// Interactive configuration for Rohloff Speedhub 500/14
title "Rohloff Speedhub 500/14"
version
{@
Version 8.0, 21.4.2006
Reason driving.
Switchable lin/log scales
francois.roulet@epfl.ch
EPFL
Swiss Federal Institute of Technology
CH-1015 Lausanne
Switzerland
@}
help
{@
There's a whole Speedhub 500/14 simulator:
You can adjust all 5 sliders for each planet gear ratio,
or geometric progression reason slider,
and the 14 gears selector.
In the "Settings" menu,
you can toggle between sorted results or not.
With the Right-click,
you can choose linear or logarithmic scale
@}
// TABLE 1
// WHEEL Number of Teeth
// Sun 19 42
// Sun 20 35
// Sun 22 42
// Sun 23 35
// Sun 36 51
// Planet 18
// Stage 18a 24
// Stage 18b 32
// Planet 21
// Stage 21a 24
// Stage 21b 32
// Planet 38
// Stage 38a 20
// Stage 38b 26
// Ring gear 24 -90
// Ring gear 25 -90
// Ring gear 39 -96
// TABLE 2
// Clutch
// <--- Brakes ---> <- Clutch ->
// Gear Step 26 27 28 29 31 32 41 Gear Ratio Step Jump
// 1st Gear x x 3.591 13.5%
// 2nd Gear x x 3.163 13.8%
// 3rd Gear x x 2.779 13.5%
// 4th Gear x x 2.448 13.5%
// 5th Gear x x 2.157 13.8%
// 6th Gear x x 1.895 13.5%
// 7th Gear x x 1.670 13.8%
// 8th Gear x x x 1.467 13.5%
// 9th Gear x x x 1.292 13.8%
// 10th Gear x x x 1.135 13.5%
// 11th Gear x x x 1.000 13.5%
// 12th Gear x x x 0.881 13.8%
// 13th Gear x x x 0.774 13.5%
// 14th Gear x x x 0.682 --
// TABLE 3
// Clutch
// Gear Step 90 91 92 93 95 96 41 Gear Ratio Step Jump
// 1st Gear x x 3.591 13.5%
// 2nd Gear x x 3.163 13.8%
// 3rd Gear x x 2.779 13.5%
// 4th Gear x x 2.448 13.5%
// 5th Gear x x 2.157 13.8%
// 6th Gear x x 1.895 13.5%
// 7th Gear x x 1.670 13.8%
// 8th Gear x x x 1.467 13.5%
// 9th Gear x x x 1.292 13.8%
// 10th Gear x x x 1.135 13.5%
// 11th Gear x x x 1.000 13.5%
// 12th Gear x x x 0.881 13.8%
// 13th Gear x x x 0.774 13.5%
// 14th Gear x x x 0.682 --
variable Re1, Re2 // Epicyclic ratios
variable Rs1, Rs2 // Sun gears ratios
variable Re3 // 3rd Epicyclic
variable Carrier // Twin Carrier regime
variable Ratios // Twin Planet ratios table
variable Shifter // Gear selector
variable Range // Full gears range
variable alpha // Ideal logarithmic slope
variable Sorted // Is sorted ?
variable Reason // Geometric Progression Reason
init (Re1, Re2, Rs1, Rs2, Re3, Carrier, Ratios, Shifter, Range, Reason, alpha, Sorted) = init
make (Ratios) = calcRatios(Re1, Re2, Rs1, Rs2)
menu "Sorted" _checkmark(Sorted) Sorted=toggle(Sorted)
function
{@
function (Re1, Re2, Rs1, Rs2, Re3, Carrier, Ratios, Shifter, Range, Reason, alpha, Sorted) = init
subplots('Global Ratios Histogram\tTwin Planet Nomogram\nGears Organigram\tGears Ratios Sliders');
// Rohloff's Metrics
Re1 = 1 + 2*24/42; // S1 = 42, F1 = 24, R1 = 90 (42+24=66 ?)
Rs1 = 32/24*42/35; // S2 = 35, F2 = 32 (35+32=67 ?)
Rs2 = 32/24*42/35; // S3 = 35, F3 = 32
Re2 = 1 + 2*24/42; // S4 = 42, F4 = 24, R2 = 90
Re3 = 1/(1 + 20/27*96/49); // R3 = 96, Big sun = 51, Small sun = 42
Reason = power(1/Re1 + 1, 1/3); // Cubic root
Carrier = 1;
Ratios = [1, 1.292, 1.467, 0.774, 1, 1.135, 0.682, 0.881, 1];
Range = ones(1, 2*9);
alpha = Reason;
Shifter = 1;
Sorted = 1;
function Sorted = toggle(Sorted)
Sorted = ~Sorted;
function drawSliders(Re1, Re2, Rs1, Rs2, Re3, Reason, Shifter)
slider(sprintf('1st Epicyclic = 1/%.2f\n1st Suns Ratio = %.2f\n2nd Suns Ratio = %.2f\n2nd Epicyclic = 1/%.2f\n3rd Epicyclic = %.3f\nReason = %.3f\nGear selector = %d', ...
Re1, Rs1, Rs2, Re2, Re3, Reason, Shifter), [Re1; Rs1; Rs2; Re2; Re3; Reason; Shifter], [2,4; 1.5,2; 1.5,2; 2,4; 1/3,2/3; 1.08,1.14; 1,14], 'LLLLLL-', 'mmcckkk', 1);
function (Ratios) = calcRatios(Re1, Re2, Rs1, Rs2)
// Progressive order: 4, 9, 8, 1, 5, 3, 2, 7, 6
// Distributive order: 1, 3, 2, 7, 9, 8, 4, 6, 5
Ratios(1) = 1;
Ratios(3) = 1/Re2 + 1;
Ratios(2) = 1/(Rs2*Re2) + 1;
Ratios(7) = Re1/(1 + Re1);
Ratios(9) = Re1/(1 + Re1) * (1/Re2 + 1);
Ratios(8) = Re1/(1 + Re1) * (1/(Rs2*Re2) + 1);
Ratios(4) = Rs1*Re1/(1 + Rs1*Re1);
Ratios(6) = Rs1*Re1/(1 + Rs1*Re1) * (1/Re2 + 1);
Ratios(5) = Rs1*Re1/(1 + Rs1*Re1) * (1/(Rs2*Re2) + 1);
function drawNomogram(Re1, Re2, Rs1, Rs2, Sorted, Shifter)
scale('linlin', [-Rs1*Re1, Rs2*Re2, 0, 1+1/Re2]);
line([1, 0], -Rs1*Re1, 'm-');
text(-Rs1*Re1, 1 + 1/Re2, 'S2', 'tl');
line([1, 0], -Re1, 'm-');
text(-Re1, 1 + 1/Re2, 'S1', 'tl');
line([1, 0], -1, 'c-');
text(-1, 1 + 1/Re2, 'R2', 'tl');
line([1, 0], 0);
text(0, 1 + 1/Re2, 'C', 'tr');
line([1, 0], 1, 'm-');
text(1, 1 + 1/Re2, 'R1', 'tr');
line([1, 0], Re2, 'c-');
text(Re2, 1 + 1/Re2, 'S4', 'tr');
line([1, 0], Rs2*Re2, 'c-');
text(Rs2*Re2, 1 + 1/Re2, 'S3', 'tr');
line([0, 1], 1, '-'); // Zero Abscissa
switch Sorted
case 0
Index = [1,2,3,4,6,7,8, 1,2,3,4,6,7,8]; // Distributive Selector Index
case 1
Index = [7,4,8,1,6,2,3, 7,4,8,1,6,2,3]; // Progressive Selector Index
end
switch Index(Shifter)
// Progressive order: 1, 2, 4, 9, 7, 5, 8, 6, 3
// Distributive order: 7, 4, 1, 3, 6, 9, 2, 5, 8
case 7
Carrier = Re1/(1 + Re1);
plot(0, Carrier, 'o');
plot([-Re1,1; -Re1,1], [0,1; 0,1], 'moM_'); // S1 blocked
plot([Re2,-1; Rs2*Re2,-1], [Carrier,Carrier; Carrier,Carrier], 'coC_'); // S4 coupled
case 4
Carrier = Rs1*Re1/(1 + Rs1*Re1);
plot(0, Carrier, 'o');
plot([-Rs1*Re1,1; -Rs1*Re1,1], [0,1; 0,1], 'moM_'); // S2 blocked
plot([Re2,-1; Rs2*Re2,-1], [Carrier,Carrier; Carrier,Carrier], 'coC_'); // S4 coupled
case 1
Carrier = 1;
plot(0, Carrier, 'o');
plot([-Re1,1; -Rs1*Re1,1], [1,1; 1,1], 'moM_'); // S1 coupled
plot([Re2,-1; Rs2*Re2,-1], [Carrier,Carrier; Carrier,Carrier], 'coC_'); // S4 coupled
case 3
Carrier = 1;
plot(0, Carrier, 'o');
plot([-Re1,1; -Rs1*Re1,1], [1,1; 1,1], 'moM_'); // S1 coupled
plot([Re2,-1; Re2,-1], [0,(1 + 1/Re2)*Carrier; 0,(1 + 1/Re2)*Carrier], 'coC_'); // S4 blocked
case 6
Carrier = Rs1*Re1/(1 + Rs1*Re1);
plot(0, Carrier, 'o');
plot([-Rs1*Re1,1; -Rs1*Re1,1], [0,1; 0,1], 'moM_'); // S2 blocked
plot([Re2,-1; Re2,-1], [0,(1 + 1/Re2)*Carrier; 0,(1 + 1/Re2)*Carrier], 'coC_'); // S4 blocked
case 9
Carrier = Re1/(1 + Re1);
plot(0, Carrier, 'o');
plot([-Re1,1; -Re1,1], [0,1; 0,1], 'moM_'); // S1 blocked
plot([Re2,-1; Re2,-1], [0,(1 + 1/Re2)*Carrier; 0,(1 + 1/Re2)*Carrier], 'coC_'); // S4 blocked
case 2
Carrier = 1;
plot(0, Carrier, 'o');
plot([-Re1,1; -Rs1*Re1,1], [1,1; 1,1], 'moM_'); // S1 coupled
plot([Rs2*Re2,-1; Rs2*Re2,-1], [0,(1 + 1/(Rs2*Re2))*Carrier; ...
0,(1 + 1/(Rs2*Re2))*Carrier], 'coC_'); // S3 blocked
case 5
Carrier = Rs1*Re1/(1 + Rs1*Re1);
plot(0, Carrier, 'o');
plot([-Rs1*Re1,1; -Rs1*Re1,1], [0,1; 0,1], 'moM_'); // S2 blocked
plot([Rs2*Re2,-1; Rs2*Re2,-1], [0,(1 + 1/(Rs2*Re2))*Carrier; ...
0,(1 + 1/(Rs2*Re2))*Carrier], 'coC_'); // S3 blocked
case 8
Carrier = Re1/(1 + Re1);
plot(0, Carrier, 'o');
plot([-Re1,1; -Re1,1], [0,1; 0,1], 'moM_'); // S1 blocked
plot([Rs2*Re2,-1; Rs2*Re2,-1], [0,(1 + 1/(Rs2*Re2))*Carrier; ...
0,(1 + 1/(Rs2*Re2))*Carrier], 'coC_'); // S3 blocked
end
function drawHistogram(Re3, Ratios, Sorted)
Index = [1,2,3,4,6,7,8]; // Usable Gears Index
Range = [Re3*Ratios(Index), Ratios(Index)];
scale('linlin/linlog', [1,2*7, min(Range),max(Range)]);
label('Gear');
line([0, 1], 1, '-');
switch Sorted
case 0 // Unsorted
bar(Range);
case 1 // Sorted
alpha = power(max(Range)/min(Range), 1/(2*7 - 1));
plot(1:2*7, min(Range)*power(alpha, 0:2*7-1), 'r');
bar(sort(Range));
end
function drawOrganigram(Ratios, Re3, Sorted, Shifter)
// plotoption('noygrid)'
scale('linlin/loglin');
label('Ratio');
switch Sorted
case 0
Index1 = [1,2,3,4,6,7,8, 1,2,3,4,6,7,8]; // Usable Gears Index
Index2 = [1,1,1,4,4,7,7, 1,1,1,4,4,7,7]; // PGT1 Index
case 1
Index1 = [7,4,8,1,6,2,3, 7,4,8,1,6,2,3]; // Usable Gears Index
Index2 = [7,4,7,1,4,1,1, 7,4,7,1,4,1,1]; // PGT1 Index
end
Index3 = [Re3,Re3,Re3,Re3,Re3,Re3,Re3, 1,1,1,1,1,1,1]; // PGT3 Index
for Pgt1 = 0:2
plot([1, Ratios(3*Pgt1 + 1); 1, Ratios(3*Pgt1 + 1)], [3,2; 3,2], 'mom_');
for Pgt2 = 1:3
plot([Ratios(3*Pgt1 + 1), Ratios(3*Pgt1 + Pgt2); ...
Ratios(3*Pgt1 + 1), Ratios(3*Pgt1 + Pgt2)], [1,1;2,1], 'coc_');
for Pgt3 = 1:2
plot([Ratios(3*Pgt1 + Pgt2), Re3*Ratios(3*Pgt1 + Pgt2); ...
Ratios(3*Pgt1 + Pgt2), Ratios(3*Pgt1 + Pgt2); ...
Ratios(3*Pgt1 + Pgt2), Re3*Ratios(3*Pgt1 + Pgt2)], ...
[0,0; 1,0; 1,0], 'bob_b_');
end
end
end
// Active Gear Highlight
plot([1,Ratios(Index2(Shifter)); Ratios(Index2(Shifter)),Ratios(Index1(Shifter))], [3,2;2,1], 'M_C_');
plot([Ratios(Index2(Shifter)); Ratios(Index1(Shifter))], [2;1], 'MoCo');
plot([Ratios(Index1(Shifter)),Index3(Shifter)*Ratios(Index1(Shifter))], [1,0], 'Y_');
plot(Index3(Shifter)*Ratios(Index1(Shifter)), 0, 'Yo');
text(max(Ratios), 3, 'Ring 1', 'tr');
line([0, 1], 2, '-');
text(max(Ratios), 2, 'Carrier', 'br');
line([0, 1], 1, '-');
text(max(Ratios), 1, 'Ring 2', 'br');
function (Re1, Re2, Rs1, Rs2, Re3, Reason, Shifter, msg) = dragSliders(Re1, Re2, Rs1, Rs2, Re3, Reason, Shifter, nb, x1)
if isempty(nb)
cancel;
end
msg = sprintf('');
switch nb
case 1
Re1 = x1;
case 2
Rs1 = x1;
case 3
Rs2 = x1;
case 4
Re2 = x1;
case 5
Re3 = x1;
case 6
Reason = x1;
Re1 = 1/(Reason^3 - 1);
Re2 = Re1;
// Rs1 = 1/(Re1*(power(1 + 1/Re1, 2/3) - 1)); // from Re1 only
Rs1 = 1/(Re1*(Reason^2 - 1)); // from Re1 & Reason
Rs2 = Rs1;
Re3 = power(Reason, -7);
msg = sprintf('Ratio spread: %g', Reason^(2*7-1));
case 7
Shifter = fix(x1 + 0.5); // +0.5 = Slider Centering
msg = sprintf('Degrees: %g', 21*(Shifter - 1)); // Camshaft Angle
end
@}
figure "Global Ratios Histogram"
draw drawHistogram(Re3, Ratios, Sorted)
figure "Twin Planet Nomogram"
draw drawNomogram(Re1, Re2, Rs1, Rs2, Sorted, Shifter)
figure "Gears Organigram"
draw drawOrganigram(Ratios, Re3, Sorted, Shifter)
figure "Gears Ratios Sliders"
draw drawSliders(Re1, Re2, Rs1, Rs2, Re3, Reason, Shifter)
mousedrag (Re1, Re2, Rs1, Rs2, Re3, Reason, Shifter, _msg) = dragSliders(Re1, Re2, Rs1, Rs2, Re3, Reason, Shifter, _nb, _x1)