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optimization_plan.jl
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### A Pluto.jl notebook ###
# v0.19.9
using Markdown
using InteractiveUtils
# ╔═╡ 5675938a-2f8e-11ed-1102-23fbe193abd6
using Symbolics
# ╔═╡ d8b32fab-a25c-42ab-8e2b-cc94ae19abf6
using PlutoUI
# ╔═╡ 66f358fc-ddd5-41c6-90de-a6287528c852
using BenchmarkTools
# ╔═╡ c395a5a2-58ba-4f88-b9fb-b59d6f2c1e8b
@variables E R Rᵣ Nₗ Nᵣ ϕ
# ╔═╡ 71b6b3c1-6fb1-4848-a36b-c799c2d91eec
@variables Q V₂₃ mᵥ ψ ω_I ω_C V_IC ϕ_I
# ╔═╡ 481338d3-b3d9-4c94-89ad-79af66991067
# ω₂ should be ω_I, ω₃ should be ω_C
# 2 = I
# 3 = C
# ╔═╡ fe49df3c-f5fb-4ca8-bbdf-48d89e1b524e
eq₁ = V_IC~E*ω_I~-(Q-E)*ω_C
# ╔═╡ 1855071f-8eb3-4644-9ffb-e75c04de10c0
eq₂ = mᵥ~ω_C/ω_I~(Nₗ-Nᵣ)/Nₗ # Adapted from equation 2 in On the lobe profile design in a cycloid reducer using instant velocity center
# ╔═╡ 04dd010c-0cbe-43a6-9e8f-a5c061870bd1
eq₂_s_ω_C = ω_C~ω_I*(Nₗ-Nᵣ)/Nₗ
# ╔═╡ bb1e9461-d4d1-4f19-9d8f-028960c94525
eq₃_1 = substitute(eq₁.rhs, Dict(eq₂_s_ω_C.lhs => eq₂_s_ω_C.rhs))
# ╔═╡ b0858596-9023-45c8-99e1-34bce3488307
eq₃_2 = simplify(eq₃_1.lhs/ω_I ~ eq₃_1.rhs/ω_I)
# ╔═╡ 5955f412-6c96-4bc6-8f20-65331cad47ea
eq₃_3 = eq₃_2.lhs*Nₗ ~ expand(eq₃_2.rhs*Nₗ)
# ╔═╡ 6a06b879-41e9-4ff4-b312-26e3b03b49af
eq₃_4 = eq₃_3.lhs-(E*Nₗ - E*Nᵣ) ~ eq₃_3.rhs-(E*Nₗ - E*Nᵣ)
# ╔═╡ 603a7182-fe97-409b-af04-6d7fc99940df
eq₃ = simplify(eq₃_4.rhs/(Nᵣ-Nₗ) ~ eq₃_4.lhs/(Nᵣ-Nₗ))
# ╔═╡ cd55e7d6-a291-46e1-bf4e-99885c00f4bb
eq₄_1 = ψ ~ tan(Q*sin(ϕ)/(R-Q*cos(ϕ)))
# ╔═╡ 63673dce-1948-4e0d-91df-33f4e2b73546
eq₄_2 = ψ ~ tan(sin(ϕ)/(R/Q-cos(ϕ)))
# ╔═╡ 65515c25-4ba4-4121-b3d2-88fc04f48018
eq₄ = substitute(eq₄_2, Dict(eq₃.lhs => eq₃.rhs))
# ╔═╡ 08003a33-bc07-4b3a-a427-7a29cf1990d4
mᵥ ~ (Nₗ-Nᵣ)/Nₗ
# ╔═╡ cae4d88e-7a77-4644-8cfd-d831d528f21d
mᵥ-1 ~ (Nₗ-Nᵣ)/Nₗ - 1
# ╔═╡ 09b84e94-0828-4f60-a5ec-1d35f74b83cf
mᵥ-1 ~ -Nᵣ/Nₗ
# ╔═╡ 03ee7ec0-9796-4602-b44c-040937996ca1
P₁ = Q*[cos(ϕ); sin(ϕ)]
# ╔═╡ c1001a53-d73e-4439-8e10-3ab451edc4bb
T_GI = [cos(ϕ_I) -sin(ϕ_I) 0.0; sin(ϕ_I) cos(ϕ_I) 0.0; 0.0 0.0 1.0]
# ╔═╡ c5157af6-aa91-4889-afdd-894a9600db51
k = (Nₗ - Nᵣ)/Nₗ
# ╔═╡ 7815a798-fefa-4e19-8f74-e001261dc62c
ϕ_C = k*ϕ_I
# ╔═╡ 23ccf7fa-62c2-494e-be90-ad3049d494ec
ϕ_IC = simplify(ϕ_C-ϕ_I)
# ╔═╡ c2888906-41c9-4a07-9512-70b9366538d9
begin
T_GC = zeros(Num, 3, 3)
T_GC[3, 3] = 1
C⃗_I = [E; 0; 1]
T_GC[1:3, 3] = T_GI*C⃗_I
T_GC[1:2, 1:2] = [cos(ϕ_C) -sin(ϕ_C); sin(ϕ_C) cos(ϕ_C)]
T_GC
end
# ╔═╡ 903130ee-4540-4425-8b2b-a05a68acdd37
T_GC[1:3, 3]
# ╔═╡ 4aefb83b-a854-4c4f-874c-3e4e2f1d878c
begin
T_CG = zeros(Num, 3, 3)
T_CG[3, 3] = 1
rot_CG = T_GC[1:2, 1:2]'
C⃗_G = -rot_CG*T_GC[1:2, 3]
T_CG[1:2, 1:2] = rot_CG
T_CG[1:2, 3] = C⃗_G
T_CG
end
# ╔═╡ 2a2ba11f-4a6b-4289-8859-0412e0b6c00a
Q⃗_I = [E*Nᵣ/(Nᵣ-Nₗ); 0]#[Q; 0; 1]
# ╔═╡ d35686b1-a552-4239-a14b-e43576aea5ef
begin
T_GR = zeros(Num, 3,3)
T_GR[3, 3] = 1
T_GR[1, 1] = 1
T_GR[2, 2] = 1
PR⃗_G = [R; 0; 1]
T_GR[1:3, 3] = PR⃗_G
T_GR
end
# ╔═╡ 2c565cc4-5163-41a7-a45e-ca78574c56a0
begin
T_RG = zeros(Num, 3, 3)
T_RG[3, 3] = 1
rot_RG = T_GR[1:2, 1:2]'
R⃗_G_2 = -rot_RG*T_GR[1:2, 3]
T_RG[1:2, 1:2] = rot_RG
T_RG[1:2, 3] = R⃗_G_2
T_RG
end
# ╔═╡ 5150a785-59b2-4692-bd72-444f7989d668
T_CR = T_CG*T_GR
# ╔═╡ 539d981d-d3ac-491f-8e08-39e61b572675
ψ_act = atan(sin(ϕ_I)/(R*(Nᵣ-Nₗ)/(E*Nᵣ)-cos(ϕ_I)))
# ╔═╡ 3aabce87-2cf1-4fa6-9b71-e91786407ec9
ψ⃗ =
# ╔═╡ 3676e62f-a09b-4c4c-a0e5-564576980ef4
Q⃗_G = (T_GI*[Q⃗_I; 0.0])[1:2]
# ╔═╡ 0d9753ca-330c-430e-b97d-843e7dc11272
Q⃗_R = simplify((T_RG*[Q⃗_G; 1.0])[1:2])
# ╔═╡ 1dbc5858-630c-49e6-8c23-a3043d4c205f
sqmag_Q⃗_r = simplify(Q⃗_R'*Q⃗_R)
# ╔═╡ c7f61dba-17d6-4685-8a52-9d15229b553f
mag_Q⃗_R = simplify(sqrt(Q⃗_R'*Q⃗_R))
# ╔═╡ 9d2c0177-75ff-4edd-8ebd-b05055253ee4
Q̂_R = Q⃗_R/mag_Q⃗_R
# ╔═╡ fe1747b0-bdc8-4016-9e7f-79ea65cb8508
PV⃗_R = [Rᵣ*Q̂_R; 1.0] #[Rᵣ*[-cos(ψ_act), sin(ψ_act)]; 1.0]
# ╔═╡ 0ac8ca2e-1cf8-49f3-9690-ed5f2aa36d88
sin_ψ =
# ╔═╡ 9826601a-8130-4f32-ac4d-3f561f927095
PV⃗_C = simplify(T_CR*PV⃗_R)
# ╔═╡ 0a563f06-ec4e-4292-9ad6-56894addeeea
build_function(PV⃗_C, [E R Rᵣ Nₗ Nᵣ ϕ_I]...)
# ╔═╡ 636591d5-62a0-497c-9edc-17e252f3dd60
PV⃗_C
# ╔═╡ 04525774-4063-4f1e-a467-8d35e84342ec
function hand_func(E, R, Rᵣ, Nₗ, Nᵣ, ϕ)
Nₗ_min_Nᵣ = (Nₗ - Nᵣ)
K_loc = Nₗ_min_Nᵣ/Nₗ
Kϕ = ϕ*K_loc
sin_ϕ = sin(ϕ)
cos_ϕ = cos(ϕ)
Nᵣ_min_Nₗ = -Nₗ_min_Nᵣ
Q_loc = E*Nᵣ/Nᵣ_min_Nₗ
Q_sin_ϕ = Q_loc*sin_ϕ
Q_cos_ϕ = Q_loc*cos_ϕ
Q_cos_ϕ_min_R = Q_cos_ϕ - R
Q_cos_ϕ_min_R_allsq = Q_cos_ϕ_min_R*Q_cos_ϕ_min_R
Nᵣ_pl_Nₗ = Nᵣ + Nₗ
A_sq = Q_cos_ϕ_min_R_allsq*Nᵣ_pl_Nₗ*Nᵣ_pl_Nₗ + sin_ϕ*sin_ϕ*Nᵣ*Nᵣ*E*E
A = sqrt(A_sq)
sin_Kϕ = sin(Kϕ)
cos_Kϕ = cos(Kϕ)
Rᵣ_Q_sin_ϕ = Rᵣ*Q_sin_ϕ
B = Rᵣ*Q_cos_ϕ_min_R*cos_Kϕ + Rᵣ_Q_sin_ϕ*sin_Kϕ
C = -Rᵣ*Q_cos_ϕ_min_R*sin_Kϕ + Rᵣ_Q_sin_ϕ*cos_Kϕ
R_min_E_cos_ϕ = R-E*cos_ϕ
E_sin_ϕ = E*sin_ϕ
D = R-E*cos_ϕ*cos_Kϕ-E_sin_ϕ*sin_Kϕ
E = -R_min_E_cos_ϕ*sin_Kϕ-E_sin_ϕ*cos_Kϕ
return [B/A+D; C/A+E]
end
# ╔═╡ c596ceb3-4349-454c-9b43-b279765e24c2
func = eval(build_function(PV⃗_C, [E R Rᵣ Nₗ Nᵣ ϕ_I]...)[1])
# ╔═╡ 4f5302af-5477-412f-9778-3c5a356aaf6b
coolest_func = func
# ╔═╡ 3d366731-b779-40b8-be41-2173ba979cd6
func(rand(), rand(), rand(), rand(), rand(), 0.0)
# ╔═╡ d66199eb-bc1b-4e9a-8c5e-674928fbfaae
@benchmark eval(func)(rand(), rand(), rand(), rand(), rand(), rand())
# ╔═╡ 396eeb75-bdb6-4588-8ed6-c2f082c2f4a2
@benchmark eval(hand_func)(rand(), rand(), rand(), rand(), rand(), rand())
# ╔═╡ 82ef3842-6eef-44f6-9393-83d3f258a8eb
E⃗_G = E*[cos(ϕ_I); sin(ϕ_I)]
# ╔═╡ 356d7c32-d03c-4d1c-8fcd-fb5bb32d704f
R⃗_G = [R; 0.0]
# ╔═╡ a94bb12e-22ba-4571-8b94-44628cc210a3
function norm(vec::T) where T <: Vector
return sqrt(vec'*vec)
end
# ╔═╡ dbc83763-e75d-41b8-a33a-98d7e62912e4
fᵢ = simplify(norm(E⃗_G - R⃗_G)/norm(Q⃗_G-R⃗_G) * (R - Q*cos(ϕ_I)))
# ╔═╡ e9dbc3e8-71dc-4e09-b579-77181ddeecbd
F_I =
# ╔═╡ 20938838-c797-4778-87d7-1422b15685bc
E⃗_G - R⃗_G
# ╔═╡ 5718ca9e-be07-4661-b746-eb62e1cef272
Q⃗_G
# ╔═╡ 0626fc31-7641-44bf-aae4-67bf42ad0ba1
R⃗_G
# ╔═╡ be13eef6-9c8f-486a-8ba4-45982ed597ee
N_L1, N_R1, N_L2, N_R2 = 6, 5, 5, 4
# ╔═╡ 283220b2-3fcb-42cf-8d06-0112a9a2dd2d
((N_L1 - N_R1)/N_L1 - (N_L2 - N_R2)/N_L2)/(1-(N_L1 - N_R1)/N_L1)
# ╔═╡ e5b562cc-3aea-4bd5-96e2-7894840705b1
1/25
# ╔═╡ abec3418-e7e6-4252-a562-8b8f09fb03e3
@variables N_l1, N_r1, N_l2, N_r2
# ╔═╡ c6f062e6-ea42-4b43-9fe8-3e55c7220ca3
ex = simplify(((N_l1 - N_r1)/N_l1 - (N_l2 - N_r2)/N_l2)/(1-(N_l1 - N_r1)/N_l1))
# ╔═╡ 0d624b39-62bc-46b3-886a-5d640ed5f360
N_L1*N_R2/N_L2/N_R1 - 1
# ╔═╡ 2c01b64a-4869-4b89-9757-d776ff4955e7
eq = 15*N_l1*N_r2 - 15*N_r1*N_l2 ~ -N_r1*N_l2
# ╔═╡ f37ac48e-f1c2-4265-b5a0-0c6488ce6fb1
N_l1 ~ Symbolics.solve_for(eq, N_l1)
# ╔═╡ a4958219-caed-4392-ba42-859a87fe7e82
zeros(Int, 20, 20, 20, 20)
# ╔═╡ 08870453-0865-43b6-b6e4-e7eeb36bd825
print(build_function(PV⃗_C, [E R Rᵣ Nₗ Nᵣ ϕ_I]...; target = Symbolics.CTarget()))
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8"
Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
[compat]
BenchmarkTools = "~1.3.1"
PlutoUI = "~0.7.40"
Symbolics = "~4.10.4"
"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
PLUTO_MANIFEST_TOML_CONTENTS = """
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