Here comes another epic response -- you have been warned :-) 25hz wrote:
First, let me say that I appreciate the effort you have gone into making the PDF plans and all the engineering work and math you've applied to the trike. It's very impressive, I think, compared to the way I sort of fly by the seat of my pants, go by feel and modify what I know and what I have seen done by others.Likewise, I really appreciate your willingness to share what you have on your own web site. I have been following your adventures in recumbent bike/trike building for quite some time now.
On the engineering side, having made so many seemingly obvious mistakes on my first prototype -- which was very "seat of your pants" -- I figured I would put a bit more work into the CAD next time round. The first project I actually did with CAD was a spray unit for a winter pumpkin crop. I spent 4 evenings doing the CAD and drafting, 1 day cutting out the metal, and 3 days fabricating, painting and connecting up the pump and hoses. My previous implement, an orbital transplanter took about 4 weeks to put together. From that experience, I decided to use CAD as much as possible, because you really save a lot of time compared to the design-as-you-go and in my case, make fewer mistakes.
I especially like how you took the tilting rear end design, and now there is a third method to do it. The vertical rocker arm like Bram Smit's, the tilting rear wheels like Paul Sims', and now your horizontal rocker arm type. I guess there's still the parallelogram type to explore yet too :) I have a couple observations/questions that I'm curious about - it might be a little rambling and not in any real order though :) So, pardon the impending epic, and onward . . .This is one of these questions that I will only be able to answer when I finish building it. My first prototype was self centering when the rider was not seated in it, but it had a completely different steering geometry, and the tilting and steering were linked together. It suffered from serious bump steer, which on a road shoulder is actually much more undesirable than one might think.I built a rear end like Paul Sims' and put it on the back of one of my pythons. When you rode it, it felt exactly like the two wheeled version. While it rode the same as the two wheeled python, it wasn't self righting any more than a python is when turning. If you got off it without the tilt lock engaged, it would flop over to the side til it hit the tilt stop. If it tilted far enough, even the CoG of the empty trike went outside the front wheel - rear wheel line and it would tip over. So, the idea is, if the CoG is lower than swing arm pivot, the trike will be statically self righting?
You are correct, these are all static 2D simulations. Thats all I really know how to do at this time. A 3D simulation would definitely be better, but even the 2D simulation despite its limitations has helped me get a much better understanding of what is going on. The nice thing about it is you can lock the tilt angle, then make one of the other dimensions driven, and drag it back and forth to see what impact is has on the seat height and CoG.>From the 3 pythons I built, due to the pivot location, the CoG track on the ground was outside that of the tracks produced by the front and rear wheel of a two wheeled python during a turn. On a trike, there would then be 4 tracks - 3 wheels, one CoG. The CoG and front wheel planes might be parallel, but they don't follow the same track in my experience, so I'm not sure about that reference in your latest PDF unless I missed the point completely - which is possible.
Yes that is my goal, my first prototype was self centering if the rider was close to center, but once it tipped, you had to lean very hard to bring it back, it it went too far you could tip over. It had a very strong tendency to oversteer.Someone mentioned whether the CoG should move towards the inside of a turn or to the outside. If the CoG moves inwards, the python will want to turn harder, it'll corner harder but it won't self-right. If the CoG moves outwards, you'll need to work a little harder to keep it in the turn, you might need to physically lean into the turn to keep it from tipping on a hard/fast corner, but it'll self-right better. I guess the magic detail is the CoG's vertical position in relation to the "virtual" tilt position. It would be cool to sit on a tilting three wheeler that just stayed upright without having the need of a tilt lock.
Looking at the angle of "B" in your latest PDF I can see how the design is automatically providing a tilt limit. From experience though, you can lean a python into a corner so hard and so fast that you have to get your hands away from the handlbars or you'll grind them on the ground. All three pythons I made have major scuff marks on the brake levers and pedal ends. You can lean so far that you end up on the sidewall of the tires where there is no tread and you can slide out on clean, bare pavement. With the trike design being self-stable, I don't see why you would need a tilt limit at all.The tilt limit wasn't something I planned, it is a function of how the geometry that provides the self centering effect works. If you increase the angle on which the tilt lock occurs past 30 degrees, the seat height no longer raises. The only way you could get around this would be to replace Items 35 on the swing arms with a Cam with a diminishing radius and use pulleys and cables that cross in the center rather than the rocker arm. If you did this, the cam would control how much the seat rose, and their would be not tilt limit, but this is too complicated for me to envisage fabricating right now, but if the steering lock proves to be too much of a problem, then this is the only alternative I have come up with.
At lower speeds you can simply do a flat turn so there's no danger of tipping over too far, or even tipping at all. All this of course is if the trike self righting force is as strong as I think it is. If you limit the tilt angle too much you could easily find yourself in a situation where you don't have enough lean to safely complete a turn. At 90 degrees, it should provide close to 45 degrees of tilt and that might not even be enough :) Was it your intention to purposefully have some lateral force on a turn so you would physically have to lean in on a turn to maintain some kind of "input" or "road sense" on the python trike design?Again this is the trade off. I do believe however, that by having the seat in a tilted position, it will be easier to lean harder than on an upright non-tilting trike, and as such your cornering speed will be much higher. On my first prototype, even with the oversteer, you could take a corner at a very high speed, the wheel would flop over, then the centripetal forces as you lifted your body would unlock the cornering and before you knew it you had done a 180 and were heading in the other direction. I only attempted this in a grassy paddock, because I really had no control over it -- but it was fun -- waahoo! :-D
It is straight, but offset from the pivot so the angle is 170 or 190 degrees between the pivot and the rod ends, depending on which side you measure it.>From the initial plans, I assumed the rocker arm was straight, but apparently it is not.
Looking at the picture, the rocker arm seems to be applying a similar kind of geometry as Ackerman compensation does to steering. If I am looking at it correctly, on a turn, the inside wheel will raise less than the outside wheel will lower, and this will artificially "lift" the outside wheel higher and should produce some or all of the lifting motion of the CoG on a turn (in addition to the normal lifting amount the main pivot provides).This is exactly right, the geometry is all about getting the inside swing arm that you are leaning on to move down by a smaller amount than the arm on the outside that is lifting you up. I have not included the main steering pivot raising in any of my assumptions, I have actually treated them as independent, as they probably should be. In my experience the tilting mechanism should function independently from the steering.
If I am looking at that right, is that artifical lifting action part of the mechanism that produces the self-centering effect?Thats all there is to it. It seems simple enough now as you describe it, but as I said in my last PDF, there were a lot of things that I though would influence it, but none of them amounted to anything more than a few millimeters. Not enough to get the seat up at all. It was only angle B that worked at all. With the rocker arm angle slightly improving it. The swing arm length also effects how high the seat raises, as does the track, but at the expense of maximum tilt. You can very easily knock it back to less than 15 degrees if you are not careful. The whole geometry is not to be trifled with, change things by small mounts and it stops working. Later when I have the results from the trike itself I will write all this info up on my web site with clearer diagrams etc. But all this is dependent on the trike actually working as expected.
If you angle the swing arms up or down you actually end up limiting the seat raising. And it raises by such a small amount 15-20mm, that a few mm really counts. Again, I wouldn't have expected this.Was there any structural/loading reason to decide that keeping the swingarms parallel to the ground was preferred to angled up or down, or was it just personal preference? With the swingarm loading being mainly radial with a little torque from the off-set wheel, the radial loading during cornering should be a non-issue, and the more the swingarms are angled up or down, the more of the torquing moment is converted to a bending moment, which squares like much better than twisting.
I ended up using 25 x 25 x 1.6mm because that is the smallest SHS profile I can get here. Smorgan Steel does have a 20 x 20 x 1.6mm in the catalog, but no one stocks it.I'm going to make a new tilting rear end for the python, but with a couple changes to your design. I'm not sure how many different metric sizes and graduations they make steel in, but up here it's mainly imperial so some sizes I mention may not be available from one scale to the next. Some questions/observations from a fabrication point of view. - Item 24 - I used to use the same as you designed, but I found I could go down to 3/4" x 1.6mm, and they are still more than strong enough. You might even be able to go down to 1.2mm. You can also use square plastic chair leg feet to close off the end so you don't need to weld it :)
- Rocker arm - I have used 1" x 1.6mm for similar tasks and it was more than strong enough for a short lever arm like your rocker arm. I'm going to use 35 x 1.2mm for mine though, because it is about 60% stronger than the 1" and about 5% lighter too.Yes I originally spec'd 25 x 25 x 1.6mm, and figured that the flex would provide a bit of spring, but then I though, what if I bent it, or tore the end off at a particularly inconspicuous occasion, better to use elastomers to provide the spring than box steel. Not that steel is as likely to fatigue like Alu, but the heat effected zone of the weld may.
I can only get 1.2mm in 304 or 316 stainless, which has a higher tensile strength than C450 (which is like your 4130) but the stainless has a much lower yield strength. I was originally going to make the whole trike out of 316 stainless but the engineering firm that is lathing out the bearing housings said it would cost quite a bit more. The stainless steel people also said they had 40 x 20 x 1.6 RHS over the phone, but when I turned up to buy some, said I must have been confused, as they only had it in Alu. So all in all my experience with stainless was bad, so I went with C450 structural steel. I can even get CroMo here from a motor racing materials supplier, but then you have to get the frame baked and quenched to get the full strength, so whats the point.
I will have to construct the 40 x 10 x 1.6mm RHS by slicing 40 x 40 x 1.6 with a table cutoff saw and welding it together.
- Swing arm - I'm going to use the same 35 x 1.2mm as I think it's strong enough to resist the twisting effect being that it's only about 15" long. I could try 1" x 1.6mm but not sure how it would handle the torsion. The smaller size tube would only be for cosmetics.Yes, when you look at the total weight on the back end, and on each arm its not that much, but from my experience on the first prototype, if you accidentally lean the trike too hard for some reason, you do load the inside swing arm quite a bit, the wheel is on an angle and all that leverage is twisting the arm, so a bit of extra strength I think is a good thing, but not so much that it becomes a battle ship!
- Item 39 - With both the swingarm and item 35 being notched and welded to item 4, do you even need the gusset? I've seen entire trike frames with only one joint like this connecting the rear end of a trike to the backbone and this swingarm assembly only has to support a portion of the total trike load. I think it would be bullet-proof without the gusset because you have a lot of bead length on the swing arm tube and item 35. Engineering wise, did the math say the gusset was needed due to the loading or it's just a "better safe than sorry" kind of deal? :)With my CAD software I can only do static loading on each piece, which isn't really that helpful, so only a few things were actually "engineered" with much certainty. In this case I agree with you, but when you consider that the riders weight on a lean is pulling against Item 35, and the rocker is pulling it slightly to the inside, a gusset is only a little extra weight and heaps of extra strength. Although I havn't drawn it that way in the design because it was a hassle, I actually plan to weld it on at a slight outward angle away from the rocker arm pivot to give it a bit of lateral support.
- Item 19 - Does the frame need to have two of these shaped in a "Y"? I understand why you did them, but if the trike tilts and the swingarms on both ends of item 22 roughly distribute the loading, there should be no/minimal twisting load on the rear end, so item 17 won't be in any danger of being twisted. In fact, I've built 3 trikes with the main backbone made out of 40 x 1.6mm (which would act as item 17) and they have crossmembers made out of only 25 x 1.6mm (which would act as item 22) and they don't twist or torque at all and these cross members are longer than your item 22 and they are on non-tilting tadpoles: http://fleettrikes.com/flying%20cross%20front.jpg http://fleettrikes.com/ice%20trike%20front.jpg http://fleettrikes.com/flying%20cross%20rs%20front.jpg I would humbly offer that you can simplify the rear frame into a T-section of #17 meeting #22, and completely get rid of both #19's. I'll build mine like that and see how it works out :)I originally had a T as you describe in the first set of plans I drew up, but there is a lot of force pulling on the rocker arm which has the effect of bowing the frame up as it pulls on item 20 with item 17 as the fulcrum with the riders weight pushing down against it on the other side. The only place for these moments to give was the T bar. So I decided to triangulate and thus the Y. You are right, if you keep Items 19, you definitely could make item 22 lighter (25 x 25 x 1.6mm).
My rod ends are M8 male and female screwed together with a lock nut, so the center to center distance is 60mm. This lifts the seat with angle B being 125 degrees. However if this proved too much, I can loosen them out another 5mm or so and this will make the seat height neutral and increase the maximum tilt. So there is a bit of adjustably built into this design.For the rod ends/Heim joints, I'm going to use 5/16" but I think 1/4" would likely work just fine too. I used 1/4" on the python delta and didn't have any problems, but I didn't have it together long enough for any real durability test ither though.
Suspension. I have an idea I want to put suspenion on it too, and there are two (hopefully) simple ways to do it, and quite likely more. One method is to cut item 16 under the seat and insert a pivot so the whole rear end is suspended. The other is to mount the rocker arm on a vertical tube which is hinged at the top and put the suspension solely on the rocker bar instead. I think the 2nd option might be the easier one. While I never really had the need for suspenion on any bent, I'm getting old and my creaking joints appreciate a little softer ride now :)I am planning to include suspension too. How I plan to do it is replace items 33 and 38 with an elastomer housing through which a bolt linking to the rod ends will go. But I agree, the rocker arm is the place to put the suspension. I had also considered having a two piece rocker arm with a hinge in the middle and an elastomer between it, but I have already spent enough on custom bearing housings for this project. If this design works, that is how I would do it in the future.
Not at all, I am grateful that you took the time to give it such a thorough review, and I have a great deal of respect for your experience in these matters, having built many more trikes than I have.I hope you don't take offense at any of my questions, comments or changes because they aren't meant to do that.
I try to minimize and/or simplify when and where I can and my intent is to help. A I said at the top, I'm very impressed with the amount of effort you have put into the design and providing plans. Some of the technical/engineering/physics aspects I'm a little fuzzy on so that's why I asked. In some of the other things, from personal experience, I think it will make it easier for you to build and/or make it lighter.Yes, I think the open design approach for us amateur enthusiasts is the way to go. Pooling our knowledge so we can stand on each others shoulders so the sum of our combined efforts becomes greater than the sum of us as individuals.
For the prototype I laced up some wheel chair hubs onto 24" rims. They were 36 spoke, nice and light, and gave a nice ride across uneven ground, but I still managed to bend them out of shape, but again that was because it was a heavy frame, with wheel flop and oversteer combined with the steering being linked to the tilting. It all put way too much weight on those poor wheels. If this design works I may use them again on a street machine with the same back end, but I may try something like Laurent's speculoos on the front.I think somewhere that you mentioned rear wheels too. On a tadpole, I pretty much used the same thing as you - 14mm axle BMX wheels with 48 spokes. The 14mm is great because of the strength needed for single side mounting. The 48 spokes are great for the high lateral loading on cornering for riders I've seen that weighed 350lbs +. In my experience though, for even a 250lb rider, I think the 48 spokes are massive overkill and I'm seriously considering going to 36 spokes on tadpoles, and maybe even down to 24 spokes (a half laced 48) at some point. Now, with a tilting python delta, guaranteed you could easily get away with 36 or 32 spoke wheels because the loading is pretty much radial. The only issue is finding 32 and 36 hole hubs with stong enough axles.
One simple source is the stroller/joggers. They come with 12, 16 and 20 inch rear wheels, and they also already have 1/2" sealed bearings AND the tires and tubes are usually included in the price. They also come with AL or steel rims and often cost less than the BMX wheels. Another option is to take a 20mm MTB hub and lace your own wheels - more expensive and more work intensive. If you already have the BMX wheels, I would take half the spokes out of them. If half-spoking them because of the radial vs lateral loading is not enough to convince you, think about the fact that teh 48 spokes are there because there's only 2 wheels total (not 3 like on your trike) and they are built to ride pipes, jumps and to drive off the roof of a two storey house onto hard pavement :) I don't know how heavy you are, but I think somewhere around 200 lbs is likely the limit for 16 or 18 spoke wheels (half spoked 32 and 36h wheels). So, anything under that weight and you're likely good to go.I plan to stick with the 48 spokes for now, the roads around the farm are pretty rough, and I have a penchant for riding off curbs and across railway tracks (we have a narrow gage main line to the sugar mill cutting right through our property) so tough rims and stiff wheels = longer working life -- as long as I can keep the dirt and dust out them.
----Few, another epic draws to a close, thanks again for all your kind words and thoughtful critique.
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