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Unread 28-04-2014, 16:04
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swerve math quiz



Given:

* 4-wheel Unicorn swerve robot

* wheels located at corners of the rectangle shown in attached Figure 2

* robot is rotating clockwise around center of rotation (red dot) at omega radians/sec as shown in attached Figures 1 and 2


Problem:

Find the steering angle and tangential speed of each of the 4 wheels in terms of omega, a, b, c, and d.

Show your work.



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Unread 28-04-2014, 16:15
Chowmaster4695 Chowmaster4695 is offline
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Re: swerve math quiz

Aware
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Unread 28-04-2014, 16:25
brennonbrimhall brennonbrimhall is offline
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Re: swerve math quiz

Quote:
Originally Posted by Ether View Post


* 4-wheel Unicorn swerve robot
What differentiates a unicorn swerve drive from a standard swerve drive?
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Unread 28-04-2014, 16:28
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Re: swerve math quiz

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Originally Posted by brennonbrimhall View Post
What differentiates a unicorn swerve drive from a standard swerve drive?
it can honk as it's swerving past a defender?
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Unread 28-04-2014, 16:30
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Re: swerve math quiz

Quote:
Originally Posted by brennonbrimhall View Post
What differentiates a unicorn swerve drive from a standard swerve drive?
Because it's magical, duh.
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Unread 28-04-2014, 16:30
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Re: swerve math quiz

Quote:
Originally Posted by brennonbrimhall View Post
What differentiates a unicorn swerve drive from a standard swerve drive?

Define "standard" swerve...

Unicorn is "4-wheel independent-steering and independent-driven drivetrain, with unlimited rotation of the wheels and sensors, and no gaps in the sensor feedback?" http://www.chiefdelphi.com/forums/sh...07&postcount=9 Oh, and it was so named by none other than JVN!

You might also call it an idealized swerve drive. A more common approach is coaxial swerve, where each side rotates together, and has a limited range of rotation (usually no more than 360 degrees). Another approach might be to have all 4 swerve modules rotate together.
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Unread 28-04-2014, 16:37
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Re: swerve math quiz

Quote:
Originally Posted by Jon Stratis View Post
Define "standard" swerve...
In a fit of boredom, I once defined 27 different types of swerve configurations
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Unread 28-04-2014, 16:49
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Re: swerve math quiz

Quote:
Originally Posted by Jon Stratis View Post
Define "standard" swerve...
Either http://www.andymark.com/product-p/am-0537.htm or http://www.andymark.com/product-p/am-0760.htm.

My definition of a standard swerve drive are four independently controlled modules, such that each can have its own velocity vectors (i.e., independent direction AND magnitude). Anything less than that is not a swerve (or so I've gathered from CD searching and speaking with mentors) -- my understanding is that a crab drive is a derivative of a swerve drive where the vectors must all be parallel (and most always have the same velocity magnitude too, though this is not a mechanical limitation).


Quote:
Originally Posted by Jon Stratis View Post
Unicorn is "4-wheel independent-steering and independent-driven drivetrain, with unlimited rotation of the wheels and sensors, and no gaps in the sensor feedback?" http://www.chiefdelphi.com/forums/sh...07&postcount=9 Oh, and it was so named by none other than JVN!

You might also call it an idealized swerve drive.
Gotcha. A true, pure swerve.

Quote:
Originally Posted by Jon Stratis View Post
A more common approach is coaxial swerve, where each side rotates together, and has a limited range of rotation (usually no more than 360 degrees).
Quote:
Originally Posted by Jon Stratis View Post
Another approach might be to have all 4 swerve modules rotate together.
I'm a little confused here -- I don't really understand what you're trying to convey with your examples, unless you're just mentioning common implementations of what are commonly referred to as swerve drives.

Assuming you're using continuous potentiometers or some other sort of continuous sensor solution and have independent direction and magnitude control of each module, how is a coaxial swerve drive like 118's Revolution design NOT a unicorn swerve drive?

Per Nate Laverdure's paper (page 2, available here), wouldn't the proper term for what you describe in quote 2 be a crab drive? That's most certainly not a unicorn swerve drive.

EDIT: Nate beat me to his paper.
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Unread 28-04-2014, 16:57
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Re: swerve math quiz

Quote:
Originally Posted by brennonbrimhall View Post
I'm a little confused here -- I don't really understand what you're trying to convey with your examples, unless you're just mentioning common implementations of what are commonly referred to as swerve drives.
He's saying that one's definition of "standard" is couched in their social context and their personal experience. These names-- even "crab drive"-- are all invented, and they mean different things to different people.
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Unread 28-04-2014, 16:58
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Re: swerve math quiz

I was simply listing common implementations that student's/teams call swerve, even though there may be more accurate terms. To me, swerve is a general concept of physically changing the direction the wheels point in order to implement an omni-directional drive system. Unicorn, crab, and coaxial could be considered to be three subsets or implementations of a swerve drive system.
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Unread 28-04-2014, 18:15
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Re: swerve math quiz

I believe 'coaxial' simply refers to how the drive motor transmits its rotation to the wheel. On a coaxial module the wheel is driven by a shaft that is coaxial with the rotation axis of the module. This allows you to mount your drive motor away from the module and have unlimited rotation.

Based on this definition you could create either a unicorn drive or a crab drive with coaxial modules.
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Unread 28-04-2014, 20:35
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Re: swerve math quiz

Lets say a, b, c, and d are in meters (because I personally like meters).

Corner 1 has a speed of ω√(b²+c²) in meters per second and angle of arctan(c/b)+π/2 in radians.
Corner 2 has a speed of ω√(a²+c²) in meters per second and angle of arctan(c/a)+π/2 in radians.
Corner 3 has a speed of ω√(a²+d²) in meters per second and angle of arctan(d/a)+π/2 in radians.
Corner 4 has a speed of ω√(b²+d²) in meters per second and angle of arctan(d/b)+π/2 in radians.


Work: (Yes I'm lazy)
http://i.imgur.com/xCsYXzw.jpg?1

For the sake of simplicity, we'll call "n" the line segment that ends at any corner of the robot and the point of rotation. Create a right triangle with n as its hypotenuse. We can call the angle in the right triangle closest to the robot, the arctangent of the opposite leg divided by the adjacent leg. Then we add pi/2 radians to find the angle of the ray perpendicular to n.

Finding the rotational speed, we first create a circle with its center at the point of rotation and n as its radius. With the right triangle from the last paragraph, n can be found with the Pythagorean Theorem, where n is the square root of the sum of the squares of the two legs. Because n is the radius of the triangle, and we want the speed of the robot in ω radians per second, we can multiply ω by the radius to get the tangential speed.

Last edited by Cyan : 28-04-2014 at 21:57.
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Unread 28-04-2014, 20:52
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Re: swerve math quiz

Quote:
Originally Posted by Cyan View Post
Corner 1 has a speed of ω√(b²+c²) in meters per second and angle of arctan(c/b)+π/2 in radians.
Corner 2 has a speed of ω√(a²+c²) in meters per second and angle of arctan(c/a)+π/2 in radians.
Corner 3 has a speed of ω√(a²+d²) in meters per second and angle of arctan(d/a)+π/2 in radians.
Corner 4 has a speed of ω√(b²+d²) in meters per second and angle of arctan(d/b)+π/2 in radians.

nice start. speeds are correct but angles are wrong.

do you want a hint about the angles, or would you prefer to work it yourself?


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Unread 28-04-2014, 21:02
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Re: swerve math quiz

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Originally Posted by Ether View Post
nice start. speeds are correct but angles are wrong.

do you want a hint about the angles, or would you prefer to work it yourself?


Would you use the reciprocal rule for arctan to simplify it?

Then,
Corner 1 has an angle of -arctan(b/c) in radians.
Corner 2 has an angle of -arctan(a/c) in radians.
Corner 3 has an angle of -arctan(a/d) in radians.
Corner 4 has an angle of -arctan(b/c) in radians.
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Unread 28-04-2014, 21:08
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Re: swerve math quiz

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Originally Posted by Cyan View Post
Would you use the reciprocal rule for arctan to simplify it?

Then,
Corner 1 has an angle of -arctan(b/c) in radians.
Corner 2 has an angle of -arctan(a/c) in radians.
Corner 3 has an angle of -arctan(a/d) in radians.
Corner 4 has an angle of -arctan(b/c) in radians.
Still no joy.


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