Recumbents and Convergent Evolution

By the late 1870’s bicycle innovators realized that there needed to be a safer alternative to the high-wheel bicycle that had become so ubiquitous. All manner of design approaches to lower the rider and move him backward prevailed, each with the intent of preventing headers, the rider pitching forward over the handlebars. These included gearing mechanisms so the size of the drive wheel could be reduced while keeping the ratio of pedaling speed to vehicle speed the same. Four bar linkages were used that moved the rider rearward as well as levers with overrunning clutches. Separate crank arms being coupled to the wheel by separate chains allowed the pedal location to be lowered, and there was the novel approach to use a single chain to drive the rear wheel. This of course was the safety bicycle and not long after its appearance, the other approaches faded away. A common design was converged upon and human-powered vehicle technology moved forward.

Now if someone were to have asked me, I would have told them that recumbents haven’t converged on a common design that satisfactorily addresses what I will call "the recumbent packaging problem"; that being, that for a proper weight distribution, the pedals want to occupy the same volume as the front wheel. But after a bit more reflection and staring at pictures of the participants in last summer’s “Roll Over America” velomobile tour, I realized that recumbents have converged on a common design, and a pretty good one at that.

I saw a post on www.bicycledesign.net about an Italian designer who was developing a rear-steering-recumbent bicycle. http://www.mohsen-saleh.com/2012/01/rws-recumbent.html#!/2012/01/rws-recumbent.html .  He was trying to solve the recumbent packaging problem.

 Now there a number of solutions to this problem. It turns out that rear-steering is the least feasible of those solutions. I should know, I spent 10 years building rear-steerer prototypes.

 

The Plywood Flyer from 1978. Possibly the first attempt at a low-rider recumbent bike, 12 years before Matt Weaver forever changed the design for high-speed recumbents with his revolutionary streamliner.

 The VelAero from 1987


In the end, the VelAero, could be balanced at moderate to high speeds, but could not be ridden slowly without weaving drastically. So I wrote up my results, published them in “Human Power” and moved on. http://www.ihpva.org/HParchive/PDF/27-v8vn1-2-1990.pdf

One place to put the cranks is behind the front wheel, like the Avatar and many other long wheelbase recumbents. The upside is a very comfortable riding posture and ease of balancing. The downside is a very long vehicle that is difficult to transport and a lightly loaded front wheel that can slip laterally on all but the driest of surfaces. Detractors to this layout claim the chain is too long. I disagree. It minimizes the angle the chain makes with the sprockets in the extreme gears and it extends chain life. 22 years of riding an Avatar, breaking the seat twice, sawing through a front derailleur, breaking a crank and breaking the frame but never having to replace a chain.

The other pole is to place the cranks far ahead of the front wheel. The vehicle shown is the aptly named Hypercycle. It is very compact but also suffers from poor weight distribution with a heavily loaded front wheel. The heavily loaded front wheel also resulted in very skittish handling.

The cranks could be located well above the front wheel like the classic racing Velocar of the 1930’s. The package is compact, and the front wheel loading is similar to a long-wheel base design. The downside is that the rider’s feet end up a significant distance above the ground, especially if the front wheel becomes large. This makes it difficult to get started from a stopped condition.

Above is my design of the above-wheel approach, the Coyote 

The cranks could overlap the front wheel with the bottom bracket near the steering axis. This is a picture of the final crank location of the EcoVia Mk2 leaning tricycle. This limits the steering angle, but surprisingly, for medium wheelbase layouts (40-48”), you don’t need much more than +/-20deg. of steering lock for all but the tightest of turns. George Georgiev has made good use of this fact with his Varna speed demons, where the rider’s legs and cranks overlap the front wheel to the extent that only a few degrees of steering lock are available. The bottom bracket height for the above configuration is 20'

If one uses a 16"dia. wheel instead of the 20"dia. wheel above and move the bottom bracket back, the bottom bracket height can be reduced to 14.4". The EvoVia MK3. The downside is the wheelbase is increased by about 6". Both layouts require use of a single chainring because there is no clearance for a front derailleur.

Another way of having the cranks overlap the front wheel, without limiting steering lock to the degree above, is to allow the cranks to pivot with the steered wheel. The worked satisfactorily for high-wheel bicycles, where the direction of the pedal force was roughly parallel with the steering axis, but with recumbent posture the pedal-force direction is closer to being perpendicular to the steering axis. Thus pedaling forces will perturb the steering and make the vehicle difficult to ride. (See the post “Arm-Power and the Avatar” below.)

http://lefthandedcyclist.blogspot.com/2012/03/arm-power-and-avatar.html

A more complex version of the cranks moving with the steered wheel is having the cranks pass through the front hub. In the Evolution Bike above, the cranks drive an infinitely-variable transmission in the hub. An interesting note, the concept recumbent shown above is nearly identical to a Polish entry in Prof. David Wilson’s “Human –Powered-Land-Vehicle Design Contest held in 1969. That vehicle used a hub transmission as well but most interesting, the laid-back steering axis passing through the contact patch of the front wheel was the same. Convergent evolution? In both designs the pedal force is closer to being parallel to the steering axis than perpendicular, so pedaling perturbations to the steering might be manageable. A most attractive package, but again the driving wheel is seeing significantly less than half of the vehicle’s weight. Another issue with hub-centered pedals is that the bottom bracket height is half the wheel diameter, so the wheel must be large enough to prevent the rider’s heels from hitting the ground when pedaling.

And yet another variation of hub-center pedals it to fix the cranks and pivot the wheel using a hub-center steering approach.  The steering lock is again restricted by the rider’s legs but the posture can be comfortable and steering is not perturbed by pedaling. Of course you must couple the cranks to the rear wheel (or front wheel for that matter). This approach requires a lot of non-standard components and has rarely been used.  

A pedal path that is elongated horizontally to minimize pedal/wheel overlap can be used. The pseudo-linear linkage above was tried on the EcoVia Mk2. Notice the two-sided pedal where the rocker link was outboard of the pedal and the coupler link was inboard of the pedal. It packaged very compactly. Unfortunately, the harmonic-velocity linear motion had pedals that came to a stop at the ends of the stroke. This significantly reduced the maximum pedaling cadence and made climbing of any type of hill prohibitive.

To eliminate the extreme velocity fluctuations associated with linear-type drives, but to preserve the squashed pedal path, I played with an egg-drive concept. A triangular link holds the pedal. This link is supported by a rocker link at the rear and a rotary crank at the front. The big circle below the egg is a 20”dia. wheel. The smaller circle behind the egg is a conventional crank for comparison. This approach is obviously a bit over the top in complexity.

And then there is the most unconventional means of addressing the packaging problem, ride the recumbent backwards. The steered wheel is in front and so is the riders head. The drive wheel is in back straddled by the rider’s legs and the vehicle conforms nicely to a teardrop cross-section with rider’s shoulders in front tapering to the rider’s feet at the rear. The idea has been used at least three times. By the inventor Milt Raymond in the mid 1980’s, by Ohio State with their “Buckeye Bullet” at one of the human-powered speed championships and most recently and most successfully with the Eiviestetto, which just wrested the hour record from the Varna Tempest (see the post “Back to the Future” below) covering almost 57miles in an hour.

http://lefthandedcyclist.blogspot.com/2011/12/back-to-future.html

Of course, there is an “out of the box” solution to the pedal/steered wheel interference problem, but purist may feel the original design intent is violated. Use two front steering wheels, place the pedals between them and drive the single back wheel.

This layout dates back before WW2 with the Fantom from Sweden. Supposedly 100,000 copies of the plans for these were sold. The layout was resurrected by Mike Burrows with his Windchetah in the late 1970’s, again used by the Vector team to break the break HPV speed records in 1980, by Carl-Georg Rasmussen with the Leitra and it has become the default layout for most velomobiles. It was while staring at a picture of a line of recumbents winding through a Portland OR. park at the beginning of the “Roll Over America” velomobile tour that I realized that seven of the nine visible vehicles looked essentially the same. They were based on the Fantom layout. The two outliers were a long-wheel base recumbent bike with a partial-fabric faring and Miles Kingsbury’s Quattro.

Sure, you could argue that a velomobile, by default, is an enclosed trike of the Fantom layout, but since velomobile is a generic term for an enclosed recumbent bicycle or tricycle, this only enforces my contention. The recumbent HPV has converged on this design approach, which I will refer to as Nufantom.  

The move toward commercial recumbent trikes appears to have been going on for some time, and now that I think about it, I have seen more Nufantom trikes than recumbent bikes on the local bike trail. It is not surprising. A new rider can adapt to riding a tricycle a lot faster than becoming confident on a recumbent bike. I have only seen a few enclosed trikes, but was recently very impressed with a Quest from Blue Velo.

Converging on a common solution allows designers to concentrate on refinements, since they don’t have to worry about the overall vehicle layout being feasible. The Quest exhibited a lot of refinements to the Nufantom approach. These included enclosed wheels for improved aerodynamics, cantilevered wheels all around for ease of flat repair, without removing the wheels, a monocoque chassis, a well thought-out suspension, Burrows-style u-joint steering controls and a very trick cover for the rear derailleur.

 As impressed as I am with the Quest, it doesn’t meet two of my criteria for a Human Powered Commuter Vehicle.  Most significantly it is too low to provide adequate visibility in traffic, and, case in point, I have only seen these vehicles on the bike trails. The other is ease-of-entry and riding posture. I suppose I could get used to the laid back seating, but my old back wouldn’t be too happy without a lumbar support. Entry and exit, however, appear to be extremely difficult, very similar to getting into a formula one car. The upside is the vehicle is statically stable for this process.

I have long felt that the recumbent bicycle is a transient form, evolving toward another vehicle. Streamlined recumbent bicycles will probably always hold the speed records, but for a utilitarian vehicle, the Nufantom-style trike seems to be the most popular option.

Arm-Power and the Avatar Recumbent

For short term, anaerobic, activities the energy available for physical activities is related to how much muscle mass can be recruited for the activity. The limitations imposed by the cardio-pulmonary system do not apply. During long term, aerobic, activities the rate of oxygen delivery to the muscles is the limiting factor in how much power an athlete can produce.

Back in the day, (prior to the HPV movement in the mid-1970s) the reining wisdom was that a cyclists employed enough muscle mass with their legs while pedaling to utilize all the oxygen the cardio-pulmonary system could deliver. Nothing would be gained by adding more muscle groups in propelling the bicycle. I strongly suspect that this idea came out of the ban of unconventional bicycles that was initiated by the Union Cyclist International in the 1930s and was not based on empirical data.

In the second edition of their book, “Textbook of Work Physiology”, Astrand & Rodahl do a literature study comparing the maximum oxygen consumption (Vo2 max) of various activities. If running uphill is scaled at 100%, horizontal running is between 95-100%, upright cycling is 92-96%, supine cycling is 82-85% and arm and leg cranking (where the load on the arms is 10-20% of the total load) is 100%. The above data must be taken with a grain of salt since it is a compilation of different tests. It does serve my purpose though, and that is to indicate that more power can be obtained by adding arm power to leg power, especially for pedaling in the recumbent position.

A major advantage to adding arm power to a recumbent is that the arms are not as involved in postural support as with an upright bike, and therefore can perform the task of propulsion while the rider remains stably mounted on the machine.

In the post “Rx for a Healthy Commute” I extol the comfort I experienced in riding an Avatar 2000 recumbent over a period of 22 years. What I didn’t mention was I never obtained upright-bicycle speeds while riding it. I attributed my lack of power to coming from a runner’s background, where more of the leg force came from the gluteus and hamstring muscles as opposed to the quadriceps muscles. I suspected that sitting on the major force generators significantly reduced my supine power output, but again I have no empirical data to substantiate this notion. On the other hand, I estimate that my recumbent speed was only about 80% that of my upright speed. This would equate to a drastic loss of power!

The bottom line, though, was I always felt I had cardio-pulmonary capacity I wasn’t using and the only way to remedy that would be to add more muscle mass to the job of propulsion.

So the question was what type of arm motion should I use?

There was an arm and leg cranked recumbent from the mid 1970s called the Manuped, invented by John Carl Thomas. It had leg cranks passing through the front wheel and hand cranks mounted on a fork above that wheel. The entire assembly pivoted to steer, and the seat and rear wheel comprised the rear portion of the frame. That’s Fred Tach (sp.?) riding a Manuped during the 1978 International Human Powered Speed Championships. I talked to Gary Hale who was riding a Manuped at the 1990 Speed Championships in Portland. Gary had made some of the frames for the Manupeds. When I asked him about the bike, he confided that it was very difficult to ride because of the arm and leg force inputs perturbing the steering. So I had a reason to not use the hand-crank-and-steer approach.

If one wants to avoid the differential force application of propelling and steering the alternative to hand cranking is a rowing motion. While rowing does not make as good of use of the legs as cycling, it involves the muscle mass of the back in addition to the arms. The decision was made to use a rowing motion for the arms and conventional pedaling for the legs. The two motions were not at all incompatible and worked quite well.

 

The basic approach is to have a rowing frame that pivots at the recumbent’s top tube and during its rotation pull a chain over a 16-tooth single-speed freewheel  attached to the left crank arm. The chain must pass under the freewheel to move the cranks in the correct direction, and therefore an idler is required to route the chain backward where it is kept taut by a screen-door spring attached to the bike frame.

 The handlebars are pivotally mounted within the rowing frame and the steering axis is perpendicular to the  rowing axis. The lever length of the rowing frame is 18.5” and it can rotate through 90deg.

The lever length for the drive chain attachment is adjustable from 3.5” to 8” in six, 0.9” increments. The chain is attached to the rowing frame by an old-style master link so it can be easily moved from one position to another. To determine the most-natural feeling position, I started riding down the street at 3.5”. After about 100’, I stopped because that was too easy and moved it to 4.4”. I rode about a quarter mile and moved it to 5.3”. By the time I was a mile away from home I was moving it back and forth between the 6.2” and 7.1”. I settled on the 6.2” position.  The resulting arm to leg motion during the power stroke (pulling the rowing lever from its most forward to most rearward position) equates to slightly less than one pedal rotation. Since the return stroke is faster than the power stroke, two pedal strokes are approximately equal to about 1.5 arm strokes.

Since less than 150 Avatars were build (mine is #085) I wanted to preserve its value, so the arm-power mechanism and the idler clamp around the frame tubes. The arm power mechanism includes a diagonal brace to stiffen the top tube against the bending moment imposed by the rowing. This approach could easily be adapted to any recumbent with the only major modification being the mounting of a single-speed freewheel on the left-hand-crank arm.

The handlebars are attached to a tube that pivots on bronze bushings that are in turn held by the rowing frame. The bottom of the handlebar tube is attached to a steering knuckle. The steering knuckle is connected to the fork by a tie-rod with spherical joints at both ends.

The key to why this design works so well is that the steering and rowing motions are decoupled. Rowing does not perturb the steering and steering does not require rowing. This occurs because the axis of the tie-rod bearing at the rowing link end passed through the rowing axis. As a result, the rowing motion does not move the tie-rod and does not perturb the steering. In fact the steering appears to be more stable while rowing. I surmise that this is because the rowing forces applied to the handlebars dampen out any unintended inputs.

Cable routing details, at handlebars and at the steering knuckle.

My seat was getting a bit wobbly so I took the opportunity to attach struts between the lower end of the diagonal brace and the ends of the seat tubes. I did loose seat adjustability by doing this. 

The only downside I can see with this approach is the added weight, added friction and the loss of the under-seat steering which I find so comfortable. On the upside the speed is significantly improved, especially on hills and it makes the bike a lot more fun to ride. It is especially fun to race along next to someone without using the arm power and then kick it in. You should see their faces! And because of the front wheel is lightly loaded, rapid application of rowing power has resulted in wheelies on a number of occasions; quite unheard of for a recumbent bicycle!

Hephaestus

Raptors Revisited

Now for those of you who are growing bored with my ongoing discussion of the Human Powered Commuter Vehicle, something completely different, dinosaur biomechanics.

It was like being a kid again, opening Adrian Desmond’s book  “Hot Blooded Dinosaurs” and seeing the picture of a sprinting dinosaur, gracefully leaning forward with tail stretched out behind. In an eye blink, the dinosaur love of my childhood (and many others as well), Tyrannosaurus Rex was replaced by this new creature, Deinonychus Antirrhopus.

Deinonychus was discovered and named by Prof. John Ostrom of the Yale-Peabody Museum in 1969. The name for this dinosaur was descriptive of the animal’s anatomy, meaning terrible claw & counter balance. Terrible claw of course referred to the sickle-shaped claw on the second digit of each foot and counter balance referred to a tail made rigid by bony extensions on the vertebrae.

Deinonychus could possibly be the most significant dinosaur discovery of the 20^th Century. The reason for this was the realization that if the sickle claw was used for attacking prey, the animal needed to be very athletic and  one that was more than likely warm blooded. To emphasize the point Robert T. Bakker, then a student of Prof. Ostrom drew a convincingly active restoration of Deinonychus, the image that graced Desmond’s book.

Prof. Ostrom also went on to observe strong similarities between the limb structure of Deinonychus and Archaeopteryx the famous proto-bird discovered in the 19^th century. Based on Archaeopteryx, Thomas Huxley advocated that birds descended from dinosaurs and because of the similarities he observed, Ostrom resurrected the idea. Of course, because of numerous fossils indicating the presence of feathers on clearly flightless dinosaurs, the bird from dinosaur decent is now accepted as fact.

21 years would pass since its discovery and Michael Crichton through his book, “Jurassic Park” and the subsequent movie would introduce the world at large to Deinonychus. Well not exactly…

Ironically, the dinosaur mentioned in the book and movie was a misnamed species, Velociraptor Antirrhopus. An amateur paleontologist, Greg Paul, had decided, incorrectly that two raptors were of the same genus. They were Velociraptor Mongoliensis and Deinonychus Antirrhopus.  Velociraptor was about 18” tall, weighed about 33lb. and had a long flat skull. Deinonychus was about 40” tall, weighed about 150lb. and had a rather deep skull.  Crichton may have known the name was incorrect and used Velociraptor anyway because it conveniently shortened to “raptor”, while I don’t know how to shorten Deinonychus except to shorten it to DA.  The movie took additional liberties by significantly enlarging their raptor to make it seem more fearsome, even though DA was fearsome anyway, hunting in packs like wolves. As life imitates art, a raptor was subsequently discovered about the size of the movie raptor, Utahraptor Ostrommaysorum, that weighed about 1100lb. After “Jurassic Park” the term raptor no longer referred to birds of prey like eagles, owls and vultures but instead to medium sized carnivorous dinosaurs with sickle-shaped claws on their feet.

Skip ahead another 15 years and the image of a raptor balancing on one foot and slashing its prey with the other is under attack.  The issue of contention is the function of the sickle-shaped claw.  One fact is that the horny talon that covered the toe ungual of the living raptor is not preserved in the fossil. As a result the actual shape of the claw can only be guessed at.

 

 The other fact is that only one living animal, a bird, the seriema, has severely curved claws used in a flesh-slicing role, but that is after the prey has been killed by smashing the body on a hard surface

 Arial raptors and cats have hooked claws and they use them as grapples to hook on to prey or for climbing, not to cut flesh with the inside edge. Cassowaries and ostriches can inflict severe injuries with the claws on their feet, but in both cases the claws are straight and the offensive motion is a forward kick. So there is a new theory that the claw was only used to scramble up the sides of prey and hold on, while the jaws did the dispatching.

Under the direction of Prof. Phil Manning at the University of Manchester, researchers built a mechanical raptor leg and evaluated the damage the sickle claw did to pig and crocodile cadavers.  The machine was designed to duplicate the leg and sickle-claw action of a 90lb. raptor. The results would definitely not be life threatening to the large sauropods that the raptors might prey upon.  The wounds to the pig cadaver were between 1.2 and 1.6” deep and the bunching skin made it difficult to extract the claw after penetration. The claw bounced off the crocodile hide. The intent of the testing was to validate the grapple and grasp theory but the results were not at all conclusive.

Before leaving the grapple & grasp theory, allow me a few observations about stress, strain and claw penetration. Strain or the stretching of the tissue is what causes damage to the animal. Strain is related to stress, and stress in its most basic form is force divided by area. The force component in the claw-induced tissue stress is the raptor’s weight since the full weight of the animal can be applied to the claw-tissue interface. The area term in the tissue stress is related to the size and shape of the claw. I find it interesting that 90lb. was chosen as that of the raptor simulated by the machine. Recall that a Velociraptor weighed about 30lb and a Deinonychus weighed 150lb. One must question what claw size was used in the machine since a Velociraptor claw would be too small and a DA claw would be too large.

Then there is the matter of shape. A claw with a circular cross-section would produce the lowest stress in the tissue during a puncture because the tensile or hoop stress at the edge of the wound would be uniform. An oval cross-section claw would produce higher stresses since more stretching would take place along the long sides of the ellipse. Finally a teardrop shape would produce the highest stresses with the peak stresses occurring at the point of the teardrop. For example, if a knife blade had been mounted to the roboraptor’s foot, the penetration would be substantial, since the cross-sectional area is small and the stresses are very high at the edge, something referred to as a stress concentration. In reality, however, bone and horn do not have the strength of steel so a claw as sharp and narrow as a knife blade is not possible.

The claw used in the machine appeared to have an oval cross-section with the short axis orientated through the thickness of the claw. The core of the claw was aluminum and it was covered with Kevlar and carbon fiber.

As an exercise to determine if the horny talon covering the toe bone could have had a sharp edge on the inner curve, I sculpted a DA claw out of .45”-thick glass-filled polycarbonate. I started with the outline of the horny talon Prof. Ostrom sketched around the second ungual with a finely-dashed line in his 1969 monograph on DA.

What resulted was a claw whose cross-section begins at the tip as an oval with the long axis through the thickness of the claw. This transitions to a flat-sided teardrop about 1.4” along the inner edge of the claw. Since the inner edge of the claw is about 3.5” long, 2.1” of the inner edge could be considered sharp. It would be interesting to see the depth of penetration with this claw used on the roboraptor.

The grapple & gasp theory has a lot of dissension. Reasons given for this range from the fact that Velociraptor’s jaws did not have enough bite force to dispatch live prey, to the fact that raptors that were probably too large to scramble up the sides of prey (Utahraptor) still possessed sickle claws. And then how does one interpret the famous Velociraptor vs. Protoceratops fossil?

When a raptor was attacking prey that was significantly larger that it and that could injure it if given the opportunity, it would be advantageous for the raptor to get in, inflict a wound or wounds and get out quickly. The raptor could uses it sickle claws as grapples to run over the back of the prey and get off before the prey could respond. The difference between this dash & slash approach and the grapple & grasp approach is in the extent to which each claw penetration injures the prey. This is probably a more probable scenario for how the sickle claw was used.

The other interesting feature of raptors (the actual family name is dromaeosaurs, named for a dinosaur discovered in 1922 and thereby predating Velociraptor from 1924) is the structure of the tail, which was stiffened for most of its length by bony rods that held it rigid while only allowing bending near the pelvis.  Again the above picture is from Prof. Ostrom’s 1969 monograph.

He suggested that lateral motion of the rigid tail could enhance “jinking” or rapid changes in direction.

A recent Velociraptor fossil discovery exhibited a tail with a moderate S-bend from side to side, so for the purposed of the subsequent discussion it will be assumed that the rigidity contributed by the caudal rods was mainly in the vertical plane.

Many bipedal dinosaurs appear to use their tails to shift their centers of gravity (c.g.) over their back legs so they can stand with their torsos horizontal, but they don’t require caudal rods to do so. Since this type of counter balance is basically a static condition, it is logical to assume that the caudal rods were required for dynamic activities, where the forces would be significantly larger.

Of particular interest is how vertical tail motion could be used to enhance the techniques employed to injure prey.

The dash & slash approach assumes that the raptor is moving continuously over its prey. The dynamics of the raptors motion is rather complex and difficult to visualize. However one can observe some of the effects of tail motion on a raptor clinging vertically to the side of its prey. The sketch above is a simple free-body diagram of a raptor in that state.  The condition here assumes that the raptor has leapt through the air and landed on the prey and is stationary vertically.  Point a is where the sickle claw attaches to the prey, point b is where the hands attach to the prey, point c is the c.g. of the raptor without its tail, point d is where the tail attaches to the body and point e is the c.g. of the tail. (I have made the simplifying assumption that the polar inertia of the tail about point d can be reduced to Mt*L4^2). With the arms grasping the prey, the raptor is in static equilibrium. This means that all the static forces sum to zero. The vertical reaction at the sickle claw, Rv, is equal to the sum of the body weight Fb and the tail weight Ft. The moment about point a =Fb*L2+Ft*(L3+L4) is reacted by the moment Rh1*L1. So statically the maximum force causing the sickle claw to penetrate the hide of the prey is the raptors weight. Now I doubt that a raptor spent much time statically hanging off the side of his prey but it is a starting point to examine the forces involved in its support.

For  the above case, if the raptor were to rotate his tail upward with an acceleration At, the force on the sickle claw would be increased over the body weight by Mt*At.  Snapping the tail up would drive the claw deeper into the prey.

Due to conservation of angular momentum, rotation of the tail while the raptor is airborne would result in an opposite rotation of the torso. The would allow the raptor to adjust its body posture with respect to the prey the same way long jumpers use their arms to adjust their body position before landing.

As the raptor lands on the prey but before its arms can grasp, there will be a tendency for it to rotate backward because of the unreacted moment of its weight acting about the claws contact point, a. Under these circumstances, if the tail is snapped downward hard enough, the torso could be made to rotate forward, allowing the hand claws to gain purchase.  Mt*At*L3 must be larger than Fb*L2 for this to happen. Note that statically Fb=Mb (the body mass)*g, the acceleration of gravity. As the animal lands Fb would be greater =Mb*(g + dg) where dg is the added deceleration to bring the raptor to a vertical stop.

Most carnivorous dinosaurs (Therapods) have the pubic bones of their pelvis facing forward. The fact that the pubic bones of raptors face rearward could be related to increasing the muscle leverage for rotating the tail in the vertical plane.

The sickle claws and the stiffened tail are very specialized adaptations in raptors. It is logical to assume that their function significantly enhances their effectiveness as predators.

Hephaestus

The Drymer and Varna Lean Forward

In my previous post (“Rx for a Healthy Commute” below), I proposed ten criteria I felt were necessary in the design of a human-powered commuter vehicle, or HPCV. In rough order of importance they are listed below.

1.       Weather Protection

2.       Statically Stable

3.       Reasonable Cruise Speed

4.       Cargo Carrying Capacity

5.       No Wider than a Bicycle

6.       Same Height as an Auto

7.       Comfortable posture and ease of entry

8.       Two-wheel drive

9.       Car-type Wheels

10.   Electric Assist for Hills

Now in the pervious post we examined the fact that criteria 5 and 6 seem to be mutually exclusive if you don’t want your tricycle to overturn while cornering. The concept of a leanable trike was proposed as a suggestion to address both criteria. The trike would lean at moderate to high speeds but the leaning mechanism could be locked out at low speeds and when the road conditions were slippery.

The concept of a leanable trike is not a new one and many auto, motorcycle and bicycle enthusiasts have experimented with the idea and at least one motorized vehicle is commercially produced.

There are basically four approaches to designing a leanable trike, two for one-wheel forward, OWF, and two for two-wheels forward, TWF layouts. Again I am only addressing wheel layouts that are symmetric about the front-to-back axis of the vehicle and layouts where the front wheel(s) do the steering.

For the OWF layout, the most common means of providing leanability is to allow the front wheel and the majority of the vehicle mass to rotate about a near horizontal pivot with respect to the rear-wheel pair. The rear wheels don’t lean and maintain their relative position to each other and to the ground.  Let us call this configuration the fixed-rear wheel or FRW for short. This FRW is popular for motorized vehicles because it allows both rear wheels to be driven the same as a non-leaning trike. In most cases the motor is part of the un-leaning mass. Since the motor mass does not tilt, the effectiveness of leaning on rollover resistance can be significantly reduced if the motor is heavy.

The Lean Machine is a prototype FRW vehicle from GM produced during the 1980s. The rear-motor pod remains stationary while the body and front wheel lean.

The Carver is a contemporary FRW leaning trike similar to the Lean Machine. The Carver is in production.

The other approach to allow an OFW vehicle to lean uses articulated-rear wheels or ARW for short. Usually a parallelogram linkage is used that moves one wheel down while moving the other wheel up. This approach is not as common as the FRW approach and is more common for human-powered trikes than motorized versions. The reason for this is it is more complicated to power the wheels for an ARW vehicle as opposed to a FRW vehicle. When used in human-powered trikes one has the additional option of driving a single rear wheel, both rear wheels or the front wheel.

 The vehicle above is the EcoVia, a prototype pedaled trike that uses the ARW approach to lean.  The drive chain connects the cranks to a drive shaft located under the seat. A gear cluster is rigidly attached to the drive shaft and two single-speed freewheels are attached at the outer ends of the drive shaft. The rear wheels are mounted on beams that rotate about the drive shaft. Each wheel has a fixed gear cog that is connected to the drive shaft freewheel by a second and third chain. A parallelogram linkage connects the beams, so as one moves down the other moves up. The dual freewheels on the ends of the drive shaft act as a positraction-style differential between the wheels. More on the EcoVia in a future post.

For TWF layouts, the most common means of leaning the vehicle it to use articulated-front wheels, AFW. Similarly to the ARW approach the wheels are interconnected, again usually by a parallelogram linkage, so as one moves down the other moves up. Of course, the TWF AFW layout has the additional complexity that the wheels must also turn. In almost all cases each wheel rotates on its own pivot and is interconnected by some form of tie rod. In many cases, the linkages for independent front suspension can be modified to couple those linkages and result in an AFW approach.

The Mercedes Life Jet is an example of the AFW approach. The rear wheel is driven in motorcycle fashion. The Life Jet uses coupled parallelogram linkages that allow suspension to be incorporated as well.

The last means of leaning a TWR trike is the fixed-front wheel approach, of FFW. I could not find a photo for an example of a FFW approach but I do recall a three-wheeled scooter that had two front wheels mounted very close together on a common axle.  

There are three methods of controlling the amount a vehicle leans to result in a turn where the resultant of the weight forces and the radial acceleration forces are aligned with the midplane of the vehicle; the balanced turn condition.  The radial acceleration force is the squared linear velocity of the vehicle divided by the radius of the turn. Therefore, the amount of banking for a balanced turn is determined by the speed of the vehicle and the tightness of the turn.

The most complex method of lean control is used in motorized vehicles that have electrical systems. A microprocessor can combine the inputs from a velocity sensor and a steering-angle sensor to arrive at the appropriate amount of lean. This signal is sent to some form of actuator that leans the vehicle.

The next method is to manually control the amount of lean. The Lean Machine had foot pedals to lean the vehicle and a hand control to do the steering. This method of two-input control doesn’t work as well when the rider’s feet are required to turn the pedals. Several vehicles have combined the steering and leaning controls into one motion.  These vehicles used coaster-type steering where the steered wheels were located at the ends of a common axle and the axle pivoted at its middle, like a child’s coaster. The pivot axis was inclined from vertical so the steering motion resulted in a tilting motion as well. These vehicles are correctly leaned for only one speed per steering angle. Since the vehicle requires less steering and more lean as the speed increases, the control is moving in the wrong direction. The control provides more lean with more steering angle. So, this approach works acceptably only for slower vehicles or where the speed range is narrow. Several children’s riding toys used this single input approach.

If the leaning system is well designed, consisting of a mechanism that leans the vehicle about an axis at ground level (mimicking the tilting of a single tire at the ground plane), than the vehicle can be ridden like a bicycle with no leaning control required. The approach, which we can call free leaning, is probably the most popular with light-weight human-powered vehicles and clearly it is the simplest. The addition of a manual lean-lock mechanism for very low speeds and slippery conditions makes this approach work for all conditions. 

There is an ever increasing amount of interest in leaning trikes in the human-powered vehicle community. One is in production from Canada and another is nearing production from the Netherlands.

http://www.varnahandcycles.com/video.htm#hc16

The Varna cargo trike is the brainchild of George Georgiev, designer and builder of the Varna Tempest, the world’s fastest HPV (refer to “Back to the Future” below). With his ability to come up with simple but elegant solutions, Georgiev has come up with a very simple design for an OWF tilting trike. The trike is made up of two portions. The front section incorporates the front wheel, steering, pedals and seat. The rear section incorporates the two rear wheels, the freewheel and space for a rather-copious-cargo rack. The two sections are connected by a horizontal pivot behind the seat support which allows the front section to tilt with respect to the rear section. The leaning is therefore accomplished by the FRW approach. Within the horizontal tubes making up the pivot is a torsion spring that resists leaning too far. So the system is basically a limiting form of free leaning. The chain is long enough that the misalignment between the tilted crank and non-tilted freewheel can be ignored. Only one of the two rear wheels is driven, the other just spins freely.  The rear-wheel track is 16”. There is also an hub-motor option for electric power assist. The cost is $3590 with electric assist and $2650 without.

The other leaning trike is the Drymer from the Netherlands. The intent is that it will be in production soon. 

http://www.youtube.com/watch?v=KtHyF8DQ9ls&feature=related

I must admit when I saw the Drymer video I thought I was watching a contemporary version of the Pedicar. The Drymer is a TWF trike that uses a AFW approach to leaning. The weight distribution of the wheels is a bit odd. Most of the weight is on the rear wheel for reasons of increased traction. As a result, each front wheel is lightly loaded and more prone to lateral slippage than is desirable. As you can see it is semi-enclosed, has a moderate cargo capacity behind the seat, 20 Liters, and has the option of a hub motor in the rear wheel for electric assist that will allow for a speed of 25kph. Cost is to be 6000 Euros for the full-up model with the body and electric assist and 3000 Euros for the base model.

So how do these vehicles measure up against the 10 HPCV criteria? I will add some speculation as to what can be done to meet the criteria if they are not already met.

1.       Weather Protection:  The Varna has no weather protection. Its long wheelbase and high rider position would make a faring rather bulky but something approximating the Lean Machines body could be made to work.

The Drymer has a body that provides some weather protection but the sides need to be enclosed to make it practical for very wet conditions

2.       Statically Stable: Since each vehicle is a trike, they can be made statically stable by locking up the lean. It is not clear that the Drymer has any lean-lock mechanism. The torsion spring on the Varna acts as a lean-limiter.

3.       Reasonable Cruise Speed: Without a body the Varna is limited to bicycle like speeds when pedaled.  A bit more streamlining on the Drymer might bump up it cruise speed to closer to 25mph.

4.       Cargo Carrying Capacity: The Varna has a very large cargo capacity. It should be noted though that the cargo does not lean. The more weight that is carried the less effective the leaning is in preventing overturning when cornering. The cargo capacity of the Drymer seems adequate.

5.       No Wider than a Bicycle: I think a target number here should be about 24” or less. The Varna is no wider than the rider’s shoulders so it is definitely narrow enough. The Drymer’s track is about 28” but there appears to be room to narrow that somewhat.

6.       Same Height as an Auto: Both vehicles have a safe rider height.

7.       Comfortable posture and ease of entry:  Both vehicles have good ease of entry and a comfortable rider posture.

8.       Two-wheel drive: There is no simple way to give the Drymer two-wheel drive. The Varna, on the other hand could have the freewheel fixed to a continuous axle and put ratchets in each wheel to provide two-wheel-drive with a positraction-type differential effect.

9.       Car-type Wheels:  Both vehicles could be converted to car-style wheels. In fact the front wheels on the Drymer are supported on only one side. So if the Drymer’s rear wheels were cantilevered and the Varna’s front wheel was cantilevered, they could employ car-style wheels where each wheel was the same.

10.   Electric Assist for Hills. Both vehicles already employ electric assist options. However, I question if hub motors are appropriate for the high-torque low-speed requirements hill climbing.

In conclusion, then, the lack of a body on the Varna trike keeps it from having any real potential as a HPCV. The Drymer, on the other hand, has a great deal of potential with more of an enclosing body and some additional aerodynamic improvements.

Hephaestus