# MATLAB: Finding Multiple Solutions to a Single Equation by Varying a Set of Variables

gearsMATLABmultivariable

Hi,
I am trying to find different gear tooth counts based on an equation for a gear ratio. I want the number of teeth for each gear to be from 20 to 60 teeth. The equation for the gear ratio is:
``N = (G1 * G4) / ((G1-G3) * (G2-G1))``
How would I go about getting a 4 column matrix with all the possible tooth count combinations?
Here is what I have so far:
``N = 200;        % Gear RatioG1 = 20:1:60;   % Gear 1 tooth countG2 = 20:1:60;   % Gear 2 tooth countG3 = 20:1:60;   % Gear 3 tooth countG4 = 20:1:60;   % Gear 4 tooth countN = (G1.*G4)./((G1-G3).*(G2-G1));  % Gear Ratio calculation``
Also, is there a way to go about getting a range of the gear ratio as well? For example, if I wanted anything within +/- 5% of the desired ratio.
Thanks!

• ``N = 200;        % Gear RatioG1 = 20:1:60;   % Gear 1 tooth countG2 = 20:1:60;   % Gear 2 tooth countG3 = 20:1:60;   % Gear 3 tooth countG4 = 20:1:60;   % Gear 4 tooth count[G1g, G2g, G3g, G4g] = ndgrid(G1, G2, G3, G4);N = (G1g.*G4g)./((G1g-G3g).*(G2g-G1g));  % Gear Ratio calculationGear1 = G1g(:); Gear2 = G2g(:); Gear3 = G3g(:); Gear4 = G4g(:); Ratio = N(:);result = table(Gear1, Gear2, Gear3, Gear4, Ratio);``