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swerve math quiz
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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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Define "standard" swerve... :D 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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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:
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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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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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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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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. |
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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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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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