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)
Red fairing Racing Amsterdam 2008


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.


This type of crank might be of good use when operated by hand:

Arm motion

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.

isometric view A (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).

lateral view 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.

isometric view C (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.

Relative motion (Click to see larger picture)


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.

Load test

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.

Top view

Construction Details

Frank Bokhorst,
Updated January 2004