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Able to cut the gear on the right.
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@ReeseWang
ReeseWang committed Nov 22, 2017
1 parent 728be83 commit e22e0a1
Showing 1 changed file with 81 additions and 45 deletions.
126 changes: 81 additions & 45 deletions generation_v2.m
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Original file line number Diff line number Diff line change
@@ -1,24 +1,24 @@
function generation_v2 ()
addpath(genpath('./'))
a = 15; % Center distance
pAngle = 30*pi/180; % Pressure Angle
module = 1; % Module
pitch = pi * module; % Curve pitch
addDist = 0.9 * module; % Addendum distance
dedDist = 1.1 * module; % Dedendum distance
posLimiterLeng = 3; % Position limiter length
errTol = 1e-4; % Error checking tolerance
angTol = 1*pi/180; % Angular tolerance, rad
toolTipRadius = 0.2; % Forming tool radius
a = 15; % Center distance
pAngle = 30*pi/180; % Pressure Angle
module = 1; % Module
pitch = pi * module; % Curve pitch
addDist = 0.9 * module; % Addendum distance
dedDist = 1.1 * module; % Dedendum distance
posLimiterLeng = 3; % Position limiter length
errTol = 1e-4; % Error checking tolerance
angTol = 2*pi/180; % Angular tolerance, rad
toolTipRadius = 0.2; % Forming tool radius
toolFullAngle = 45*pi/180;
toolFluteLength = 5;
toolDiameter = 3.175;
toolStickOut = 15;
cutSteps = 2; % How many steps to simulate a rack using tip tool
cutDepth = 0.2; % Z step
dfReverse = true; % Reverse the role of driver and follower (pos don't change)
machineRef = true; % Demo in machine reference frame to avoid audience confusion.
leftRotateMargin = 1*pi/180; % Rotate margin of driver
cutSteps = 2; % How many steps to simulate a rack using tip tool
cutDepth = 0.2; % Z step
dfReverse = true; % Reverse the role of driver and follower (pos don't change)
machineRef = true; % Demo in machine reference frame to avoid audience confusion.
leftRotateMargin = 1*pi/180; % Rotate margin of driver

%% Read input, interpolate, and generate pitch curves.
filename = 'fp.txt';
Expand All @@ -35,8 +35,8 @@ function generation_v2 ()
polData(1,:) = polData(2,:) - leftRotateMargin/(polData(3,1) - polData(2,1))*(polData(3,:) - polData(2,:));
polData(end,:) = polData(end-1,:) - leftRotateMargin/(polData(end-1,1) - polData(end-2,1))*(polData(end-1,:) - polData(end-2,:));
dfStruct = spline(polData(:,1), polData(:,2)); % driverAngle = f(followerAngle)
ddfStruct = fnder(dfStruct); % 2nd order derivative
fStruct = fnint(dfStruct); % Original form
ddfStruct = fnder(dfStruct); % 2nd order derivative
fStruct = fnint(dfStruct); % Original form
offset = -ppval(fStruct, 0);
fFunc = @(theta) ppval(fStruct, theta) + offset; % Ensure f(0) = 0
dfFunc = @(theta) ppval(dfStruct, theta);
Expand All @@ -45,21 +45,21 @@ function generation_v2 ()

dDRFunc = @(theta) a * ddfFunc(theta)./(1 + dfFunc(theta)).^2; % r_d' = a * f''(theta) / (1 + f'(theta))^2
dsFunc = @(theta) sqrt(leftRadiusFunc(theta).^2 + dDRFunc(theta).^2); % ds = sqrt(r^2 + (df/dtheta)^2) dtheta
tagentFunc = @(theta) ddfFunc(theta)./(dfFunc(theta).*(1+dfFunc(theta))); % tan(alpha-theta)=f''[theta]/(f'[theta](1+f'[theta]))
tangentFunc = @(theta) ddfFunc(theta)./(dfFunc(theta).*(1+dfFunc(theta))); % tan(alpha-theta)=f''[theta]/(f'[theta](1+f'[theta]))

leftPolarAngles = polData(1,1):angTol:polData(end,1);
if leftPolarAngles(end) < polData(end,1) % Last value should reach the max in domain
if leftPolarAngles(end) < polData(end,1) % Last value should reach the max in domain
leftPolarAngles = [leftPolarAngles polData(end,1)];
end
leftPolarAngles = leftPolarAngles';

rightPolarAngles = fFunc(leftPolarAngles);
rightPitchPolarRadius = a * 1./(1+dfFunc(leftPolarAngles));
leftPitchPolarRadius = a - rightPitchPolarRadius;
leftTangentAngles = tagentFunc(leftPolarAngles);
%rightTangentAngles = -tagentFunc(leftPolarAngles); % Not necessary
leftTangentAngles = tangentFunc(leftPolarAngles);
%rightTangentAngles = -tangentFunc(leftPolarAngles); % Not necessary

%% XY coords of driver follower pitch line, extend by tagent
%% XY coords of driver follower pitch line, extend by tangent
[leftPitch(:,1), leftPitch(:,2)] = pol2cart(leftPolarAngles, leftPitchPolarRadius);
[rightPitch(:,1), rightPitch(:,2)] = pol2cart(rightPolarAngles, rightPitchPolarRadius);
tanAngle = leftPolarAngles(end) - leftTangentAngles(end);
Expand All @@ -77,8 +77,8 @@ function generation_v2 ()
rightPitch = [ ...
rightPitch(1,:) - posLimiterLeng * [-sin(tanAngle) cos(tanAngle)]; rightPitch];

plot(leftPitch(:,1), leftPitch(:,2), - rightPitch(:,1) + a, rightPitch(:,2));
axis equal
%plot(leftPitch(:,1), leftPitch(:,2), - rightPitch(:,1) + a, rightPitch(:,2));
%axis equal

%% Integrate pitch arc lengths.
pitchArcLengths = zeros(size(leftPolarAngles));
Expand Down Expand Up @@ -111,7 +111,7 @@ function generation_v2 ()
for i = 1:size(rackZigZag, 1)
rackZigZag(i,1) = zigZagHalfHight * (-1)^i;
end
if rackZigZag(end,1) < 0 % Driver should drive the follower at the end
if rackZigZag(end,1) < 0 % Driver should drive the follower at the end
rackZigZag = [rackZigZag; zigZagHalfHight rackZigZag(end,2) + pitch/2];
end
if dfReverse
Expand Down Expand Up @@ -176,45 +176,65 @@ function generation_v2 ()
set(ax, 'XLim', [-a 2*a], 'YLim', [-a a], 'YLimMode', 'manual', 'DataAspectRatio', [1 1 1])
hold all
lph = fill(leftProfile(:,1), leftProfile(:,2), 'y');
inh = fill([0], [0], 'b'); % Intersection, materials being cut
inh = fill([0], [0], 'b'); % Intersection, materials being cut
zh = plot(rackZigZag(:,1), rackZigZag(:,2), '-.'); % Zigzag, rack to simulate
tch = plot(toolCut(:,1), toolCut(:,2)); % Cutting portion of the tool
trh = plot([0 0], [0 1]); % Tool reference vector
tch = plot(toolCut(:,1), toolCut(:,2)); % Cutting portion of the tool
trh = plot([0 0], [0 1]); % Tool reference vector
rectangle('Position', [-1 -1 2 2]*a/10, 'Curvature', [1 1]);

dothecut(false);
isRightGear = false;
cutTeeth;
isRightGear = true;
cutTeeth();

function dothecut (isRightGear)
for offsIdx = 1:size(cutOffsets, 1) % For every cut offset
function cutTeeth()
if isRightGear
polarAngles = rightPolarAngles;
tangentAngles = -leftTangentAngles;
pitchPolarRadius = rightPitchPolarRadius;
else
polarAngles = leftPolarAngles;
tangentAngles = leftTangentAngles;
pitchPolarRadius = leftPitchPolarRadius;
end
for offsIdx = 1:size(cutOffsets, 1) % For every cut offset
toolCutThisPass = rotPolygon(toolCut, sin(cutOffsets(offsIdx,1)), ... % Rotate 90 degrees cw additionally
-cos(cutOffsets(offsIdx,1)), [0 cutOffsets(offsIdx,2)]);
toolNonCutThisPass = rotPolygon(toolNonCut, sin(cutOffsets(offsIdx,1)), ...
-cos(cutOffsets(offsIdx,1)), [0 cutOffsets(offsIdx,2)]);
toolRefVectorThisPass = rotPolygon([0 0; 0 1], sin(cutOffsets(offsIdx,1)), ...
-cos(cutOffsets(offsIdx,1)), [0 cutOffsets(offsIdx,2)]);
for i = find(rackZigZag(:,1) < 0)' % For every tooth
for i = find(rackZigZag(:,1) < 0)' % For every tooth
toolCutThisTooth = toolCutThisPass + [-dedDist+toolTipRadius rackZigZag(i,2)];
toolRefVectorThisTooth = toolRefVectorThisPass + [-dedDist+toolTipRadius rackZigZag(i,2)];
for j = 1:size(leftPolarAngles, 1)
cosrot = cos(leftPolarAngles(j) - leftTangentAngles(j));
sinrot = sin(leftPolarAngles(j) - leftTangentAngles(j));
for j = 1:size(polarAngles, 1)
cosrot = cos(polarAngles(j) - tangentAngles(j));
sinrot = sin(polarAngles(j) - tangentAngles(j));
anchor = [0 pitchArcLengths(j)];
move = leftPitchPolarRadius(j) * ...
[cos(leftPolarAngles(j)) sin(leftPolarAngles(j))] - anchor;
move = pitchPolarRadius(j) * ...
[cos(polarAngles(j)) sin(polarAngles(j))] - anchor;
fun = @(x) rotPolygon(x, cosrot, sinrot, move, anchor);
toolCutNow = fun(toolCutThisTooth);
toolRefVectorNow = fun(toolRefVectorThisTooth);
zigZagNow = fun(rackZigZag);
temp = polyclip(leftProfile, toolCutNow, 'int');
if ~isempty(temp{1}) % If has intersection
if isRightGear
temp = polyclip(rightProfile, toolCutNow, 'int');
else
temp = polyclip(leftProfile, toolCutNow, 'int');
end
if ~isempty(temp{1}) % If has intersection
toolCutNow = {toolCutNow};
toolRefVectorNow = {toolRefVectorNow};
if j == 1 % First cut of the tooth, might need Z step cut
if j == 1 % First cut of the tooth, might need Z step cut
fun = @(x) x{end} + ...
cutDepth * normr(toolRefVectorNow{1}(2,:) - toolRefVectorNow{1}(1,:));
while true
toolCutNow{end+1} = fun(toolCutNow);
temp = polyclip(leftProfile, toolCutNow{end}, 'int');
if isRightGear
temp = polyclip(rightProfile, toolCutNow{end}, 'int');
else
temp = polyclip(leftProfile, toolCutNow{end}, 'int');
end
if isempty(temp{1})
toolCutNow(end) = [];
break
Expand All @@ -228,10 +248,19 @@ function dothecut (isRightGear)
assert(isempty(toolRefVectorNow))
break
end
temp = polyclip(leftProfile, toolCutNow{end}, 'int');
if isRightGear
temp = polyclip(rightProfile, toolCutNow{end}, 'int');
else
temp = polyclip(leftProfile, toolCutNow{end}, 'int');
end
intersection = [temp{1}{1}, temp{2}{1}];
temp = polyclip(leftProfile, toolCutNow{end}, 'dif');
leftProfile = [temp{1}{1} temp{2}{1}];
if isRightGear
temp = polyclip(rightProfile, toolCutNow{end}, 'dif');
rightProfile = [temp{1}{1} temp{2}{1}];
else
temp = polyclip(leftProfile, toolCutNow{end}, 'dif');
leftProfile = [temp{1}{1} temp{2}{1}];
end
if machineRef
fun = @(x) rotPolygon(x, ...
toolRefVectorNow{end}(2,2) - toolRefVectorNow{end}(1,2), ...
Expand All @@ -240,7 +269,11 @@ function dothecut (isRightGear)
fun = @(x) x;
end
replot(inh, fun(intersection));
replot(lph, fun(leftProfile));
if isRightGear
replot(lph, fun(rightProfile));
else
replot(lph, fun(leftProfile));
end
replot(zh, fun(zigZagNow));
replot(tch, fun(toolCutNow{end}));
replot(trh, fun(toolRefVectorNow{end}));
Expand All @@ -256,6 +289,9 @@ function dothecut (isRightGear)


function replot(h, x, y)
if isRightGear
x(:,1) = -x(:,1) + a;
end
if ~exist('y', 'var')
set(h, 'XData', x(:,1), 'YData', x(:,2));
else
Expand Down

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