# Example 6.1
MKS(kN, deg)
ra = [0, 6] m
rb = [0, 0] m
rc = [5, 3] m
rd = [10, 0] m
f[2] = -2 kN
# Overall Equilibrium
BEGIN
   ax = 1 N
   ay = 1 N
   a = [ax, ay]
   b[1] = 1 N
   sumF = a + b + f
   sumM = cross(ra, a) + cross(rb, b) + cross(rd, f)
END
solve(sumF[1], sumF[2], sumM[3], ax, ay, b[1])
# Joint A
BEGIN
   tac = 1 N
   eac = (rd - ra) / mag(rd - ra)
   tab = 1 N
   eab[2] = -1
   sumF = a + tac * eac + tab * eab
END
solve(sumF[1], sumF[2], tac, tab)
# Joint B
BEGIN
    tbd[1] = 1 N
    sumF = b + tab * (-eab) + tbd
END
solve(sumF[1], tbd[1])



# Example 6.2
MKS(kN, deg)
ra = [0, 6] m
rb = [0, 0] m
rc = [5, 3] m
rd = [10, 0] m
# normalize by 1 kN
f[2] = -1 kN
# Overall Equilibrium
BEGIN
   ax = 1 N
   ay = 1 N
   a = [ax, ay]
   b[1] = 1 N
   sumF = a + b + f
   sumM = cross(ra, a) + cross(rb, b) + cross(rd, f)
END
solve(sumF[1], sumF[2], sumM[3], ax, ay, b[1])
# Joint A
BEGIN
   tac = 1 N
   eac = (rd - ra) / mag(rd - ra)
   tab = 1 N
   eab[2] = -1
   sumF = a + tac * eac + tab * eab
END
solve(sumF[1], sumF[2], tac, tab)
# Joint B
BEGIN
    tbd[1] = 1 N
    sumF = b + tab * (-eab) + tbd
END
solve(sumF[1], tbd[1])
# link forces
tac
tab
mag(tbd)
S_link = 10 kN
f_max = (S_link / tac)  kN



# Example 6.3
MKS(N, deg)
f = 1 N
# Joint C
a = 15 deg
tbc = -f / (2 * sin(a))
# joint B
BEGIN
   tab = 1 N
   alp  = 10 deg
   sumF = PolarVec(tab, alp) - [0, 1 ] N + PolarVec(tbc, a)
END
solve(sumF[1], sumF[2], alp, tab)

  

# Example 6.4
MKS(kN, deg)
f[2] = -100 kN
q = 45 deg
tcj = -f[2] / sin(q)



# Example 6.5
MKS(N, deg)
ra = [0, 0] m
rb = [1, 0 ] m
re = [2, 0] m
rh = [3, 0 ] m
rk = [4, 0] m
fb[2] = -1 N
fe[2] = -2 N
fh[2] = -1 N
# Reaction Forces
BEGIN
   ax = 1 N
   ay = 1 N
   a = [ax, ay]
   k[2] = 1 N
   sumF = a + k + fb + fe + fh
   sumM = cross(ra, a) + cross(rb, fb) + cross(re, fe) + cross(rh, fh) + cross(rk, k)
END
solve(sumF[1], sumF[2], sumM[3], ax, ay, k[2])
# Section
rd = [1, 2] m
BEGIN
   tdg[1] = 1 N
   tbe[1] = 1 N
   sumF = a + tdg + tbe
   sumM = cross(ra - rb, a) + cross(rd - rb, tdg)
END
solve(sumF[1], sumM[3], tdg[1], tbe[1])





# Example 6.6
MKS(mm, N, N m, deg)
ra = [0, 400] mm
rb = [600, 400] mm
rc = [1000, 0] mm
M0[3] = 200 N m
BEGIN
   # Reactions
   ax = 0 N
   ay = 1 N
   a = [ax, ay]
   c[2] = -ay
   sumF = a + c
   sumM = cross(ra, a) + cross(rc, c) + M0
   # Member BC
   bx = 0 N
   by = -c[2]
   b = [bx, by]
   sumFB = b + c
   sumMB = cross(rb, b) + cross(rc,c) + M0
END
solve(sumMB[3], ay)




# Example 6.7
IPS
ra = [0, 0] in
rd = [0, 18] in
rw = [16, 12] in
w[2] = -40 lb
#Reactions
BEGIN
   ax = 1 lb
   ay = 1 lb
   a = [ax, ay]
   d[1] = 1 lb
   sumF = a + d + w
   sumM = cross(ra, a) + cross(rd, d) + cross(rw, w)
END
solve(sumF[1], sumF[2], sumM[3], ax, ay, d[1])
# Wheel
gg = [-40, -40] lb
alp = atan(6/8)
# Member AD
rr = [0, 6] in
rc = [0, 12] in
BEGIN
   r = 1 N
   fr = PolarVec(r, alp)
   cx = 1 N
   cy = 1 N
   c = [cx, cy]
   sumF = a + d + fr + c
   sumM = cross(ra, a) + cross(rd, d) + cross(rr, fr) + cross(rc, c)
END
solve(sumF[1], sumF[2], sumM[3], r, cx, cy)




# Example 6.8
Member AD
ra = [0, 300] mm
rf = [400, 300] mm
rd = [800, 0] mm
f = [0, -120] N
BEGIN
   a[2] = 1 N
   dx = 1 N
   dy = 1 N
   d = [dx, dy]
   sumF = f + a + d
   sumM = cross(rf, f) + cross(ra, a) + cross(rd, d)
END
solve(sumF[1], sumF[2], sumM[3], a[2], dx, dy)
#CENTER MEMBER
rb = [0, 0] m
rf = [400, 0] mm
re = [800, 0] mm
BEGIN
    f2 = [-300] N
    ex = 1 N
    ey = -dy
    e = [ex, dy]
    bx = 1 N
    by = 1 N
    b = [bx, by]
    f = [0, -180] N
    sumF = b + f + f2 + e + d
    sumM = cross(rf, f) + cross(re, f2 + e + d)
END
solve(sumF[1], sumF[2], sumM[3], ex, bx, by)
#lower member
# TBD



# Example 6.9
a = atan(30/ 70)
f = 150 N
BEGIN
  dx = 1 N
  dy = 1 N
  r = 1 N
  e = 1 N
  fx = dx + r * cos(a)
  fy = dy - r * sin(a) + f

  MB = (30 mm) * dy - (100 mm) * f
  MC = -30 mm * e - 30 mm * dx
END
solve(fx,fy,MB,MC, dx, dy, r, e)
MechAdv = e / f



# Example 6.10
# not quite right
a = 0.02 m^2
patm = 10e5 Pa
R = 150 mm
b = 350 mm
d = 150 mm
len = 1050 mm
M1 = 40 N m
BEGIN
  alp = 10 deg; deg
  p = 1 Pa

  q = 1 N
  beta = atan(R * sin(alp) / sqrt(b^2 - R^2 * sin(alp)^2))

  qv = PolarVec(q, beta)
  rab = PolarVec(R, alp)

  v = a * (len - d - sqrt(b^2 - R^2 * sin(alp)^2) + R * cos(alp))
  v0 = a * (len - d - b + R)
  f = a * patm * (v0 / v - 1)

   fx = f - qv[1]

  M = mag(cross(rab, qv))
  err = M - M1
END
solve(err, alp)


# Homework Problems:

TBD