RWS recumbent bicycle

Preface

After one year of having a concept of rear wheel steering bike, finally got the hands dirty to complete the design of Alpha version and make its prototype…

Recumbent bikes have their own pros and cons comparing to upright bikes. They are more ergonomic and very comfortable compared to upright bikes and also have a great advantage in aerodynamics.

There are also drawbacks associated with these type of bikes Here I don’t want to make a list of all disadvantages.

But the main objectives that pushed me into starting this project were:

-          To get rid of long chains of current recumbent bikes:

-          To get rid of Interference of legs with steering front wheel, which results in conventional supine position of the body for common recumbent bikes.

-          Designing a recumbent  bike with more potential to be used in urban environments .( a bike that is easier to stop and start the movement  considering constant traffic interruption in cities)

The design concept:

This new concept is rear wheel steering front wheel drive recumbent with power transfer system directly on front wheel. Power Direct power transfer has been achieved by using a specially designed epicyclic gearing set with possible progressive shifting system. Steering mechanism is placed on rear wheel and is composed of a 4 bar linked kinematic system in order to achieve a lean steer RWS which surprisingly is configured with negative trail(read more on steering description).  The design is a try to adapt recumbent bikes for urban use and change the nature of this bike from sports cycling to urban transportation cycling …

But before everything there are issues that should be indicated:

Potential advantages of a rear wheel steering , front wheel drive recumbent bikes( of which we can mention simpler transmission  mechanism and separation of steering wheel and brake wheel)  has inspired many designers to go for a RWS system design, In Late 70’s US National highway safety administration(NHSA) commissioned a project  to develop a  Safe motor bike with key idea of lower center of mass, longer wheel base and separation of steering and braking…The last requirement leads naturally to a design with rear-wheel steering, since the front wheel provides the major contribution to the braking force. The result was reported to NHSA with a recommendation that it was pointless to build a prototype because the motorcycle could apparently not be ridden.

In spite of the all the negative signs of considering RWS Bikes inherently unstable, I started my own adventure with the hope to achieve some advances… the least achievement would be better understanding of bikes by studying  dynamical behavior of RWS.

But what makes front-steering bicycles, FSBs stable and rear-steering bicycles, RSBs, unridable?

 Here is a simplest response to this question that I quote from HPV magazine, By Craig J Cornelius:

“In simplest form, a bicycle can be thought of as two-mass system. The larger mass is made up of the main frame, the rider and the driven wheel, and the smaller mass is made up of the steering frame(fork), steered wheel, handle bars , etc. the rider maintains stability by directly controlling system velocity , steering angle and lean angle indirectly.During a steady-state Maneuver either riding in straight line or executing a constant acceleration turn, the two major system perturbations are to steering angle, which primarily relates to steering frame or to the lean angle which primarily relates to main frame.A correctly designed FSB has a mechanism to correct each of these disturbances. Disturbances to the steering angle are corrected for by the phenomenon of caster. Caster or positive trail is defined as the distance the steered wheel’s ground contact patch is behind the intersection of  steering axis and the ground, behind being is defined as the opposite the direction of desired motion. Positive trail results in a torque being developed whenever the plane of the steered wheel is not aligned with the direction of the motion. For small steering angles this torque is roughly proportional to the steering angle and acts to reduce the steering angle. As a result any disturbance to the steering angle is corrected by the negative feedback associated with positive trail.Disturbance to the lean angle are corrected by the phenomenon of lean steer. The kinematics of a typical bicycle are such that the tendency of the system to reduce its potential energy results in a torque that steers the bicycle in the direction that it is leaned. As a result as a result, a disturbance which causes the main frame to lean sideways, initiates a turn in the direction of the fall. The radial acceleration due to that turn results in a force that acts to lift the bicycle out of the fall. As with positive trail lean steer results in negative feedback to the disturbance that initiates it.The mechanism of positive trail and lean steer allow a bicycle to be ridden with the rider’s hand of the handlebars. In addition these mechanisms are usually strong enough to allow a bicycle to remain upright in the absence of the rider above some minimum speed.The auto stability of a FWS bike is direct result of positive trail and lean steer. Fortunately both mechanisms occur together in an FSB.In RSB positive trail results in reversed Lean steer and conversely lean steer is present only with negative trail.  I have investigated numerous combinations of fork offset and fork rake for single pivot steering systems as well as a number of four bar linkage positioning Mechanisms, and have not found a steering method that combines both positive trail and lean steer. This inability to obtain both disturbances correcting Mechanism in the same configuration is why RSBs are inherently unstable.
In designing a simple RSB, then, one must choose among positive trail, Lean steer, or a neutral configuration that exhibits neither phenomenon.”

For further studies  The following articles are more detailed: Bicycle dynamics and control, By Karl J. Åström and also Bicycle dynamics By Arend Schwab.

RWS recumbent; Steering solution with negative trail…

The critical point of an RWS concept however is to find a solution to make a stable design: My solution for this problem is a kinematic mechanism for steering which provides both Lean steer and positive trail effects in the same time.

To solve the problem of instability of RWS I had to devise a mechanism that provides sort of a instantaneous steering axis.

As you can see in demonstration of steering mechanism, steering axis is far behind the wheel’s contact patch with the ground… with conventional definition of the trail or caster, this configuration results in negative trail and consequently the inability of controlling the bike in higher speeds, But the thing that makes this design different is the fact that steering axis

in this mechanism is not stationary and it actually moves instantly by steering the wheel;

This mechanism is configured in a way that although it seems to have a negative trail configuration, but disturbances caused by steering develops a torque that tends to correct steering (in contrary of what we expect from negative trail which tends to steer violently upon steering)

This configuration also provides lean steer effect due to tendency of the system to reduce potential energy while leaning.

Direct Power transmition: (Planetary Hub Gear)

Planetary Hub gear.

Having a fixes front wheel has 2 main advantages:

-          separation of steering and braking

-          Possibility to use hub gears directly on the front wheel.

As I was planning to build the prototype of this RWS bike and there is nothing as hub gear in market for direct power transfer system without using chain, I have designed my own planetary gear for this bike.

I had a concept about a hub gear which would installed directly on the front wheel without any need to chain, here I simplified it for prototyping and the result is a 2 speed planetary gear set that could be easily prototyped.

Planetary gear ratio depends on which part is fixed and which part is moving:

Planetary gears are usually made of A ring gear, a sun gear, and a set of 3 or 4 planetary gears that are linked together.

I have used ring/Sun/Planetary Gears with relatively 42/18/12 teeth.

Working out the gear ratio of a planetary gear train can be tricky. Let's denote the following:

Tr	Turns of the ring gear
Ts	Turns of the sun gear
Ty	Turns of the planetary gear carrier (the Y shaped thing in the previous photo)
R	Ring gear teeth
S	Sun gear teeth
P	Planet gear teeth

The turning ratio is as follows:

( R + S ) ×T_y = (R × T_r )+( T_s × S)

 By default I would fix outer ring by a disk brake, In this case the gear ratio is 3.33( 1 +42/18) but there is this opportunity to release the disk brake and let the outer ring to rotate, in this case output ratio differs from fixed configuration and it’s suitable for starting  the bicycle movement.video1 video2

By using a disk brake which in our case is used as a clutch, we can let the disk and consequently the ring gear to rotate… depending on the brake pressure ,gear ratio would change from 3.33 to 1.00 and this gear shifter works in a linear way.

I already know that there is some waste of energy due to friction, I still have not calculated the amount of this wasted energy, so till performing a proper calculation and test, let’s say that we use this gear set just as a 2 speed gearbox. High gear of 3.33 and low gear ratio of 1.00

Click to view assembly process

 2 different ratio modes  would be achieved like this: (Note that in this design the pedal is used as the planetary carrier. So the driving components are 3 planetary gears and the sun is driven component)

1-      High Gear:

If we hold the ring gear in a fixed position, T_r will always be zero. So we can remove those terms from the above formula, and we get: T_s /T_y = (R+S)/S=(18+ 42/18) =3.3         

With the fixed disk & Ring gear, and the planet gears connected to the pedals as driving elements, turning the pedals and consequently the set of 3 planetary gear carrier, would cause the sun gear and consequently the hub and wheel, to turn 3.3 times.

2-      low gear:

According to the formula, and considering that planetary gear carrier as the driving  element, if  We let the disk and ring gear to rotate, the sun gear would turn with a less angular velocity, at its extreme if we let the ring to turn freely, it would be  ring that rotates with a low gear ratio but higher torque, and the sun gear would not turn at all. As you see it literally mean that by controlling of ring’s rotation we can adjust the ratio of rotation of sun gear and hub and wheel in a linear manner.

Again to avoid any kind of waste we let the ring to rotate freely without any friction but we would limit the rotation by a freewheel bearing that doesn’t allow the ring to overrun the hub and the sun gear… this would result an equilibrium of

Tr	=Ts	=Ty

And the gear ratio equals to T_y  / T_s  =1 which is a convenient ratio to gain speed while starting the bicycle movement.

I am also very keen to know if linear gear change would work efficiently or not, so in very near future I am going to conduct the efficiency test of this gear set.

Sexy bicycle

Ergonomic bicycle design

More Photos of the bike...

Known Issues with current design:

·         Long wheelbase which results in larger turning radius.

·         Weight distribution: almost 60% rear to 40% front wheel; I would probably have to change this configuration for next design

·         Using cable to steer the rear wheel seems that is not so practical, I used cable as it enables us to integrate bicycle seat and steering handle bars. Connecting the handle bars stem to seat is an advantage as by adjusting the position of seat, the handle bars would also be in the right place without any further adjustments.

·         The steering center of gravity is located in a position which doesn’t contribute to lean steering and actually it produces a reverse torque that resists against lean steer.

The whole design is not yet ridable as a result of aforementioned issues.

Known Issues with current prototype:

•   Despite my efforts to build a high quality prototype, This model is still too wobbly...I could have done a better job...
• 
  
•