File:HarmonicDriveAni.gif

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Summary
DescriptionHarmonicDriveAni.gif |
English: Harmonic-Drive Animation (strain wave gear (SWG)). (Colors in the drawing correspond to the Cross section File:Harmonic drive cross Legend.svg.)
Ncircular_spline = 42 (blue); Nflex_spline= 42-2 = 40 (red); Ratio = 40/(42-40) = 20 Deutsch: Harmonic-Drive Animation (Spannungswellengetriebe, Wellgetriebe oder Gleitkeilgetriebe). (Die Farbkodierung entspricht der Schnittzeichnung File:Harmonic drive cross Legend.svg.) zInnenverzahnung = 42 (blue); zFlexspline= 42-2 = 40 (red); i = 40/(42-40) = 20 |
Date | |
Source | Own work |
Author | Jahobr |
GIF development InfoField | |
Source code InfoField | MATLAB codefunction HarmonicDriveAni()
% source code for drawing a HarmonicDrive
% this is by no means a "simulation". It is a hack job that produces a gif
%
% 2016-12-05 Jahobr (reworked 2017-09-16)
nTeethOutGear = 42;
nTeethFlex = nTeethOutGear-2;
modul = 0.1; % modul
colEdge = [0 0 0 ]; % Edge color
colFlex = [1 0.2 0.2]; % FlexSpline color
colWave = [0.1 0.7 0.1]; % WaveGen color
colGear = [0.2 0.2 1 ]; % static OuterGear color
nFrames = 100;
frameAngles = linspace(0,-pi,nFrames+1); % rotate clockwise
frameAngles = frameAngles(1:end-1); % delete redundant frame
[pathstr,fname] = fileparts(which(mfilename)); % save files under the same name and at file location
figHandle = figure(15674454);
clf
axesHandle = axes;
hold(axesHandle,'on')
axis equal
xlim([-3 3])
ylim([-3 3])
set(figHandle, 'Units','pixel');
set(figHandle, 'position',[1 1 700 700]); % [x y width height]
set(axesHandle, 'position',[-0.05 -0.05 1.1 1.1]); % stretch axis bigger as figure, easy way to get rid of ticks [x y width height]
set(figHandle,'GraphicsSmoothing','on') % requires at least version 2014b
for iFrame = 1:nFrames
angleWaveGen = frameAngles(iFrame);
angleFlexTeeth = angleWaveGen*(nTeethFlex-nTeethOutGear)/nTeethFlex; % angle of the flexspline
cla(axesHandle);
%% %%%%%%%% draw OuterGear (static) %%%%%%%%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
effectiveDiameter = modul*nTeethOutGear;
toothTipDiameter = effectiveDiameter-1.4*modul;
toothBottomDiameter = effectiveDiameter+1.6*modul;
angleBetweenTeeth = 2*pi/nTeethOutGear; % angle between 2 teeth
angleOffPoints = (0:angleBetweenTeeth/8:(2*pi));
%% outerEdge
maxDiameter = toothBottomDiameter*1.2; % definition of outer line
maxXY = samplesEllipse(maxDiameter,maxDiameter,500);
patch(maxXY(:,1),maxXY(:,2),colGear,'EdgeColor',colEdge,'LineWidth',0.5) % full outer disc
%% inner teeth
radiusOffPoints = angleOffPoints; % init
radiusOffPoints(1:8:end) = toothBottomDiameter/2; % middle bottom
radiusOffPoints(2:8:end) = toothBottomDiameter/2; % left bottom
radiusOffPoints(3:8:end) = effectiveDiameter/2; % rising edge
radiusOffPoints(4:8:end) = toothTipDiameter/2; % right top
radiusOffPoints(5:8:end) = toothTipDiameter/2; % middle top
radiusOffPoints(6:8:end) = toothTipDiameter/2; % left top
radiusOffPoints(7:8:end) = effectiveDiameter/2; % falling edge
radiusOffPoints(8:8:end) = toothBottomDiameter/2; % right bottom
[X,Y] = pol2cart(angleOffPoints,radiusOffPoints);
patch(X,Y,[1 1 1],'EdgeColor',colEdge,'LineWidth',0.5) % overlay white area for inner teeth
%% %%%%%%%%% draw Flexspline %%%%%%%%%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % deform estimation based on tooth distance (using the circumferences); could be automated!
% U1 = 42*pi % Circumference of OuterGear
% U1 =
% 131.9469
%
% U2 = pi*sqrt(2*((42/2)^2+(0.9022*42/2)^2)) * 42/40 % Circumference of Flexspline * 42/40
% U2 =
% 131.9435
deform = 0.9022;
deformedDiameter = effectiveDiameter*deform; % scale down, but teeth must still have the same distance
rootEffectiveDia = effectiveDiameter-1.6*modul; % fixed offset
rootDeformedDia = deformedDiameter-1.6*modul; % fixed offset
topEffectiveDia = effectiveDiameter+1.4*modul; % fixed offset
topDeformedDia = deformedDiameter+1.4*modul; % fixed offset
% % an equidistant sampled ellipse is needed, to keep the tooth distance constant all the way around
offsetOnCircumference = (-angleWaveGen+angleFlexTeeth)/2/pi; % compensation + own_rotation , normalization to "circumference"
equiEffeXY = equidistantSamplesEllipse(effectiveDiameter,deformedDiameter,nTeethFlex*8, offsetOnCircumference); % points on effective diameter
equiRootXY = equidistantSamplesEllipse(rootEffectiveDia, rootDeformedDia, nTeethFlex*8, offsetOnCircumference); % points with inwards offset
equiOutXY = equidistantSamplesEllipse(topEffectiveDia, topDeformedDia, nTeethFlex*8, offsetOnCircumference); % points with outwards offset
toothXY = equiEffeXY; % intit
toothXY(1:8:end,:) = equiOutXY(1:8:end,:); % middle top I######I
toothXY(2:8:end,:) = equiOutXY(2:8:end,:); % left top I######+
% toothXY(3:8:end) init did it I####/
toothXY(4:8:end,:) = equiRootXY(4:8:end,:); % right bottom I##+
toothXY(5:8:end,:) = equiRootXY(5:8:end,:); % middle bottom I##I
toothXY(6:8:end,:) = equiRootXY(6:8:end,:); % left bottom I##+
% toothXY(7:8:end) init did it I####\
toothXY(8:8:end,:) = equiOutXY(8:8:end,:); % right top I######+
[toothXY] = rotateCordiantes(toothXY,angleWaveGen);
patch(toothXY(:,1),toothXY(:,2),colFlex,'EdgeColor',colEdge,'LineWidth',0.5) %draw flexspline with teeth
%% hole
holeEffectiveDia = effectiveDiameter-5*modul; % fixed inwards offset
holeDeformedDia = deformedDiameter-5*modul; % fixed inwards offset
holePathXY = samplesEllipse(holeEffectiveDia,holeDeformedDia,500);
holePathXY = rotateCordiantes(holePathXY,angleWaveGen);
patch(holePathXY(:,1),holePathXY(:,2),[1 1 1],'EdgeColor',colEdge,'LineWidth',0.5) % draw hole of deformed ring
%% %%%%%%%%% draw wave generator %%%%%%%%%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
waveEffectiveDia = holeEffectiveDia; % touch flex spline
waveDeformedDia = holeDeformedDia-5*modul; % extra air gap to spline, to make it more obvious
wavePathXY = samplesEllipse(waveEffectiveDia,waveDeformedDia,500);
[wavePathXY] = rotateCordiantes(wavePathXY,angleWaveGen);
patch(wavePathXY(:,1),wavePathXY(:,2),colWave,'EdgeColor',colEdge,'LineWidth',0.5) % draw wave generator
%% central shaft
shaftPathXY = samplesEllipse(effectiveDiameter/2.5,effectiveDiameter/2.5,500);
plot(axesHandle,shaftPathXY(:,1),shaftPathXY(:,2),'LineWidth',0.8,'color',colEdge); % draw central shaft outline
%% %%%%%%%%% save animation %%%%%%%%%
%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
drawnow;
f = getframe(figHandle);
if iFrame == 1 % create colormap
[im,map] = rgb2ind(f.cdata,32,'nodither'); % 32 colors % create color map %% THE FIRST FRAME MUST INCLUDE ALL COLORES !!!
% FIX WHITE, rgb2ind sets white to [0.9961 0.9961 0.9961], which is annoying
[~,wIndex] = max(sum(map,2)); % find "white"
map(wIndex,:) = 1; % make it truly white
im(1,1,1,nFrames) = 0; % allocate
if ~isempty(which('plot2svg'))
plot2svg(fullfile(pathstr, [fname '_Frame1.svg']),figHandle) % by Juerg Schwizer
else
disp('plot2svg.m not available; see http://www.zhinst.com/blogs/schwizer/');
end
end
imtemp = rgb2ind(f.cdata,map,'nodither');
im(:,:,1,iFrame) = imtemp;
end
imwrite(im,map,fullfile(pathstr, [fname '.gif']),'DelayTime',1/30,'LoopCount',inf) % save gif
disp([fname '.gif has ' num2str(numel(im)/10^6 ,4) ' Megapixels']) % Category:Animated GIF files exceeding the 50 MP limit
%%% equidistantSamplesEllipse test code
% figure(455467);clf;hold on;
%
% equidistantXY = equidistantSamplesEllipse(1.5,0.5,40,0.1);
% plot(equidistantXY(:,1),equidistantXY(:,2),'bx-')
%
%
% equidistantXY = equidistantSamplesEllipse(2,1,40,1);
% plot(equidistantXY(:,1),equidistantXY(:,2),'bx-')
%
% equidistantXY = equidistantSamplesEllipse(3,2,40,0.5);
% plot(equidistantXY(:,1),equidistantXY(:,2),'bx-')
%
% equidistantXY = equidistantSamplesEllipse(4,3,40,0);
% plot(equidistantXY(:,1),equidistantXY(:,2),'bx-')
% pathXY = samplesEllipse(4,3,41);
% plot(pathXY(1:end-1,1),pathXY(1:end-1,2),'ro-')
%
% plot([4 -4]/2,[0 0],'-k')
function equidistantXY = equidistantSamplesEllipse(diameterH,diameterV,nPoints,offset)
% Inputs:
% diameterH horizontal diameter
% diameterV vertical diameter
% nPoints number of resampled points
% offsetFraction between 0 and 1 in circumference of ellipse
pathXY = samplesEllipse(diameterH,diameterV,1000); % create ellipse
stepLengths = sqrt(sum(diff(pathXY,[],1).^2,2)); % distance between the points
stepLengths = [0; stepLengths]; % add the starting point
cumulativeLen = cumsum(stepLengths); % cumulative sum
circumference = cumulativeLen(end);
finalStepLocs = linspace(0,1, nPoints+1)+offset; % equidistant distribution
finalStepLocs = finalStepLocs(1:end-1); % remove redundant point
finalStepLocs = mod(finalStepLocs,1)*circumference; % unwrap and scale to circumference
equidistantXY = interp1(cumulativeLen, pathXY, finalStepLocs);
function pathXY = samplesEllipse(diameterH,diameterV,nPoints)
% point of ellipse; points start on the right, counterclockwise
% first and last points are the same
%
% Inputs:
% diameterH horizontal diameter
% diameterV vertical diameter
% nPoints number of points
p = linspace(0,2*pi,nPoints)';
pathXY = [cos(p)*diameterH/2 sin(p)*diameterV/2]; % create ellipse
function [xy] = rotateCordiantes(xy,anglee)
% [x1 y1; x2 y2; x3 y3; ...] coordinates to rotate
% anglee angle of rotation in [rad]
rotM = [cos(anglee) -sin(anglee); sin(anglee) cos(anglee)];
xy = (rotM*xy')';
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 15:20, 29 April 2023 | ![]() | 700 × 700 (2.36 MB) | wikimediacommons>Jahobr | Reverted to version as of 15:09, 17 November 2020 (UTC) |
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