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Unread 07-08-2018, 01:20 PM
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Most useful basic equations/reference for FRC/FTC?

So Im making a 1 page quick reference for my team.

If you had a 1 page basic Equation/Reference sheet for FRC/FTC what would you want on it?

Things I'm thinking of
  • Some Pythagorean triplets.
  • An example of force and speed in some basic gear configurations
  • Arm force equations & diagrams
  • projectile motion equations & diagram
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Unread 07-08-2018, 01:37 PM
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Re: Most useful basic equations/reference for FRC/FTC?

Here's a short list of equations that I have used in FRC and FTC:

Code:
Geometry
sin^2(x)+cos^2(x)=1
C=2*pi*r

Mechanics
F=ma (and its angular complement T=I*alpha)
at^2+vt+k=x
W=Fd (the calculus definition W=integral F ds is also useful)
w=mg

Electricity
V=IR
P=VI

Gears
Ratio = Driving teeth / driven teeth (also true for belts)
Center distance = (Pitch Diameter 1 + Pitch Diameter 2) / 2 + Center Add
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Unread 07-08-2018, 03:42 PM
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Re: Most useful basic equations/reference for FRC/FTC?

Not mechanically oriented so here's a PID equation:

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Unread 07-08-2018, 05:05 PM
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Re: Most useful basic equations/reference for FRC/FTC?

DC motor equations
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Unread 07-08-2018, 05:11 PM
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Re: Most useful basic equations/reference for FRC/FTC?

Quote:
Originally Posted by Michael Hill View Post
DC motor equations
^this
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Unread 07-08-2018, 05:21 PM
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Re: Most useful basic equations/reference for FRC/FTC?

DC motor equations, with explanations:

http://motors.vex.com/introduction
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Unread 07-08-2018, 07:32 PM
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Re: Most useful basic equations/reference for FRC/FTC?

V=I*R

And all of its various derivatives.
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Unread 07-08-2018, 08:32 PM
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Re: Most useful basic equations/reference for FRC/FTC?

for gears: pitch diameter = # teeth / diametrical pitch
for pullies: pitch diameter = (# teeth * pitch) / pi
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Unread 07-08-2018, 09:26 PM
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Re: Most useful basic equations/reference for FRC/FTC?

All you need is F = m*a and you can derive the rest.
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Unread 07-08-2018, 10:06 PM
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Re: Most useful basic equations/reference for FRC/FTC?

It appears you're talking about for design time.

Along this line:

Quote:
Originally Posted by Stuart View Post
  • Some Pythagorean triplets.
I'd add some near-pythagorean triplets that are "close enough" to 30 and 45 degree angles to build Versaframe triangles without drilling holes in either gussets or tubes:

30/60/90 triangle: 152 + 262 ~ 302
45/45/90 triangle: 122 + 122 ~ 172

We used 15/26/30 (actually 7.5", 13", 15") on our 2017 robot and 12/12/17 on our 2018 competition robot; the errors were small enough in both cases that we had no problem fitting the rivets. I have also used 30x26 and 15x13 tiling patterns to make honeycomb wallpaper. Also, as it turns out, the 5/12/13 pythagorean triple is close enough to a 22 1/2 degree angle for many practical purposes.


Nickbrickmaster: This really should be ΣF = ma, and you also need Freaction = -Faction. All the F's and a's should be annotated as vector quantities. Then you can derive the rest. The derivations get shorter if you add ΣΓ = Iα with Γ and α being pseudo-vectors.

I might also add the equation for effective gear ratio of a planetary gearbox with a fixed ring: Rp = Rring/Rsun + 1.

Pneumatic cylinder equation: F=pA [also works for hydraulics, but not useful for FRC).

Some energy/work equations! Likely some I'm missing, here are a few:
  • Ekinetic = mv2/2 or Iω2/2
  • Egravitational = mgh
  • Espring = kx2/2
  • Epneumatic (slow) = pV

Edit: even on a one-pager, there should be some room for the key numbers of the legal motors (stall and free current, stall torque, free speed, peak power). Also, some conversion factors. Top of the list: 1 rpm ~ 0.1047 radians/sec.
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Last edited by GeeTwo : 07-08-2018 at 10:30 PM.
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Unread 07-09-2018, 08:37 AM
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Re: Most useful basic equations/reference for FRC/FTC?

This, if you're a district team
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Unread 07-09-2018, 09:44 PM
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Re: Most useful basic equations/reference for FRC/FTC?

Quote:
Originally Posted by deslusionary View Post
Not mechanically oriented so here's a PID equation:

Attachment 23479
Don’t most people write for their constants to all be positive? If so, shouldn’t the derivative term have the opposite sign?
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Unread 07-09-2018, 10:14 PM
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Re: Most useful basic equations/reference for FRC/FTC?

Quote:
Originally Posted by jhill42 View Post
Don’t most people write for their constants to all be positive? If so, shouldn’t the derivative term have the opposite sign?
There are a bajillion forms of the PID equation people use.
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Unread 07-09-2018, 10:49 PM
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Re: Most useful basic equations/reference for FRC/FTC?

From one of my favorite professors and I'm sure a bunch of other places, here are the fundamental equations for a few different engineering disciplines:

Electrical Engineers: V = I*R (Ohm's Law)

Mechanical Engineers: F = M*a (Newton's 2nd Law)

Civil Engineers: "if it goes uphill you gotta pump it" (... most civil engineers)
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Unread 07-10-2018, 07:45 AM
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Re: Most useful basic equations/reference for FRC/FTC?

Quote:
Originally Posted by Ginger Power View Post
From one of my favorite professors and I'm sure a bunch of other places, here are the fundamental equations for a few different engineering disciplines:

Electrical Engineers: V = I*R (Ohm's Law)

Mechanical Engineers: F = M*a (Newton's 2nd Law)

Civil Engineers: "if it goes uphill you gotta pump it" (... most civil engineers)
TIL will.i.am is a civil engineer.
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