Skateboard physics: one-spring truck (and the dead-zone problem)

In this entry I want to write down a couple of things that relate to a project that might or might not happen in the future. It’s an idea by a friend (whose handle is “Holden”), who already built a few two-spring trucks. His dream was (still is) to built a one-spring truck.

Holden believes that the fewer the parts that have to compress/decompress, the less the wasted energy in friction. It follows that if a design could utilize one spring instead of two, it would be an improvement.

Why a spring and not a bushing? Because steel springs have minimal energy loss due to compression and decompression. PU bushings compress and decompress with their polymers. Those polymers decay and after a few months of use we need to change them for fresh ones. The decay itself indicates there’s energy loss.

The idea for a feasible one-spring truck came from a member of the Pavedwave forum, inspired in turn by a Lego. The user with the handle “Red leader” proposed to hook the spring’s one end on the the hanger and the other end on the base-plate, so that roughly the middle of the spring hovers over the pivot axis. Thus, when the truck turns, the spring compresses.

One problem with this: it would be necessary to have a significant amount of “rake” (i.e. axle offset): distance between the axle (the line connecting the wheels’ centers) and the pivot axis (the line around which the axle rotates). OR, if you don’t want to have any axle offset, you would need to mount the bottom end of the spring on a point significantly far from the axle, but which point (obviously) needs to rotate with the axle around the pivot axis. Therefore, I ask this: how do you avoid having to mount the spring far below the axle (a problem pertinent to the rear truck which is low angled) or build the axle far in front of the pivot axis (problem pertinent to the front truck which is high angled)? Red leader wrote:

Basically, there needs to be the correct spacing between the axle line and the connection point (and really, all the connection points and ratios) to make the spring tension (both compression and rebound) work well enough. I think that if the upper spring mount was located too close to the pivot point, you’d lose spring tension. Likewise, if you had the lower spring mount too close to the pivot point, same thing. There has to be an ideal distance vs spring pressure ration that would need to be found for it to work. Potentially, because the angle of the front truck on an LDP setup is pretty angled (in the drawing, it is straight up and down for the drawing’s sake), you could probably have a spring bottom attachment point below the axle and with the entire contraption being at an angle, it still wouldn’t sit below the axle once tilted. This it why it would be good to start with the front truck. I don’t know if this design would be possible in a ‘high tension’ setup like the rear truck.

Another problem was pointed out by Nickie. They wrote:

The return to center would be pretty blurry with a progressive dead zone where the spring tension gives zero torque even with the strongest tension.

I spent some time graphing the two designs’ (1- and 2-spring) axle torque, using Step. [never mind the numbers, it’s the shape of the curve that matters]. Two springs, one on each side, looks quite linear:

With one-spring, I would guess the axle mount point of the spring should be as far from the pivot axis as the base-plate mount point (i.e., equidistant), so that compression for any length of spring would be maximum. Nickie was right: the dead-zone is quite wide.

I decided to see what happens if you mount the spring in 1) different relative distances from the axis, 2) same mount distance but a spring with different stiffness and 3) same mounting and stiffness but different rest lengths (i.e., compression in the neutral/centered position). What I came up with is good news for Red leader’s and Holden’s idea and the dead-zone problem: if we start with the spring in tension then it’s torque graph becomes more linear.

Here’s mounting the spring further behind but not compressed in neutral (i.e. no turn); same as for a harder spring (didn’t get a screenshot for that) [i.e., cases 1) and 2) above]. Dead-zone’s still here:

Finally, here it’s mounted in the same position (equal distances from pivot axis), but pre-compressed in neutral [superimposed with the no-tension curve, for easy visual comparison]; the dead-zone problem disappears if you start with a spring in compression (even just a little; in this simulation I only added 5% more length-at-rest to the spring). In retrospect it makes total sense: of course the spring will push back if it’s compressed to begin with!

The conclusion I draw is that the push-back profile is very adjustable with one spring (more so than with two springs) [see graph below for a comparison between a 0% and a 3% pre-compressed spring]. Also, the pivot axis needs not necessarily be in the middle of the spring (see third graph), so we shouldn’t let that be a constraint.

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