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Types of Drives?
Hello Everyone,
I am currently looking at different types of gearboxes and how to optimize them. This has led to my looking at the various types of overall drive systems. I believe I understand what skid and crab drive are, but I am clueless about what a swerve drive is. Can someone please explain what these (and any unnamed) drive types are? Thanks, indieFan |
"crab" and "swerve" are two names for the same drive type
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The term Crab, comes from... well, a crab. If you have ever seen a crab walk, you know that crabs walk sideways. This makes sense since omni-directional drives can go sideways like a crab. The term swerve is attributed to the agile motion of omni-directional drives. You never really know where they are going next, they just swerve all over the place very gracefully... most of the time anyway :yikes: |
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a killough(sp?) platform or 'holonomic drive' has three degrees of freedom, and therefore is a 'true' omni-directional drive. old thread on the subject the first FIRST killough platform (i believe) was built by team 857 in 2002, and was called the 'kiwi-drive'. |
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Its been worked on, and should actually be mechanically simpler and much more robust than last year's drive. Of course, we will only go ahead if it is consistant with our strategy, which will be decided come January. The programming will be tough, but thats not my deptartment (i'm just the lead designer). Control should be a breeze. If we manage to get the solid-state gyro online enough to give us a consistant heading so that pushing the joystick north, regardless of the facing of the robot, will cause the robot to move north. and same with all the other directions. With a twist-stick joystick, we can add translational and rotational movement all into one hand . . . it is a good plan, I think. We will see. The biggest problem will be to make the chips and drills run at the same speed not only at 100% throttle, but at all the various percentages in between. Like I said, we will see how things go. |
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-Pat |
Alright... after thinking about it, I guess my definition of an omni-directional drive would be:
A driving mechanism that allows 360 degree directional movement independent from the frame. My thoughts are that you NEVER can or need to go in more than one direction at a time... so being able to do them all at the same time is a pointless criteria. Therefore, under this definition, I consider Swerve Drive an omni-directional drive :yikes: |
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That being said, however, swerve is more than enough mobility for just about anybody. There are advantages to swerve over Killough, and vice-versa, but you can do well with either. |
when I say that i will be tough to make the chips and drills to run at the same speed . . . I do not mean at full power. However, as I understand these things, if you were to take a chip and a drill, gear them so their free RPM's are equal, and then increase the voltage from zero to twelve at the same rate, the different motors will have different rates of increasing . . . ness . . . . osity . . . . or something. I mean, that, while you can sync the motors at 12 volts, they won't nescessarily be synced when you are giving them half power. Does this make sense? So, our base will run a straight line at full speed, but will pull to one side at half power and stuff. This isn't that large a problem, but its something to think about.
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Speed, Power, And, Maneuvarubalty
SPAM seems to do well with Tank treds Start, With, Attacking, My, Pproblems Speed, Width, Agility, Manurvibilty, Power And i just made these up for Swamp A Crab drive seems Great because you can point all your power in any direction, But omni wheels only a fraction at the most half in any given direction |
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The best options is to gear the motors such that the torque-speed curve lines are parallel for both motors. Then, for the motor with more power (ie the one further away on the torque-speed graph), you want to multiply the voltage applied by a constant less than one to bring the curve inward to the weaker motor. For example, the weaker motors would be used fully (PWM range -127 to 127) while the stronger motors would not be used fully (something like -108 to 108). This does waste power, but believe me, with four powered motors geared to an appropriate gear ratio and with high-traction wheels (see below), you will not have a power problem. Ensuring the same torque-speed curve using my method above will also help a LOT with control problems. There will still be some variance from motor to motor and over time and with varying heat conditions: If I were to do it, I would actually place encoders on each wheel, and use feedback control to ensure the robot is going in the commanded direction... But I don't know if FIRST rules allow purchasing of encoders. I know there are teams that make their own with the optical sensors. But to start with, ignore the encoders idea, and if things don't work well enough, you might consider it. Now, about wheels, I have a lot of experience designing omniwheels, Here is a design I worked on last year (I've also attached a picture of final product): Exploded view of wheel Engineering Drawing Engineering Drawing of Lexan "Hub" Engineering Drawing of Roller (small rollers around the wheel) CAD View of Robot w/ Wheels The wheels have lexan hubs and delrin or aluminum rollers with rubber Buta-N o-rings wrapped around the outside of the rollers. The coefficient of friction between wheel and ground of this particular design is 1.3 for a felt-like material. I suspect it is at least 1.5 (probably closer to 2.0) on a FIRST carpet. You can machine very similar wheels with manual mill & lathe, but you will need a rotary table to do the lexan pieces. It is better if you have access to CNC. You will also need to make larger wheels, probably about double the size of these wheels (which are 2" diameter). You can order O-Rings from McMaster or try and find them at a hardware store. If you are really interested, you can actually read our mechanical design documentation at: Cornell Robocup 2003 Mechanical Design Documentation There may be some things of use in the documentation that I did not include here. Good luck! And let me know if you have any questions. - Patrick |
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Keep in mind that with the 4-wheel omnidrectional platform you can have your Y-axis geared for high-speed and your X-axis geared for high-torque without motor fighting. As said above, with robots drive systems there are three variables to control. Heading, Y-axis velocity, and X-axis velocity. Tank drive gives control over heading and y-axis velocity, but you can only manipulate one of those at any given moment. 2-wheel / caster drive gives a little bit more control over the two, and you can even do both at the same time for turns up to 45 degrees. However, you cannot make a 90 degree or more turn while maintaining Y-axis velocity. Swerve/crab drive gives the illusion of omnidirectionibility due to the ability to change the robot heading without changing robot orientation. Still, you only have control over robot heading and Y-axis velocity. Although, you have the ability to manipulate both at the same time. 3-wheel/4-wheel holonomic drive systems have true capability to manipulate all 3 at once, as Jeff said above. It's possible to change robot heading/orientation while maintaining a constant velocity in a certain direction. |
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Guys, this debate is basically just about terminology. Everyone has their own.
Here is mine (and 229s): Omni-Wheel - A wheel that rotates normally and functions as a wheel, but can also be moved perpendicular to it's rotation. Like the wheel Patrick posted above. Many teams use these to aid in turning. (Hotbot 2001) Omni-Drive - A drivetrain that consists of multiple "sets" of omni wheels in different (usually at perp.) directions. This alows the robot to move in any direction simply by powering the different wheels at different speeds. (think Metal-In-Motion 2002, which was a 6 wheeled variety. A 4 wheeled variety can be seen here .) I would consider 857's kiwi-drive to fall under this category. Crab Drive - This type of drivetrain has 2 sets of drivetrains set perp. to each other. Instead of using omni-wheels and having all wheels on the ground, it somehow actuates things so that only one set is on the ground at a given time. (Good examples of this include WPI 2003, 358 2003, TRIBE 2002). Swerve Drive - The individual wheels can "spin" changing the heading of the robot. It can move in any direction. (think Wildstang 2003/2002, Chief Delphi 2001/2002) There are many variations on this. 2-Wheel Swerve- Two wheels "spin" like a normal swerve drive (See above) the other wheels are either casters, or omni-wheels (see definition above). (see Chief Delphi 1998/2000). Articulated-Steering - Some, or all of the wheels will turn like a car to aid in turning. 2 cool examples of this include Hotbot and Thunderchickens 2003. Skid-Steering, or Tank Drive - This is the most standard type of drivetrain. All the wheels/tracks/whatever are pointed in one direction. The robot turns by reversing one side, while powering the other side forward. Examples of this include... almost everyone. When a robot in this configuration is turning, some energy is lost to "side load" because the robot is essentially dragging some of it's wheels across the floor sideways. Some teams use dropdown casters/skids to aid in turning. This is just my terminology for things. It isn't always the most "technically correct" terminology, but this is what I've developed over 4 years in this program. *shrug* it works for us. Perhaps this will benefit, someone.... John |
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adj : not directional; being in or involving all directions Let's apply this to radio waves. Sure, with a rotator a directional antenna can signal in a certain direction well, and has the ability to change directions, but can it signal in multiple directions at once? No. As the definition says, the crab/swerve/synchro drive is directional. It cannot move along other axises without first changing the direction of the wheels. True holonomic drives have this instantaneous ability to move in other axises than oriented. Some more reading. A suitable analogy would be if I cold move really fast, say 1/4 the speed of light. I could say I teleported myself. To the average person, they'd believe it, but the educated person knows better. This analogy is suitable because the fast and powerful motors we have allow us to turn the swerve wheels very fast. If we did not have such powerful motors, the limitations would become aparent. Everyone is entitled to their own opinion, I'm just telling you the dictionary and accepted definition. Nobody said yes couldn't mean no. |
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say you have the wheels like so: . . _ . .[_] you only get .5 of possible max power if you are moving directly verticle or horizontal. however, you go diagonally (45 deg. from horizontal) you will get full power. To PatrickRd: Thanks for the offer of help with the omniwheels, however we don't have access to a machine shop and I think the best way to go is to buy our wheels. I found this source (kornylak) that looks perfect, about 5 inch diameter, polyurethane rollers (wooo!), made of aluminum. Only downside is the wheels we would need would total to 516 USD. We can probably do that . . . . if we raise 6large in time to apply for the NASA grant again. pics: The wheels pictured have 3 rollers, you need two wheels back-back to provide for 360 degrees of rotation. Here are schematics: linkies: omniwheel I think that this is the best way to go for long-term durability and for overall funcionality (any rollers we make probably will not be as efficient as these. downside, is again, 64 dollers per wheel. But we will be able to swing it. I asked Kornylak is they would like to sponsor us, so maybe we can swing it for cheaper. Who knows. These are what I'm drawing around as of now. edit: These wheels are also ideal because they are nearly circular, so there will be smooth weight transfer from one roller to another and it will make for a smoother ride than, say, the lexan/disc wheel you pictured above. It is also probably lots easier on the wheel and the gearbox. I'm reading that documentation, its pretty cool. Especially your nod to strongbad: "Eating one battery . . . . Eating Five Batteris" It was so serious up until then, too. I guess you college students just didn't have it in you to stay that way, huh? |
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Main Entry: om·ni·di·rec·tion·al Pronunciation: "äm-ni-d&-'rek-shn&l, -"nI-, -(")dI-, -sh&-n&l Function: adjective Date: 1927 : being in or involving all directions Same as your definition above. So, if you put boxes on both a killough and a swerve drive, both boxes could move in ALL directions without changing the orientation of the box. Since this fits the definitions above, both killough and swerve are omnidirectional. Yes, you can be more technical and argue that swerve can't do them all at once... but like I said before, what is the point? You can't physically be going in two directions at the same time, so why make that a criteria? :yikes: Again, these are my thoughts. I don't however want this turning into a flame war; we should all have the ability to reason and debate without getting angry or start calling each other names. Oh, one more thing. Quote:
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None of the proposed drive systems are omnidirectional because they don't involve the z-axis.
:p |
what would the z axis even be? Logic would say it would involve up and down motion, but common sense would tell you that would never be useful in a drivetrain.
Cory |
the three axis as far as FIRST is concerned are x, y, and theta (the angle)
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:D :p :cool: |
Thanks John,
That's exactly the information I was looking for. indieFan |
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BTW, two of our robot names our "Burninator" and "The Cheat" Some comments on the wheels you found: The design concerns me because a wheel roller is not always in contact with the ground. Usually with this type of wheel there are staggered rollers, such that there always is a roller in contact. So the wheel will be rolling without friction one instant, and then a split second later be scraping against the ground. Please correct me if I'm misinterpreting the design of the wheel. Good luck, I really hope to see more omni-drives around this year :) Seriously, if you run into any roadblocks at all you can't figure out please contact me at prd8@cornell.edu. I'd even make the wheels for your team if I had more time, just to see a four-wheel omni FIRST robot. - Patrick |
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Actually, upon further consideration I will make a deal to any teams out there interesting in constructing an omni-drive. Here's the deal (of course, let me know someone if this breaks a FIRST rule, I will not do this if it does):
That's the deal. The deadline's is Dec. 15. I will send them out at latest the first week of competition (you will have all the dimensions well before to do designs). - Patrick |
Patrick:
you did miss a detail: Those wheels are designed to be put back to back two on an axel,180 degrees apart, so you have six rollers per axle, with either one or two always being in contact, and a nearly circular shap for smoothness. I contacted Kornylak, and they said that the wheels have a .874" hex bore. Is this type of axle readily available? Can I get bearings and standard size gears that will go on this axel? If not I may have to take you up on that offer. I began chassis design the other day (this is all pending on whether this years game will allow for this sort of thing . . ) and I came up with a way to build a solid chassis with four long rectangles of aluminum plate and some angle peices. Light, should be strong, and damaged peices could be easily switched out. as of now, its just a sketch, but tommorow I will calculate sizes and dimensions and whatnot. Maybe I will even begin the gearboxes. Who knows? er, about the omnidirectional debate. This may clarify things. Group A says that killough/similair are the only true FIRST omni because they can move in any x,y direction in an instant. They say that swerve/crab drive is not omnidirectional because the crab modules must turn, so that all a crab module is a quickly reconfigureable chassis, but it can't zoom north and then east with only a few instants in between to do all that accelration stuff, but it can go north, rotate its wheels to the E-W line, thus reconfiguring the chassis, and go east . . . Personally, I think that omniwheel-based systems are cheaper and easier (built like a tank drive, only put the wheels at 90 degrees to each other) to construct, but quality omniwheels are hard to build or obtain. I think that the kornylaks are winners, and I hope that our bot this year reflects that. Essentially, all our robot design is is four wheel drive, one motor per wheel independant of the others, turn the wheels perpendicular to each other, and then put omniwheels on the drive shaft. Same gearboxes. No steering mechanism that uses extra stuff, just standard gearboxes. I just hope it works. But, I'd say the killough platform is as KISS-style as you can go with all these 'omnidirectional' drives described in this thread. |
Kind of like these wheels I spotted at the airport in Zurich, Switzerland :D
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- Patrick |
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Swerve drive steering's official name is synchro-drive. |
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I think we will buy .874" hex stock, and use it as a hub for the wheels, . . as in it just fits onto a standard smaller circular shaft, and is secured using cotter pins or something of that nature. BTW: that airport picture is awesome! Did you try to ride on it (I know I would have)? |
You might need to order .875 hex stock, which is slightly oversized, but will make a good press fit into the wheel. As for centering the hole, the best option is actually to put it in a lathe and drill out the hole that way. The second best option is to mount the piece vertically and use a milling machine. Then use a zeroing tool to locate the center of the hex stock. Then you can drill it out quite easily.
But it sounds like you don't have either... So my recommendation is to mark very carefully the center of the hex and use a centerpunch to ensure the drill bit will not drift. Then mount the hex in a drilling press, and drill through. You'll probably need to start with a small drill (1/8)" and then work up to the final size (1/4" and then 3/8"). If you have a reamer, it would be a good idea to drill just under 3/8" and then use the 3/8" reamer to do the final cut. The key to making this work is mounting the hex perfectly horizontal. Use a right angle of some sort to do this. You'll probably get some no-good pieces using this method. But some will be good. If the hole is centered on both sides of the hex, it should be good. If it is only off by 0.005" or less, then I do not think a slight wobble will affect performance too much. - Patrick |
tough to decide what's what
we never got caught up in definitions when we built our drivetrain............
since there is so much talk about omni-drives, i thought i'd let you know that we're still waiting to use our next generation Kiwi Drive............stay tuned, its been two years in the works. for now, check out our old video from the pre-season of 2002, this was a video we unveiled before competing with our reworked chassis. it was more fun to drive than to watch. :) http://stuweb.ee.mtu.edu/~alkrajew/FIRST/kiwi.mpg |
True Dat!
First make it work, then wory anout what to call it |
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Depending on the exact schedule you plan for construction of the wheels, as I interpret the rules, this may not be allowed. Your message is not clear about when you will be constructing the wheels - right after your December 15 deadline, or during the first week of the competition. Under the current FIRST rules (emphasized to point out that we don't yet know what will be in the final version of the rules for 2004), it would be illegal if you start manufacturing the wheels prior to the kick-off, and any team using your wheels would be in violation of the rules. All materials and components on the robot must be manufactured ONLY during the competition period (other than those bought as straight off-the-shelf commercial commodity items, e.g. you can purchase and use a Banner sensor that was actually manufactured by the factory earlier). Wheels that you manufacture prior to the start of the competition cannot legally be used on your robot, or by any other team. You can share your designs all you want to. But you cannot, and other teams cannot, start to actually build the wheels prior to kick-off. -dave |
Hi Dave,
Thanks for the reply. It turns out my design couldn't be used anyway, since O-Rings are not allowed :-/ Maybe I'll be able to come up with an alternative. thanks Patrick |
Why wouldn't o-rings be allowed? They are listed in small parts?
Our rollers were initially delrin with rubber o-rings. |
<<<ajlapp wrote...>>>
for now, check out our old video from the pre-season of 2002, this was a video we unveiled before competing with our reworked chassis. it was more fun to drive than to watch. http://stuweb.ee.mtu.edu/~alkrajew/FIRST/kiwi.mpg <<<>>> I disagree!!! Very cool to watch. I have toyed with the idea and always stop when I look at power loses. But in terms of being able to manuver it would be pretty cool Thanks for reminding us about it |
no problem
power loss sucks, but we designed around the power loss.........
the robot we used that year had no power what so ever, because we designed strictly to pick up balls. last year we didn't use it, because of power loss, instead we built a tried and true swerve. don't give up yet, there are ways to use the kiwi and keep power on the turf, trust me ;) |
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You see, with three wheel killough(kiwi), if you spin all three wheels you get a robot that is turning . . and you won't get all three motors adding forward power. With four wheel, you can have all four motors putting all their power into forward push. Whether or not you are powerful at that point depends on your traction, and polyurethane is a great sticky thing, and your gearratios, which are entirely up to the team. In motion, some energy is lost to the omniwheels inefficiency, but if you buy 'real' omni wheels, as linked above by myself, you get nearly the same efficiency as say, a tank drive going forwards. So you see. You get to make the same choice between power and speed you do when designing a tank drive, but you get super maneuverability thrown it! No extra charge! Well, a little for the wheels, but not too much! |
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As for which, crab drive or an omniwheel design, is better, I don't know. It depends on your design strategy. If your strategy (or the game) requires torque over mobility, then a tank/crab drive is better, because all 4 motors contribute 100% of the available torque to the direction of motion. If mobility is considered to be advantageous over torque, then an omni-wheel design might be better. However, an omni-wheel design does present a programming challenge, or opportunity, depending how you look at it. One idea I had for last year was a saucer-shaped wedge robot and use a digital compass and programming to create relativistic motion (from the drivers POV). However, even though local magnetic interference can be compensated for (your own motors), other robots would be a challenge. You could do the same thing with an accelerometer, but the error would add up, and toward the end the robot may not go in the desired direction. |
see if anyone remembers our solutions
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no programming needed, no calibration tricky of potentiometers |
Patrick,
O-rings are perfectly fine, provided that they are accounted for per rule K3. The rule that I would be worried about is rule m17 (traction devices). As far as off-the-shelf components go, the term off-the-shelf isn't used in k3 but is used in the parts use flowchart. It is also used in m1, but only in reference to previous years components. Given that FIRST always said refer to the flow chart if there are any questions, I would say that your wheels are not allowed if they are manufactured before kickoff, but I wish that FIRST would use consistant terminology throughout the rules. Edit: ignore the rules hyperlinks and just look them up in your manual or on hyperrules |
By 'real' i meant professionally made with either low friction non-bearing rollers or bearings for the rollers. Also, professionally produced omniwheels are more likely to withstand a beating.
And, i believe it is possible to get 100% motor torque using four wheels. look at it this way, ._ {_} . where the '{' and '_' are the wheels. say you power the {} wheels in the same direction. you get full power/torque out of them. Say you power the '_' wheels in the same dircetion, same deal. Now lets say we geared the motors so that when only one set of wheels are powered, you get 6 feet/second and whatever push that translates to. If you power BOTH sets you get the robot traveling in a diagonal, at the new speed 6rt(2) feet per second, and a new power that is sgrt(2) times the power of an individual set of wheels. so, you get 2x the power of one set of wheels, and one set of wheels gives you the same power from he motors that a tank drive would, so with twices the motors ou get twice the power of a four-motor tank drive, which gives you 100% power except for gearing and wheel inefficiencies. I don't see where your 70% is coming from . . perhaps I can get a link to an explanation . . . ? at the 45' diagonals you get 100% power out of the motors. The only way it isn't as powerful as a tankdrive at same geared to he same speed is that you are loosing power to make the rollers turn, which is a near-negligable loss. I don't understand how it could be different . . I accept that you only get full power at the 45' diagonals, but that is still another axis of freedom on which full power is available over a tank-drive. edit: your idea about using a compass/angular acceleration sensor: We have been planning that since last season. It will be in place using one or two solid-state gyros. Error will add up, but we may build a control that allows for the secondary driver to manually adjust the robot's percieved heading so the error can be corrected as the match progresses. edit: I looked over your post a second time, and it is true that at the diagonals you get sgrt(2) times the power of each individual set of wheels, but I think you failed to consider that you ALSO get sqrt(2) times the speed, so twice the power. You gotta look at both. And you need a driver who is aware of all of this. |
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Now, if you travel diagonally, the angle of the vector with respect to the axis is 45 degrees. The vector can be split into its forward (y) and sideways (x) components. We have total Power (P), Power in the direction of travel (Py), Power in the sideways directions (Px), Motor power for one set of wheels, MS1, and motor power for another set of wheels, MS2. Py for the left set of diagonal wheels is MS1 sin 45 = P * 0.70. Py for the right side of diagonal wheels is MS2 sin 135 = P * 0.70. Now when you add these, you have to keep in mind that you're only taking into account the power for an individual set of wheels. When you do the multiplication and addition, you can see that you'll end up with LESS power than available. Then there's the power in the x direction Px = MS1 * cos 45 = MS1 * 0.70 for one set of wheels. For the other set, you have Px = MS2 * cos 135 = MS2 * -0.70. You can see that the power in the x direction is lost because the motors can cancel eachother out. Keep in mind that power is a function of both SPEED and TORQUE. The same equations can be used for both speed and torque individually. If you want, I can draw some force diagrams later to further prove my point. |
say you have two motor sets, as you said MS1 and MS2. Each turns its wheels to give, say, 5 feet/second travel and 10 Newtons of force (numbers off, but to illustrate my point)
in a tank drive setup, the speeds of the motors DO NOT add, so you get a drive that gives 5 feet/second and 20 Newtons of force. In a four wheel omni setup, the speed increases, and so does the power, so you get 5rt(2) or 7.07feet/second speed, AND 14.14 N of force. Say you adjust the gearing on this omni drive so that instead you get 5.0 f/s diagonal speed. you multiply the gearing by 5.00/7.07 . . . so now you have less speed, but at the diagonals you would have 5 fps. but you also get more force out of the motors, namely 14.14 N out of each set. make those two legs in a rt triangle and the total is 20N QED: same sets of motors will give you 5 fps w/ 20N in BOTH tank and Omni configuration. edit: if it helps, think about it like this: in both setups you have every motor turning as hard as it can. You said yourself (or someone else did) that four wheel omni is not inherently inefficient. Where does that 30% of yours go? |
Well, I posted in another thread about this, but I'll put it here, anyway.
Basically, I (and I'm sure many other teams) have been busy this summer designing a Multi-drive system, that functions as Skid steer, Crab, Car, and Angle, all at the simple touch of a button. The design is set, the parts inventoried, it's been prototyped several times, each a success. The entire system costs about $800, which includes the Chassis, drive components, and spare parts. It has an estimated weight of about 40lbs w/o electronics. The system also has several backups. For example, if two of our wheel assemblies (somehow) were magically crushed by a couple hundred pounds of force, (I think they'll be as durable as the chassis, and they are well protected) and we don't have enough parts to rebuild them, the system can be converted into a basic skid-steering system by removing parts, and without any reprogramming. This would give us a quick fix at competition if the worst happened. It is all controlled by 1 joystick, which gives even output to the motors. As well, each wheel assembly is equipped with the proper sensory to detect it's motion, and each pivot drive has the appropriate sensory to detect the wheel's angles. This, accompanied with a Gyro, will give us an edge in auto mode, and we hope to develop a program similar to the StangPS's WildDraw to generate autonomous code. We're planning ahead this year... Don't be surprised if our bot is complete before the 3rd week starts! |
Let me clarify what I said earlier, with all this algebra and whatnot:
You have two sets of wheels. Each can turn at X rpm's and has a stall torque of Y. using a gear ratio of Z, set giving you X/Z RPM's and Y*Z Nm of torque. With a wheel radius of R, this gives you (2piR)(X/Z) m/s, and (YZ)/R N of push. Say you arrange the two sets in a tank-style drive. Your top speed DOES NOT INCREASE. Your force is doubled. You now have a top speed of (2piR)(X/Z) m/s and a stall force of (2YZ)/R. now arrange the sets perpendicular to each other with omni wheels. One set drives the robot in the horizontal direction, the other set drives the robot in the verticle direction. The final speed and power of the robot is the sum of the vectors. We are looking at the 45deg angle case, where both sets are driving full power. For the sake of simplicity, we look at the right-up case. the speed vector to the right is this: sqrt(((2piR)(X/Z))^2+((2piR)(X/Z))^2) You understand? Its a right triangle, on leg being the right speed vector, the other the up speed vector. The final speed vector is the hypotenuese. It simplifies into rt(2)(2piR)(X/Z) Same this with the force vectors. Final result is sqrt(2((YZ)/R)^2)). which also simplifies into rt(2)((YZ)/R)Do you accept this? Say you adjust the gear ratio (Z) on the omni setup to match the top speeds. the top speed of the omni =sqrt(2((2piR)(X/Z))^2). The top speed of the tank is (2piR)(X/Z). so Z(new), the new gear ratio for the omni platform = sqrt(2((2piR)(X/Z))^2) (2piR)(X/Z) which simplifies into sqrt(2) 1 so, replace Z in the omni calculations with Zrt(2) the final speed vector was equal to rt(2)(2piR)(X/Z). Replacing Z with Zrt(2), we obtain (2piR)(X/Z). Fancy that! Exactly the top speed of the tank style drive. Lets try the stall force now! rt(2)(YZ)/R. Replace Z with Zrt(2) and you get 2(YZ)/R Yah! same as tank-style! So, in summary. The tank drive can give you this: Speed=(2piR)(X/Z) Stall Force=2(YZ)/R The omni drive base gives you this: Speed=(2piR)(X/Z) Stall Force=2(YZ)/R where X=free RPM's of motor, Y= stall torque of motor Z=gear ratio R=Radius of wheel. |
Re: see if anyone remembers our solutions
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::Raises hand:: You guys tied three joysticks together at the same configuration of your motors, correct? |
:::blinks:::
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