Solution #1 Sec.3 Calcs

OBJECTIVE: create a nodal diagram of just the motor bracket, and find the reaction forces (from the point where the bracket meets the trailing arm) for each known loading case

(^^ this is the bracket being solved)

OUTPUT: a list of reaction forces (Cx, Cy, Dx, Dy, Ez, mEx, mEy) as shown in the sketch below, that will be used as inputs to sim the trailing arm (https://uwmidsun.atlassian.net/wiki/spaces/MECH/pages/3317628999)

NODAL DIAGRAM:

See the following google drawing to show how the nodal is defined:
https://docs.google.com/drawings/d/1yLfxzWdcE1xLYA0lFEhJRNb2bxs31Vjpd-iqGs2PIZE/edit

GEOMETRIC CONSTANTS: (measured in SOLIDWORKS, these probably won’t change because the current design is passing sims)

l = 15mm
d= 32.7mm
s = 0mm OR 6.35mm (doesn’t really matter)

SOLVING:

We can immediately identify that the problem is statically indeterminant (6 equations and 7 unknowns), but the solution will only have a dimension of 1 (so only two variables are left ‘floating’ in terms of 1 another)

With hand solving (and the matlab script), we see that the two ‘floating’ variables are Cx and Dx. We can only conclude that Cx + Dx = F, where F is a constant value such as 2200 N (based on the constants). As such, we will just simulate two ‘worst case scenario’s where Cx = F and Dx = 0 for one scenario, and then vice-versa for the other.

OUTPUT:

From @Ted Stager 's matlab script, these are the max forces ever experienced:

We can see that almost all cases will occur at max compression (lambda = 28.78 deg), and then simplify to 4 binary combinations, to produce 2^4 = 16 permutations from below: