion shafts are rotating in the same direction as one another and the propulsion differential, steering differential and shaft connection means are adapted such that when the variable speed reversible motor is not rotating the propulsion shafts have equal angular velocity and rotation ofthe variable speed reversible motor causes an equal and opposite change in the angular velocities ofthe propulsion shafts.

2. A differential driving system according to claim 1 wherein the shaft connection means is adapted such that each propulsion shaft is connected for rotation in the same direction with a gear ofthe steering differential.

3. A differential driving system according to claim 1 wherein the shaft connection means is adapted such that each propulsion shaft is connected for opposed rotation with a gear ofthe steering differential.

4. A differential driving system according to any preceding claim wherein each differential has a planet carrier, a sun gear and an annular gear and the propulsion differential has its sun and annular gears each connected to rotate with a propulsion shaft and has its planet carrier adapted to be driven by a driving motor, the propulsion differential being such that no rotation ofthe planet carrier ensures that rotation of one ofthe gears connected to a propulsion shaft causes the other gear to rotate in the opposite direction.

5. A differential driving system according to claim 4 wherein the steering differential is adapted such that with no rotation ofthe planet carrier, rotation ofthe sun gear causes the annular gear to rotate in the opposite direction and wherein the steering differential has its sun and annular gears each connected to rotate with a steering shaft, the planet carrier ofthe steering differential is driven, via a carrier driving means, by one ofthe propulsion shafts, the other propulsion shaft being adapted to drive, via a shaft driving means, one ofthe steering shafts, the other steering shaft being driven by the variable speed reversible motor and the shaft driving means and carrier driving means introduce predetermined drive ratios such that, in use, when the variable speed reversible motor is not rotating then the angular velocities ofthe two propulsion shafts are equal.

6. A differential driving system according to claim 4 wherein the steering differential is adapted such that with no rotation ofthe planet carrier, rotation ofthe sun gear causes the annular gear to rotate in the same direction and wherein the steering differential has its sun and annular gears each connected to rotate with a steering shaft, each steering shaft being driven, via a shaft driving means, by one ofthe propulsion half shafts, the planet carrier being driven, via a carrier driving means, by the variable speed reversible motor and the shaft driving means introduce predetermined drive ratios such that, in use, when the variable speed reversible motor is not rotating then the angular velocities ofthe two propulsion shafts are equal.

7. A differential driving system according to any preceding claim wherein the variable speed reversible motor is a hydraulic motor.

8. A differential driving system according to any preceding claim wherein the propulsion differential is a conventional differential having an intemal ratio between its sun and annular gears of 1:1.

9. A differential driving system according to any preceding claim wherein the propulsion differential is a bevel gear differential.

10. A differential driving system according to claim 5 wherein the steering differential is a conventional bevel gear differential with an intemal ratio between its sun and annular gears of 1 : 1 and wherein the ratio, introduced by the carrier driving means, ofthe angular velocity ofthe propulsion half shaft which drives the steering differential planet carrier and the angular velocity ofthe planet carrier itself is 1 :2X when the ratio ofthe angular velocity ofthe steering half shaft to the propulsion half shaft linked by the shaft driving means is 1 :X, where X is some real number.

11. A steering system for skid steer vehicles comprising a differential driving system according to any preceding claim wherein the variable speed reversible motor is adapted to be controllable by a vehicle steer means and is adapted not to rotate for straight mnning and to rotate in opposite directions for left and right steer.

12. A steering system for skid steer vehicles according to claim 11 wherein the variable speed reversible motor is calibrated to increase in angular velocity linearly with increased steer input, up to a pre-set maximum value.

13. A tracked vehicle supported on two parallel, independently drivable tracks driven by a track drive wheel, a vehicle motor and a steering system according to claim 11 or claim 12 wherein one propulsion shaft connects to a track drive wheel of one track and the other propulsion shaft connects to the track drive wheel ofthe other track.

14. A differential driving system substantially as described herein with reference to figures 1-3 ofthe accompanying drawings.