Gears

$P_d=\frac{T}{D}=\frac{1}{m}

$m=\frac{D}{T}=\frac{1}{P_d}

$P_c=\frac{πD}{T}=πm

$π=P_cP_d

$P_c=2t+B

$t=\frac{P_c-B}{2}

$C.R.=\frac{\sqrt{(R_o^2-R_b^2)_g}+\sqrt{(R_o^2-R_b^2)_p}-csin\theta}{P_ccos\theta}

$C=\frac{D_g\pm D_p}{2}$

$C=\frac{T_g \pm T_p}{2P_d}

$C=\frac{P_c(T_g \pm T_p)}{2π}

$C=\frac{m(T_g \pm T_p)}{2}

$W_h=a+d=W_r+c

$W_r=2a

$c=d-a

Peanut
$T=F_tr_{driver}

$F_{tot}=\sqrt{F_a^2+F_t^2+F_r^2}

$F_r=F_ttan\phi$
$tan\phi=\frac{F_r}{F_t}

$F_a=F_ttan\psi$
$tan\psi=\frac{F_a}{F_t}

$tan\phi_N=tan\phi cos\psi

$P_{cN}=P_ccos\psi

$P_{dN}=\frac{P_d}{cos\psi}

$P=F_{tw}V_w=\frac{NT}{factor}$
$T=F_{tw}r_w

$\psi=tan^{-1}\left(\frac{L}{πD_w}\right)$

L=nP
n= single, double, triple

$F_s=F_{tw}\left(\frac{sin\phi_N}{sin\psi cos\phi_N +fcos\psi}\right)

$F_{tg}=F_s\left(\frac{cos\psi cos\phi_N - fsin\psi}{sin\phi_N}\right)

$tan\gamma_p=\frac{sin\theta}{SR+cos\theta}

$\theta=\gamma_p+\gamma_g

$tan\gamma_p=\frac{1}{SR}$
$90°=\gamma_g+\gamma_p

$L=\frac{1}{2}\sqrt{D_g^2+D_p^2}

$b=\frac{L}{3}$
$b=\frac{10}{P_d}$

whichever is lower

$F_a=F_ttan\phi sin\gamma_p

$F_r=F_ttan\phi cos\gamma_p

$T=F_tr_{mean}

$r_{mean}=\frac{D_p-bsin\gamma_p}{2}

$D_{op}=2a+2$
$D_{op}=\frac{N_p+2}{P_d}

$t=\frac{P_c}{2}

$D_{rp}=D_g-2a

$D_{rg}=D_g-2d

$D_{og}=\frac{N_p+2}{P_d}$
$D_{og}=D_g+2a

$B=S-T$
$B=\frac{0.03}{P_d}$ to $\frac{0.04}{P_d}$
$0.035/P_d