Thierry-GearsManiac

In other words, slowly moving away from the concept of multipurpose/versatile-but-less-efficient gears (often found in construction sets) to efficient, specialized, industry-like ones (hence the separation between spur and truely bevel gears).

I'm sure that Akiyuki will fix the torsion of the central axle soon : he already faced this kind of problem, as showed in this video from himself : https://www.youtube.com/watch?v=drmlBqzqJSo Although he can't build a thick axle here, between the output gear and the "rotor", there are possibilities to add 2 or 4 supporting structures between the Z40 output gear and some of the axle-made beams (which hold the vertical rails) in order to relieve the central axle. As an extra option, we can also use a bigger output gear like a turntable or a ring of banana gears, attaching it the same way on the "rotor".

And, as a thoretical reminder, a rule of thumb I found once somewhere on a LEGO-related website states that the tolerance for gear distances is +-0.05 stud. (therefore, in this case, with sqrt(2) = approx. 1.41, VS the optimal distance of 1.25, we have 0.16 more, which is way too much)

Z12, Z20 pure spur gear variations, including the clutch variant... ... but when will LEGO complete the Technic gear range with the Z32 size ? It currently only exists as a custom design. (I can't imagine/mention all new use cases it will cover, beginning with easy 1:4 ratios, despite the half stud spacing)

It reminds me this variant of a locker-based Geneva mechanism : I noticed this principle long time ago in several door lock types, but I never thought about implementing it in LEGO for intermittent rotation.

It reminds me the intermittent mechanism found in this old GBC Cardan Lift version : In order to achieve the intermittent motion, any oscillating planetary mechanism (a differential is a special case of planetary mechanism) can do the trick. As I observed in several designs (usually GBC modules), the simplest LEGO implementation of an intermittent motion (now found everywhere) relies on an eccentric gear. Examples : Torso's Cardan Lift, Tomáš Ullrich's Draw Bridge, and countless of other designs. But, with any of these solutions, because the output gear's speed changes continuously, it never stops completely : close to zero for a more or less long time, then high on a brief period (but I currently don't master the theory or the factors which govern the steepness of the transition).

On my side, here is the video of the "rhomboid chain drive" passive arm in action : https://diode.zone/w/89d1z9XTv6yCJRfXFx6Ay6 The arm segments are 10 studs long (spacing between the centers of the axles). Built using half-thickness beams/liftarms (in order to stay at 3-stud thickness), they are slightly stiffer than an axle-and-connectors build, reducing pitch and yaw for the cradle. By chance (again), the chain didn't require tensioning gears (although I provided room for them, using triangle liftarms) and therefore exhibited no backlash ==> (almost) no roll. Tests with big gears pending : "Expert Builder" gears do in fact have a very low backlash : 1/2 tooth for 4 meshings from one end to the other, thus a very low angular backlash. (for information, the modulus is 1/3 stud, i.e. the tooth length on the pitch circle is pi/3 = approximately 1 stud) "splat gears" experiment not yet built, only quickly tested. With a modulus of 1/2 stud and using the biggest possible gears (Z14) as end gears and idlers, the whole arm length is no more than 2*14 = 28 studs when unfolded at 180°. Aesthetically speaking, these gears could be used for giving a "kid's toy" style to the device (one could build the frame as a wall of bricks of a single color, typically white, but I don't have enough of them) That's why I prefer to finish building of the module in its current form...

@Ankoku — KEN （レゴテクニック勢） (@kenken_lego) November 3, 2021 A revival of Akiyuki's Cycloid Drive (but with a much lower number of "teeth") !!! — くう (@ZVwQnK5poHS87nv) February 4, 2022 Although the trammel of Archimedes has already been implemented in this old mesmerizing standalone GBC (where used as a 4-way splitter), and in Riku Katsumata's Orbit Overlap module (where it spins on its center and ejects balls), I had not been able to find another use of it. I however tried to think about it when starting LEGO again two/three years ago (I would have liked to design a GBC module who would make use, almost this way, of two variations of this mechanism but I gave up when discovering how difficult it is to tame the balls (even on much simpler usual mechanisms). I however managed to prototype a "trammel of Archimedes without guiding rails" (it relies on gears), but it's too flexible for picking up balls, and therefore can only be used as a kinetic sculpture (perhaps should I finish and publish it, but it's a small design compared to everything here).

Although I ordered all my Z36 gears on Bricklink (a few years ago), I'll try to find traceability/identifying markings on both of them... EDIT20220227 : the Z36 gear on the left (probably the current version, same as pictured on Bricklink) has no markings at all, whereas the one on the right has "51436" and "01-02" deep in the blind holes around the center axle hole, on one side. Yes, I already encountered this kind of situation when thinking about other symmetrical designs involving the meshing of identical Technic gears (either directly or with a worm gear between them). But I don't think that LEGO will create tooth phase variants for every Technic gear size, otherwise many people won't notice these subtle difference among variants, mixing up them, and having trouble when paralleling them. With teeth numbers being multiples of 4, the phase remains the same for any 90° insertion orientation on an axle. Other gear families however contain gears with teeth numbers either odd multiples of 2 (all splat gears for example) ==> half phase per 90° step, or purely odd (all old "Expert Designer" ones) ==> quarter phase per 90° step.

As seen on your video, the stiff telescopic rack does still improve the reliability by stabilizing the cradle, more precisely by reducing its pitch (back-and-forth tilting) and yaw (left/right turning), despite the weight of the cradle and its load, and even in the absence of gear-based permanent roll (i.e. side tilting) control. The stiffness of the arm also plays an important role in both of our design variations. The only critical point that has to be solved (already solved in your previous design) is the roll cancellation at the entrance and the exit, thanks to a wall on the outer side and a funnel-like guide on the inner side (on the input structure).

Something else. Something never seen before between versions of Technic double-beveled gears : on the Z36 one, besides the difference on the rim (its thickness) and the hub (shape details), the phase of the teeth is inverted : "peaks" aligned with beams on the thick one on the left (probably the latest version) "valleys" aligned with beams on the thin one on the right (probably the older version ; only two of them in my inventory) However, the tooth phase doesn't change between versions for the Z20 and the Z12 (I placed the latest versions on the right).

For the Mini figure, I unfortunately own very few of them (including accessories). Here is a close up picture of my current mechanism : (removed from the module, rear view ; the black 4x2 L-shaped liftarm was attached to the frame ; a few extra #44 connectors nearby = the parts used for the elbow) In my build, the spacing between the axles of adjacent Z36 gears is 4.5 studs (or here, approximated by the hypotenuse of a 4x2 right-angled triangle). Therefore each arm segment is 9 studs long, and the maximum allowed radius of the unfolded arm must stay below 18 minus a few studs (i.e. never undergoing a 180° angle). However, your drive mechanism design is much bigger : the half width and height of the square traveled by the cradle pivot is 12 studs (frame), plus approximately 4 studs (distance between a sprocket's center and the pivot mounted on a tread link passing on it). The biggest distance from the cradle's pivot to the center is therefore 23-24 studs, which means that you'll have to either build a very much longer arm system (i.e. more than 12 studs for each arm segment = more than my bulky turntable-based early prototype), or reduce the size of the drive mechanism. Therefore, if we keep its size as-is, in order to increase the length of the arm segments, one must either : add extra idler gears, at the expense of a slightly higher backlash. For example, adding two Z20 gears per arm segment would increase their lengths to 14 studs. (EDIT20220224 : use the (big) "splat" (a.k.a. "flower petal") gears, hoping that their higher/worse linear backlash will be mitigated by their bigger radius/diameter, keeping the angular backlash low enough on the end gears. The other big gear families ("Expert Builder" and "Samsonite") probably have the worst linear backlash). switch to the folding diamond-shaped (or rhomboid) chain solution (I plan to show it in action in an upcoming video), because the upsizing is only a matter of adding chain (or tread) links, which doesn't increase the backlash ; the only challenge is to adjust the optional tensioners. On another side, your use of the sliding rack (a pair of parts I don't own yet) does give me some extra ideas : trying the telescopic shaft solution (or even the use of the sliding Z8 pinion (11955)).

OK, but this arm alone won't prevent the cradle's axle from spinning with respect to the frame. On my side, slowly working on my prototype, I managed at last to make a video of it in action, using the geared arm variant (rebuilt with Z36 gears only) : https://diode.zone/w/aNr5BcPZWSpTCHq2VeYzCk I just noticed I forgot to show how impossible it is to tilt the cradle (at least beyond the backlash), but the moving of the passive gears speaks for itself. The bar supporting the minifig shows the circular translation of the elbow gear.

@Doug72 In your proposal, there seem to be too many degrees of freedom, so that the joint holding the cradle will be able to rotate freely on some range of angles. it's almost like having two successive standard hinges (i.e. three bars) instead of geared hinges (although the kinematics are slightly different). You can try it by attaching the center end on a stand and manipulating the other end with one of your hands. @aeh5040 Parallelogram linkages (i.e. two in series) could have done the trick as well : I've already thought about them. But if one wants to prevent the parallelogram from turning over (and failing by getting crossed in the absence of a 3rd link like in Schmidt couplings), then the center point would have to be outside the rectangular tread and the two arm segments long enough. A Schmidt coupling could indeed work, but because it constrains the input and the output to be single-sided and on opposite sides, it would result in a rather bulky build : from the rear to the front, there are : 1. the input stand holding the input "star" ; 2. all the intermediate parts of the coupling ; 3. the output "star" ; 4. the tread (traversed by the axle joining the output "star" to the cradle) ; 5. the cradle ; 6. a stand holding the frame of the tread drive (otherwise it would float in the air !) Instead, if some Schmidt coupling flavor is still desired, one could still design a hybrid arm system where the "arm" would be the first half of a Schmidt coupling and the "forearm" would be any single geared arm segment flavor (spur gears, chain etc...), so that the output axle can now extend on both sides (to the cradle in front, and to the tread behind).

Here is my (very slow) beginning : First test of the core mechanism, 20*14 frame, with the bevel gears-based arm : Because of the thickness of this variation, I had to recess it into the rectangle while giving the sprockets a double-sided support and preventing the arm from colliding the tread. By chance, the tread length fits perfectly without the need of a tensioner. Unfortunately, the whole arm is too short and reverse-folds itself when almost fully extended. Therefore I reduced the height to 12 studs (but a tensioner is now required). Here is a quick-and-dirty height test (after building a cradle as well) : Unfortunately, there is too much backlash that may later prevent a reliable alignment between the cradle and the pickup area : rotation backlash caused by the bevel gearing twist backlash and forearm flexibility because of the single-sided support of the gears I therefore plan to give up on recessing the mechanism, to dismiss the bevel gear solution and to revert to the 14-stud height : I already rebuilt enhanced versions of the spur gear arm system and the folding rhomboid chain, only 3-stud thick and with proper bracing (i.e. double-sided, thanks to half-thickness beams/liftarms or specific axle-and-connectors build) : coming later...