Cycloid drive

Miles Kingsbury reports a 90% efficiency on his cycloid drive:

"We have also found that although the drive is mechanically very efficient, physiologically it was not so good. We did a number of tests and found it was only about 90% as efficient as a circular drive. In the end we decided this inefficiency was caused because the main leg muscles were performing a 50% duty cycle compared with only about half that on a circular drive. Although it seems that this higher duty cycle should help efficiency, it doesn’t allow the muscles to recover and get rid of lactic acid build up, causing a severe burning sensation! ".

I will try to make a multi body analysis of this drive. It may be the problem is the kinetic energy of the thigh, calf and foot at the extreme positions. The cyclist has to do work for decelerating and accelerating his legs at the returns.

A page of Human Power, the technical journal of the IHPVA issue Volume 8 No2, spring 1990

Lineair drive

The conventional pedal rotates around the crank axle. In a velomobile with rotating pedals the feet are not only moving in driving direction but also up and down. Should the up and downwards motion be done away with the nose of the velomobile could be much lower. That may improve the aerodynamics of the body.

multi body of a human leg

Instead of a rotating crank we could use an oscillating crank. The pedals would move for and backwards while the crank rotates 60º only. The cranks could be connected via 2 sprag clutches to the wheels. But than the pedal speed would be almost constant. Only at both extreme positions the pedal speed would have to change very fast to the opposite direction. Is that comfortable and efficient?

motion of center of gravity of thigh, calf and foot [m]

To get an impression about the losses that could be created I calculated the kinetic energy of the thigh, calf and feet of a human leg while driving the lineair drive. At the returning positions they are 2 and 5 Joule. The last value is when the leg is stretched. Humans (animals too) are able to optimize their motion. It could be that we would stretch out our foot in the last phase to reach the most stretched leg position. In that case the kinetic energy of the thigh and calf would be recuperated. I think this is what we do while we are running.

kinetic energies Et: translation, Er: rotation

But in the most pessimistic approach all kinetic energy would get lost: 7 Joule at every stroke. At a normal frequency of 1.5 Hz that would amount up to 2*7*1.5=21 Watt. That is an enormous  amount. A normal bicyclist produces 75 to 150 Watt! It may be that the foot motion has to be decelerated and accelerated in a controlled way at the returns. This kind of loss may exist in the rowing bike too. Is there anyone out there who has done experiments with lineair drives? Paul Jaray developed a similar drive in 1920. Miles Kingbury developed an interesting alternative: the K-drive. The Human Power-team is experimenting with it too.