User:Bvangenn0235/ENES-100/Project2

Week1 Narrative: 09/16/2013 - 09/22/2013
Put on "Polar Print" team with Ryan and Carlos. Objective is to design a polar printer capable of using three intersecting triangles to orient the printer head both vertically and horizontally using polar mathematics. Began investigating at Arduino.cc for code designs on Arduino for controlling stepper motor. Investigated https://www.khanacademy.org/math/calculus/derivative_applications to create relationship for 90 degree triangle sides and their rate of change(formula in Canvas email):

"... This is my formula for the triangle on the delta printer: r^2 = x^2 + k^2 in which case x = bottom side that changes length; r = hypotenuse that changes length; k = constant value on the triangle. I derived the formula for the distance with respect to time (df(t)/dt such that f(t) is variable equal to length of a side on triangle) * = multiplied by: 1/2 * k^2 * 2x * (dx/dt) * (x^2 + K^2)^-1/2 = k^2 * 2x * (dx/dt) If we have the value of x, (dx/dt), and the new x value then I think we can figure out r, (dr/dt), and the new r with this equation. Please review this formula and correct any flaws you see and email the corrections to me and other member of our team, as I am unaware of his contact information at this time. Thank you From, Brandon van Gennip".

Week2 Narrative: 09/23/2103 - 09/29/2013
Investigated codes for running stepper motor with motor shield. Two potential codes selected:

1. http://arduino.cc/en/Tutorial/StepperUnipolar; 2. http://learn.adafruit.com/adafruit-motor-shield/using-stepper-motors;

Group final selection: code 2. Began setting up Arduino based of code 2.

Week3 Narrative: 09/30/2013 - 10/06/2013
Added code 2 (renamed AFMotor) to Arduino "sketch>libraries" as an example code. Setup chart to determine motor coil and center tap wires based of resistance between wires:

Set up determined that black and brown are coil 1, yellow and red are coil 1, and orange is the center tap. Worked with Mr.Z (local mathematician) to create formulas relating triangles to rates of change and to polar coordinates (formula in Canvas email):

" Oct 5 at 7:01pm Brandon Van Gennip I have redefined the triangle formula to derive with the change in a time interval instead of relating the rate of change of the hypotenuse to the rate of change of the side. In this formula: r = hypotenuse; ri = rate of change of side r; x = side that changes; xi = rate of change of side x r(ri) = x(xi)

When rearranged we can find the rate of change of r when given the rate of change of x and the sides r and x: ri = x(xi)/r

In addition we can determine the distance achieved from the gears by multiplying the change in degree (in radians) multiplied by the radius total D = ar in which a = angle in radians; r = radius. By this logic, circumference of a circle (C = 2πr) will give us the total distance achieved per one rotation. Please email me via Canvas if you have any corrections/discrepancies. From, Brandon van Gennip Oct 8 at 6:48pm Brandon Van Gennip I believe I have found a way to graph the arch we need. By plotting the printer head (point O) we can create circles that intersect based of manipulation of the distance from point O to the stepper motors on the bottom (this distance is equivalent to the bottom side of the three triangles that changes). By using this formula: y =(± (r^2 - (x - v)^2)^1/2) + h ( translation of " (y - h)^2 + (x - v)^2 = r^2 ") This will allow us to determine the polar arch (defined by radius "r") without the need of theta defining an angle. However because this formula only forms one arch, it would have to be repeated for each triangle with a unique center (h and v) and unique radius to tell the length of the bottom side. This would also require that the grid be set up so that each space represents a distance value which would have to be converted into rotations for the motor. I was also curious as to what our design was for the triangles to turn back and forth. This formula will not work unless: 1) the bottom and hypotenuse side of each triangle can change lengths; 2) the triangles can rotate left and right on the axis where the constant side meets the hypotenuse and the bottom side; 3) the triangles can rotate on their axis and changes side lengths at the same time. Please email me back with any corrections, notes or concerns. From, Brandon van Gennip".

Week4 Narrative: 10/07/2013 - 10/09/2013
''Visited https://www.khanacademy.org/math/trigonometry/parametric_equations for information on converting corinthian coordinates to polar coordinates. Presented to class for aid in establishing relationship between all three triangles (see Oct 8 letter in Week3 Narrative). ''