Elliptical Drivetrain
This page describes the construction of a bicycle drivetrain in
which the pedals move not in a circular path, but either a linear
or else elliptical path.
Various reasons for such an unconventional design have been put
forward. One of these is that on a recumbent bike, perhaps a more
aerodynamic fairing design becomes possible. An example is the
"K-drive", as used on the Kingsbury "Kingcycle" in a successful
speed record-breaking attempt in the early 1990's in the United
Kingdom.
The picture of an unknown racer shown below clearly illustrates the kind of
fairing shape that can be used (on right, Amsterdam 2008)
Background
There are many varieties of non-circular pedalling
systems, and hundreds of patents have been granted. To the best
of my knowledge, the K-drive has not been patented. There is a
1995 patent granted to A.Stiller and D.Walton (US pat. 5419572)
for a design based on Cardan gears, which is a planetary
gear system in which, any point on the periphery of a
circle rolling inside another circle describes a
hypocycloid. If the diameter of the two circles is exactly
in the ratio 2:1 then the movement is linear. Stiller et
al. describe an invention using Cardan gears for a bicycle
pedal drive, and mention that exactly the same effect can be obtained
using a chain and sprockets instead of gears.
Some historical examples, and other contemporary work:
Building an elliptical drive
A sprocket and gear arrangement will give linear motion if the
two crank arms are equal in length. In the Kingcycle K-drive an
elliptical path was chosen, obtained by making the secondary
crank shorter than the primary crank (see construction details
below). This kind of motion is illustrated in the animated
sequences shown below.
The primary crank length is 120mm and the secondary crank length is
75mm, so the elliptical pedal path has a major axis of 390mm and a
minor axis of 90mm.
Handcycling
This type of crank might be of good use when operated by hand:
Click on the image above to find more details.
Design Details
The biggest challenge in the design is to combine strength and
compact size. Bicycle pedals take relatively high loads at low
speeds. The crank assembly occupies a space of no more than
15 cm wide between the rider's feet (sometimes called the
Q-factor). In a conventional design the
entire crank assembly forms a single unit that rotates on a pair
of bearings mounted to the bike frame. In an elliptical system,
however, each crank is articulated in two parts with a short stub
axle at the fulcrum. Within this space a secondary chain must be
accomodated on the left and the right side, each with a sprocket
fixed to the bearing shell (the so-called BB or bottom bracket
shell). For maximum efficiency these articulated cranks rotate
on ball bearings, and given the high loads, a pair of bearings is
required. Bearings and chains come in fixed sizes (unless very
costly custom-made component are to be used) and thus impose
constraints on the design. Moveover, the chainwheel must lie
inside the secondary chain and yet clear the bicycle frame in
such a way that the chain can be routed to the wheel (an
exception would be if a huge chainwheel with a radius larger than
the length of the primary crank were used). These critical
lateral dimensions must be considered in the design.
Below are three CAD images to illustrate the concepts (note CAD was
not used for the actual design phase). Only the right-hand side
is shown. Figure A below shows the several 'layers' of components
and how they rotate (blue arrows). Note that makethe secondary crank
rotates in a direction counter to the primary crank onto which
the chainwheel (green in the figure below) is fixed. The
stationary sprocket fixed to the BB bearing shell is shown in
grey, and the bearings for the stub axle are in red. Note also
the slack in the secondary chain. In the animated sequences but
not shown in the CAD images, it will be seen that a spring-loaded
idler wheel takes up this slack.
(Click to see larger CAD generated image)
Figure B below shows the lateral dimensions and clearances
between the main components (the primary and secondary cranks are
light blue in Figure B).
(Click to see larger CAD generated image)
Figure C shows the relative lengths of the primary (120mm) and secondary
cranks (75mm), as well as how the shaft (in blue) is affixed to the
primary crank.
(Click to see larger CAD generated image)
In the picture below, which was taken with a slow shutter speed
so that motion is blurred, you can clearly see that the secondary chain
is stationary relative to the BB.
(Click to see larger picture)
Construction
A working prototype has been built, and the video clips below
show it being run under realistic load conditions on a testbed
that I built. The load was provided by mounting a conventional
18t freewheel on the driveshaft of a spray-painting air compressor
which is normally powered by a 1hp electric motor. Here the motor
is actually being powered by the pedal cranks.
With suitable
gearing it was possible to pedal at a realistic "road" speed and
load while driving the compressor at about 1/4 normal speed.
Some critical lateral dimensions are shown in a view of the assembly
as seen from above, mounted with two sturdy U-bolts on the test frame.
Q = 150mm is the distance between pedals as normally defined;
A = 100mm is the distance between center-lines of the two secondary
chains; B = 90mm is the inside clearance between the two primary cranks.
Click on the image to see a larger view.
Construction Details
Frank Bokhorst,
Updated January 2004
(Click to see larger CAD generated image)
(Click to see larger CAD generated image)
(Click to see larger CAD generated image)
(Click to see larger picture)
