%Animate_Four_Bar_Polodes creates a GUI for viewing and animating arbitrary
% four bar mechanisms and their corresponding polodes. The GUI allows you
% to animate forwards and reverse, invert the mechanism, change the
% animation speed, and modify the link lengths.
%
% A "Link Length Options" drop down box gives 15 predefined
% mechanism variations to choose from.
%
% When the link lengths slider bar is changed, please press the "Change
% Links" button to recompute the polode and mechanism paths.
%
% Note that this program does not give user control for change points.
% _-_,, ,, _-_- ,,
% ( // || /, _ ; || '
% _|| /'\\ ||/\\ \\/\\ || __ < \, \\/\/\ ||/\ \\ \\/\\ _-_,
% _|| || || || || || || ~||- - /-|| || | | ||_< || || || ||_.
% || || || || || || || ||===|| (( || || | | || | || || || ~ ||
% -__-, \\,/ \\ |/ \\ \\ ( \_, | \/\\ \\/\\/ \\,\ \\ \\ \\ ,-_-
% _/ `
%
% John Hawkins
% Kinematics
% Final Exam Project
% For professor Don Riley
% December 2009
function Animate_Four_Bar_Polodes
% Define the link lengths r with r(1) as ground
h.r=[ 2 4 6 3.5];
INITIALIZE;
function INITIALIZE
warning off;
GRASHOFTEST;
if ~h.isconstructible
errordlg('Desired mechanism is not constructible or does not move.')
return
end
ANIMATIONSETTINGS;
CALCULATIONS;
MAKEFIGURE;
INITIALPLOTS;
end
function GRASHOFTEST
[s,n]=min(h.r);
h.inputLIndex=n;
[l,x]=max(h.r);
midInds=1:4; midInds([n,x])=[];
p=h.r(midInds(1));
q=h.r(midInds(2));
if l>=s+p+q %Test for constructability
h.isconstructible=false;
else %Constructible
h.isconstructible=true;
if s+l<=p+q %Test for Grashof mechanism
h.isgrashof=true;
%Determining of Mechanism Type
ascending=sort(h.r);
ExtraChangePoint=false;
if s+l==p+q
if ascending(1)==ascending(4)
h.mechType='Triple Change Point Mechanism';
ExtraChangePoint=true;
elseif ascending(1)==ascending(2) && ascending(3)==ascending(4)
h.mechType='Double Change Point Mechanism';
ExtraChangePoint=true;
else
h.mechType='Change Point';
end
else
h.mechType='Grashof';
end
if ~ExtraChangePoint
switch n
case 1
h.mechType=[h.mechType,' Crank-Rocker-Rocker Mechanism'];
case 2
h.mechType=[h.mechType,' Rocker-Crank-Rocker Mechanism'];
case 3
h.mechType=[h.mechType,' Rocker-Rocker-Crank Mechanism'];
case 4
h.mechType=[h.mechType,' Crank-Crank-Crank Mechanism'];
end
end
h.L=[h.r(n:end),h.r(1:n-1)];
% The L matrix is simply a cyclical permutation of the link lengths
% which places the shortest link as the input. This allows for easier
% calculation of grashof mechanism positions. The whole mechanism will
% later be rotated for correct display.
h.dtheta1=0:359;
else %Non-grashof
h.isgrashof=false;
h.L=h.r;
h.inputLIndex=1;
%Mechanism Classification
switch n
case 1
h.mechType='Class 2 Rocker-Rocker-Rocker Non-Grashof Mechanism';
case 2
h.mechType='Class 3 Rocker-Rocker-Rocker Non-Grashof Mechanism';
case 3
h.mechType='Class 4 Rocker-Rocker-Rocker Non-Grashof Mechanism';
case 4
h.mechType='Class 1 Rocker-Rocker-Rocker Non-Grashof Mechanism';
end
if h.r(1) + h.r(4) < h.r(2) + h.r(3) %Inward limited non-grashof
h.rtheta1prime=acos(( h.r(4)^2+h.r(1)^2-(h.r(3)-h.r(2))^2) / (2*h.r(4)*h.r(1)) );
h.dtheta1prime=180/pi*h.rtheta1prime;
h.dtheta1=linspace(h.dtheta1prime,360-h.dtheta1prime,360-2*h.dtheta1prime);
else %Outward limited non-grashof
h.rtheta1prime=acos(( h.r(4)^2+h.r(1)^2-(h.r(3)+h.r(2))^2) / (2*h.r(4)*h.r(1)) );
h.dtheta1prime=180/pi*h.rtheta1prime;
h.dtheta1=linspace(-h.dtheta1prime,h.dtheta1prime,2*h.dtheta1prime);
end
end
end
end
function ANIMATIONSETTINGS
h.cstep = find(h.dtheta1==70);
if isempty(h.cstep)
h.cstep = numel(h.dtheta1);
end
h.rstep = h.cstep;
h.switched = false;
h.increment = 1;
h.animate = false;
h.usercstep = '';
h.basetime=.1;
h.minSpeed=1;
h.maxSpeed=6;
val=h.maxSpeed;
h.pause=.5/2^val;
pause off;
end
function CALCULATIONS
%Calculations for position of basic 4-bar
h.rtheta1 = h.dtheta1*pi/180;
h.xa = h.L(1)*cos(h.rtheta1); h.ya = h.L(1)*sin(h.rtheta1);
d = sqrt(h.L(4)^2+h.L(1)^2-2*h.L(4)*h.L(1)*cos(h.rtheta1));
rbeta = acos((h.L(2)^2-d.^2-h.L(3)^2)./(-2*d*h.L(3)));
rdelta = atan2(h.ya,h.L(4)-h.xa);
h.rtheta3 = pi-rbeta-rdelta;
h.dtheta3 = h.rtheta3*180/pi;
h.xb = h.L(4)+h.L(3)*cos(h.rtheta3); h.yb = h.L(3)*sin(h.rtheta3);
h.rtheta2 = atan2(h.yb-h.ya,h.xb-h.xa);
h.dtheta2 = h.rtheta2*180/pi;
%Determine which IC to find
if h.inputLIndex==1 || h.inputLIndex==3
x1a=0; y1a=0;
x1b=h.xa; y1b=h.ya;
x2a=h.L(4); y2a=0;
x2b=h.xb; y2b=h.yb;
else
x1a=h.xa; y1a=h.ya;
x1b=h.xb; y1b=h.yb;
x2a=0; y2a=0;
x2b=h.L(4); y2b=0;
end
%Calculation of Fixed Polode
m1=(y1b-y1a)./(x1b-x1a);
m2=(y2b-y2a)./(x2b-x2a);
h.xic=(m1.*x1a-m2.*x2a+y2a-y1a)./(m1-m2);
h.yic=m1.*(h.xic-x1a)+y1a;
%Build the position cell array
h.PosArray = BUILDPOSITIONARRAY;
end
function MAKEFIGURE
xmin=-2.2; xmax=5.2;
ymin=-2.2; ymax=4.2;
h.startAxis=[xmin xmax ymin ymax];
%Units are in centimeters
figL=1; figB=2; figR=1; figT=3;
axL=2; axB=1.5; axT=2;
panSpace=1; panW=6.5; panR=1.5;
MarginT=.8; MarginL=.4; MarginB=.2; MarginR=.4;
StartButtonH=1; InterButtonSpace=.2; InvertButtonH=.9;
PreTitleSpace=.4; TitleH=.5; PostTitleSpace=.1;
Indent=.5; ToolH=.5;
PreEditSpace=.2; EditW=1.1;
InterBoxSpace=0;
LinkTextW=1.1; InterSliderSpace=.2; PreLinkButtonSpace=.2;
PreZoomButtonSpace=.5; ZoomButtonH=.7; ZoomButtonW=2.7;
PopupH=.6; PostPopupSpace=.2; PopupIndent=.8;
SignatureH=.8; PreSignatureSpace=.3;
PreHelpButtonSpace=.3; HelpButtonH=.7;
BoxH=ToolH;
panH=MarginB+4*BoxH+3*InterBoxSpace+4*(PostTitleSpace+TitleH+PreTitleSpace)+...
6*ToolH+2*InvertButtonH+3*InterButtonSpace+StartButtonH+MarginT+...
3*InterSliderSpace+PreZoomButtonSpace+2*ZoomButtonH+...
PopupH+PostPopupSpace+SignatureH+PreSignatureSpace+...
PreHelpButtonSpace+HelpButtonH; %-...
% PreTitleSpace-PostTitleSpace-TitleH-ToolH; %Removal of SpeedSlider
ButtonW=panW-MarginL-MarginR;
ToolW=panW-MarginL-MarginR-Indent;
%
if isappdata(0,'base_unit')
% leave it alone
else
setappdata(0,'base_unit',get(0,'units'));
end % Remember base unit and reset at close.
set(0,'Units','centimeters');
ScreenDims = get(0,'ScreenSize');
screenW=ScreenDims(3);
screenH=ScreenDims(4);
h.HWratio=(ymax-ymin)/(xmax-xmin);
maxFigH=screenH-figB-figT;
maxFigW=screenW-figL-figR;
if maxFigH < h.HWratio*maxFigW
figH=maxFigH;
axH=figH-axB-axT;
axW=axH/h.HWratio;
figW=axL+axW+panSpace+panW+panR;
else
figW=maxFigW;
axW=figW-axL-panSpace-panW-panR;
axH=axW*h.HWratio;
figH=axB+axH+axT;
end
if figH<panH+1
dif=panH+1-figH;
figH=panH+1;
figB=figB-dif;
axB=axB+dif;
end
figL=(screenW-figW)/2;
panB=(figH-panH)/2;
panL=axL+axW+panSpace;
h.fig = figure('Name','Four-Bar Mechanism with Polodes',...
'Units','centimeters','Position',[figL figB figW figH],...
'NumberTitle','off','ReSize','off','CloseRequestFcn',@close_fig);
axes('Units','centimeters','position',[axL axB axW axH]);
axis equal;
axis([xmin xmax ymin ymax]);
panel=uipanel('Units','centimeters','position',[panL panB panW panH],...
'title','Control Panel','fontsize',12,'fontweight','bold',...
'fontname','times');
%StartStop Button
currentB = panH-MarginT-StartButtonH;
h.StartButton=uicontrol(panel,'units','centimeters',...
'string','START','fontname','times','fontsize',28,...
'position',[MarginL currentB ButtonW StartButtonH],...
'callback',@STARTSTOP,'foregroundcolor',1/255*[42 121 17]);
%Invert Button
currentB = currentB-InterButtonSpace-InvertButtonH;
h.InvertButton=uicontrol(panel,'units','centimeters',...
'style','toggle','string','Invert Mechanism',...
'fontname','times','fontsize',20,...
'position',[MarginL currentB ButtonW InvertButtonH],...
'callback',@INVERT);
%Reverse Button
currentB = currentB-InterButtonSpace-InvertButtonH;
h.ReverseButton=uicontrol(panel,'units','centimeters',...
'string','Reverse',...
'fontname','times','fontsize',20,...
'position',[MarginL currentB ButtonW InvertButtonH],...
'callback',@REVERSE);
%Speed Slider
currentB = currentB-PreTitleSpace-TitleH;
uicontrol(panel,'units','centimeters',...
'style','text','string','Speed','fontname','times',...
'fontsize',12,'fontweight','bold','fontangle','italic',...
'position',[MarginL currentB ButtonW TitleH],...
'horizontalalignment','left');
currentB = currentB-PostTitleSpace-ToolH;
h.SpeedSlider=uicontrol(panel,'units','centimeters',...
'style','slider','min',h.minSpeed,'max',h.maxSpeed,'value',h.maxSpeed,...
'sliderstep',1/(h.maxSpeed-h.minSpeed)*[1 1],'callback',@SPEED_SLIDER,...
'position',[MarginL+Indent currentB ToolW ToolH]);
%Input Angle Slider
currentB = currentB-PreTitleSpace-TitleH;
uicontrol(panel,'units','centimeters',...
'style','text','string','Reference Link Angle','fontname','times',...
'fontsize',12,'fontweight','bold','fontangle','italic',...
'position',[MarginL currentB ButtonW TitleH],...
'horizontalalignment','left');
currentB = currentB-PostTitleSpace-ToolH;
h.PositionSlider=uicontrol(panel,'units','centimeters',...
'style','slider','min',min(h.dtheta1),'max',max(h.dtheta1),...
'value',h.dtheta1(h.cstep),...
'sliderstep',1/numel(h.dtheta1)*[1 5],'callback',@POSITION_SLIDER,...
'position',[MarginL+Indent currentB ToolW-EditW-PreEditSpace ToolH]);
h.PositionEdit=uicontrol(panel,'units','centimeters',...
'style','edit','string',sprintf('%.1f',h.dtheta1(h.cstep)),...
'callback',@POSITION_EDIT,...
'fontname','times','fontsize',12,...
'position',[panW-MarginR-EditW currentB EditW ToolH]);
%Link Lengths
minL=0.001; maxL=10;
currentB = currentB-PreTitleSpace-TitleH;
uicontrol(panel,'units','centimeters',...
'style','text','string','Link Lengths','fontname','times',...
'fontsize',12,'fontweight','bold','fontangle','italic',...
'position',[MarginL currentB ButtonW TitleH],...
'horizontalalignment','left');
currentB = currentB-PostTitleSpace-PopupH;
h.Popup=uicontrol(panel,'units','centimeters',...
'style','popup','callback',@OPTIONS,'fontname','times',...
'fontsize',11,...
'string',['Link Length Options...|Current|Previous|',...
'GCCC Example|GCRR Example|GRCR Example|GRRC Example|',...
'RRR1 Example|RRR2 Example|RRR3 Example|RRR4 Example|',...
'SCCC Example|SCRR Example|SRCR Example|SRRC Example|',...
'Parallelogram (S2X)|Deltoid (S2X)|Square (S3X)'],...
'position',[MarginL+PopupIndent currentB ButtonW-2*PopupIndent PopupH]);
Links={'Input','Coupler','Output','Ground'};
for k=1:4
if k==1
currentB = currentB-PostPopupSpace-PopupH;
else
currentB = currentB-InterSliderSpace-ToolH;
end
uicontrol(panel,'units','centimeters',...
'style','text','string',Links{k},'fontname','times',...
'fontsize',8,... %'fontweight','bold','fontangle','italic',...
'position',[MarginL currentB LinkTextW ToolH],...
'horizontalalignment','left');
h.LinkSlider(k)=uicontrol(panel,'units','centimeters',...
'style','slider','min',minL,'max',maxL,...
'value',h.r(k),...
'sliderstep',1/(maxL-minL)*[.05 1],'callback',@LINK_SLIDER,...
'position',[MarginL+LinkTextW currentB ButtonW-EditW-PreEditSpace-LinkTextW ToolH]);
h.LinkEdit(k)=uicontrol(panel,'units','centimeters',...
'style','edit','string',num2str(h.r(k)),...
'callback',@LINK_EDIT,...
'fontname','times','fontsize',12,...
'position',[panW-MarginR-EditW currentB EditW ToolH]);
end
currentB = currentB-PreLinkButtonSpace-ZoomButtonH;
h.ChangeLinksButton=uicontrol(panel,'units','centimeters',...
'string','Change Links',...
'fontname','times','fontsize',14,...
'position',[MarginL+Indent currentB ButtonW-2*Indent ZoomButtonH],...
'callback',@CHANGELINKS);
%Display Options
currentB = currentB-PreTitleSpace-TitleH;
uicontrol(panel,'units','centimeters',...
'style','text','string','Display','fontname','times',...
'fontsize',12,'fontweight','bold','fontangle','italic',...
'position',[MarginL currentB ButtonW TitleH],...
'horizontalalignment','left');
currentB = currentB-PostTitleSpace-BoxH;
h.PolodesCheckbox=uicontrol(panel,'units','centimeters',...
'style','checkbox','value',1,'string','Polodes',...
'fontname','times','fontsize',11,...
'position',[MarginL+Indent currentB ToolW BoxH],...
'Callback',@POLODES_CHECKBOX);
currentB = currentB-InterBoxSpace-BoxH;
h.JointPathsCheckbox=uicontrol(panel,'units','centimeters',...
'style','checkbox','value',1,'string','Joint Paths',...
'fontname','times','fontsize',11,...
'position',[MarginL+Indent currentB ToolW BoxH],...
'Callback',@JOINTPATHS_CHECKBOX);
currentB = currentB-InterBoxSpace-BoxH;
h.AnglesCheckbox=uicontrol(panel,'units','centimeters',...
'style','checkbox','value',1,'string','Angles',...
'fontname','times','fontsize',11,...
'position',[MarginL+Indent currentB ToolW BoxH],...
'Callback',@ANGLES_CHECKBOX);
currentB = currentB-InterBoxSpace-BoxH;
h.CoordsCheckbox=uicontrol(panel,'units','centimeters',...
'style','checkbox','value',0,'string','Point Coordinates',...
'fontname','times','fontsize',11,...
'position',[MarginL+Indent currentB ToolW BoxH],...
'Callback',@COORDS_CHECKBOX);
%Zoom Controls
currentB = currentB-PreZoomButtonSpace-ZoomButtonH;
h.AutoZoomButton=uicontrol(panel,'units','centimeters',...
'string','Auto Zoom',...
'fontname','times','fontsize',14,...
'position',[MarginL currentB ZoomButtonW ZoomButtonH],...
'callback',@AUTOZOOM);
h.AllZoomButton=uicontrol(panel,'units','centimeters',...
'string','Zoom Fit',...
'fontname','times','fontsize',14,...
'position',[panW-MarginR-ZoomButtonW currentB ZoomButtonW ZoomButtonH],...
'callback',@ZOOMALL);
%Help Button
currentB = currentB-PreHelpButtonSpace-HelpButtonH;
h.HelpButton=uicontrol(panel,'units','centimeters',...
'string','Instructions',...
'fontname','times','fontsize',14,...
'position',[MarginL+PopupIndent currentB ButtonW-2*PopupIndent HelpButtonH],...
'callback',@HELPDIALOG);
%Signature
currentB = currentB-PreSignatureSpace-SignatureH;
uicontrol(panel,'units','centimeters',...
'style','text','string','Program by John Hawkins','fontname','times',...'Monotype Corsiva',...
'fontsize',14,...'fontangle','italic',...
'position',[MarginL currentB ButtonW SignatureH],...
'horizontalalignment','center');
drawnow
end
function INITIALPLOTS
hold on;
plot(0,0,'k');
h.FigTitle=title(h.mechType,...
'FontSize',20,'FontName','Times');
AUTOZOOM(0,0,0);
% axis(h.startAxis);
[x,y,a] = COORDINATES;
FixedXIC=[];
FixedYIC=[];
JointPathX1=[]; JointPathX2=[];
JointPathY2=[]; JointPathY2=[];
for k=1:numel(h.xa)
FixedXIC(k)=h.PosArray(1,5,k,k);
FixedYIC(k)=h.PosArray(2,5,k,k);
JointPathX1(k)=h.PosArray(1,2,k,k);
JointPathX2(k)=h.PosArray(1,3,k,k);
JointPathY1(k)=h.PosArray(2,2,k,k);
JointPathY2(k)=h.PosArray(2,3,k,k);
end
h.FixedICMatrix=[FixedXIC;FixedYIC;ones(1,numel(FixedXIC))];
h.JointPath1=plot(JointPathX1,JointPathY1,'.','color',[.7,.7,1]);
h.JointPath2=plot(JointPathX2,JointPathY2,'.','color',[.7,.7,1]);
h.FixedPolode = plot(FixedXIC,FixedYIC,'.k');
h.ic = plot(x.ic,y.ic,'-.b');
h.MovingPolode = plot(x.MovingPolode,y.MovingPolode,'.b');
h.h.L(4) = plot(x.h.L4,y.h.L4,'r-.');
h.fourbar = plot(x.fourbar,y.fourbar,'r');
h.dots = plot(x.fourbar,y.fourbar,'ro');
h.base = plot(x.h.L4,y.h.L4,'r^','LineWidth',3);
h.coordO = text(x.coordO,y.coordO,sprintf('(%.2f,%.2f)',0,0),...
'horizontalalignment','right','visible','off');
h.coordA = text(x.coordA,y.coordA,sprintf('(%.2f,%.2f)',h.xa(h.cstep),h.ya(h.cstep)),...
'HorizontalAlignment','right','visible','off');
h.coordB = text(x.coordB,y.coordB,sprintf('(%.2f,%.2f)',...
h.xb(h.cstep),h.yb(h.cstep)),'visible','off');
h.coordE = text(x.coordE,y.coordE,sprintf('(%.2f,%.2f)',h.L(4),0),...
'visible','off');
h.angleO = text(x.angleO,y.angleO,sprintf('%.1f^o',a.angleO),...
'horizontalalignment','center');
h.angleA = text(x.angleA,y.angleA,sprintf('%.1f^o',a.angleA),...
'horizontalalignment','center');
h.angleB = text(x.angleB,y.angleB,sprintf('%.1f^o',a.angleB),...
'horizontalalignment','center');
h.angleE = text(x.angleE,y.angleE,sprintf('%.1f^o',a.angleE),...
'horizontalalignment','center');
end
function PosArray = BUILDPOSITIONARRAY
%Builds a 3-by-5-by-numel(dtheta1)-by-numel(dtheta1) matrix,
%which can most easily be viewed as a 2D matrix of 2D
%'FirstValues' matrices. The 'rows and columns' of the outer
%matrix (indices 3 and 4), correspond to rotations the coordinate
%system will have to go through to generate the moving polode. The
%diagonal of this matrix comprises the case when the two rotations
%are the same, canceling each other out. Hence, the non-inverted
%mechanism is the diagonal of this matrix. The moving polode
%corresponds to all the IC values of whichever row is currently being
%viewed.
FirstValues = zeros(3,5,numel(h.dtheta1));
for k = 1:numel(h.dtheta1)
FirstValues(:,:,k) = [ 0 h.xa(k) h.xb(k) h.L(4) h.xic(k);
0 h.ya(k) h.yb(k) 0 h.yic(k);
1 1 1 1 1 ];
end
switch h.inputLIndex
case 1
InvTheta=h.rtheta2;
XA=h.xa;
YA=h.ya;
h.rtheta1Real=h.rtheta1;
h.rtheta2Real=h.rtheta2;
h.rtheta3Real=h.rtheta3;
h.dtheta1Real=h.dtheta1;
h.dtheta2Real=h.dtheta2;
h.dtheta3Real=h.dtheta3;
case 2
Px=h.L(4)*ones(numel(h.xa),1);
Py=zeros(numel(h.xa),1);
theta=h.rtheta3;
FirstValues=[FirstValues(:,4,:),FirstValues(:,1,:),FirstValues(:,2,:),...
FirstValues(:,3,:),FirstValues(:,5,:)];
case 3
Px=h.xb; Py=h.yb;
theta=-(pi-h.rtheta2);
FirstValues=[FirstValues(:,3,:),FirstValues(:,4,:),FirstValues(:,1,:),...
FirstValues(:,2,:),FirstValues(:,5,:)];
case 4
Px=h.xa; Py=h.ya;
theta=-(pi-h.rtheta1);
FirstValues=[FirstValues(:,2,:),FirstValues(:,3,:),FirstValues(:,4,:),...
FirstValues(:,1,:),FirstValues(:,5,:)];
end
if h.inputLIndex>1
for k=1:numel(h.xa)
%FirstValues(:,:,k) = inv(TMAT2D(Px(k),Py(k),theta(k)))*FirstValues(:,:,k);
FirstValues(:,:,k) = (TMAT2D(Px(k),Py(k),theta(k)))\FirstValues(:,:,k);
end
InvTheta=atan2(FirstValues(2,3,:)-FirstValues(2,2,:),...
FirstValues(1,3,:)-FirstValues(1,2,:));
XA=FirstValues(1,2,:);
YA=FirstValues(2,2,:);
XB=FirstValues(1,3,:);
YB=FirstValues(2,3,:);
XE=FirstValues(1,4,:);
h.rtheta1Real=atan2(YA,XA);
h.rtheta2Real=atan2(YB-YA,XB-XA);
h.rtheta3Real=atan2(YB,XB-XE);
h.dtheta1Real=180/pi*h.rtheta1Real;
h.dtheta2Real=180/pi*h.rtheta2Real;
h.dtheta3Real=180/pi*h.rtheta3Real;
end
PosArray = zeros(3,5,numel(h.dtheta1),numel(h.dtheta1));
TMatrix=[];
for k = 1:numel(h.dtheta1)
TMatrix(:,:,k)=TMAT2D(XA(k),YA(k),InvTheta(k));
InvTMatrix(:,:,k)=inv(TMatrix(:,:,k));
end
for k = 1:numel(h.dtheta1)
for q = 1:numel(h.dtheta1)
PosArray(:,:,k,q) = TMatrix(:,:,k)*InvTMatrix(:,:,q)*FirstValues(:,:,q);
end
end
end
function T = TMAT2D(x,y,theta)
%Theta in radians
ctheta = cos(theta);
stheta = sin(theta);
T = [ctheta -stheta x;
stheta ctheta y;
0 0 1];
end
function [x,y,a] = COORDINATES
if ~h.switched
h.rstep = h.cstep;
end
CurPos = h.PosArray(:,:,h.rstep,h.cstep);
XO = CurPos(1,1); YO = CurPos(2,1);
XA = CurPos(1,2); YA = CurPos(2,2);
XB = CurPos(1,3); YB = CurPos(2,3);
XE = CurPos(1,4); YE = CurPos(2,4);
XIC = CurPos(1,5); YIC = CurPos(2,5);
if ~h.switched
x.h.L4 = [XO,XE]; y.h.L4 = [YO,YE];
x.fourbar = [XO,XA,XB,XE];
y.fourbar = [YO,YA,YB,YE];
else
x.h.L4 = [XA,XB]; y.h.L4 = [YA,YB];
x.fourbar = [XA,XO,XE,XB];
y.fourbar = [YA,YO,YE,YB];
end
x.ic = [XO,XA,XIC,XB,XE];
y.ic = [YO,YA,YIC,YB,YE];
x.MovingPolode = squeeze(h.PosArray(1,5,h.rstep,:));
y.MovingPolode = squeeze(h.PosArray(2,5,h.rstep,:));
x.coordO = XO-.2; y.coordO = YO;
x.coordA = XA-.2; y.coordA = YA;
x.coordB = XB+.2; y.coordB = YB;
x.coordE = XE+.2; y.coordE = YE;
a.angleO=h.dtheta1Real(h.cstep);
a.angleA=h.dtheta2Real(h.cstep)+180-h.dtheta1Real(h.cstep);
if a.angleA>360
a.angleA=a.angleA-360;
end
a.angleE=180-h.dtheta3Real(h.cstep);
a.angleB=360-a.angleO-a.angleA-a.angleE;
if a.angleB>360
a.angleB=a.angleB-360;
end
a.offset=atan2(YE-YO,XE-XO);
dis=.1*max(h.r);
x.angleO=XO+dis*cos(a.offset+h.rtheta1Real(h.cstep)/2);
y.angleO=YO+dis*sin(a.offset+h.rtheta1Real(h.cstep)/2);
x.angleA=XA+dis*cos(a.offset+h.rtheta2Real(h.cstep)-pi/180*a.angleA/2);
y.angleA=YA+dis*sin(a.offset+h.rtheta2Real(h.cstep)-pi/180*a.angleA/2);
x.angleB=XB+dis*cos(a.offset+pi+h.rtheta3Real(h.cstep)-pi/180*a.angleB/2);
y.angleB=YB+dis*sin(a.offset+pi+h.rtheta3Real(h.cstep)-pi/180*a.angleB/2);
x.angleE=XE+dis*cos(a.offset+h.rtheta3Real(h.cstep)+pi/180*a.angleE/2);
y.angleE=YE+dis*sin(a.offset+h.rtheta3Real(h.cstep)+pi/180*a.angleE/2);
end
function REDRAW
if h.isgrashof
if h.cstep > numel(h.xa)
h.cstep = 1;
elseif h.cstep < 1
h.cstep = numel(h.xa);
end
else
if h.cstep > numel(h.xa)
h.cstep = numel(h.xa);
h.increment = -1*h.increment;
elseif h.cstep < 1
h.cstep = 1;
h.increment = -1*h.increment;
end
end
[x,y,a] = COORDINATES;
set(h.h.L(4),'XData',x.h.L4,'YData',y.h.L4);
set(h.fourbar,'XData',x.fourbar,'YData',y.fourbar);
set(h.dots,'XData',x.fourbar,'YData',y.fourbar);
set(h.ic,'XData',x.ic,'YData',y.ic);
CurPos = h.PosArray(:,:,h.rstep,h.cstep);
XO = CurPos(1,1); YO = CurPos(2,1);
XA = CurPos(1,2); YA = CurPos(2,2);
XB = CurPos(1,3); YB = CurPos(2,3);
XE = CurPos(1,4); YE = CurPos(2,4);
XIC = CurPos(1,5); YIC = CurPos(2,5);
set(h.coordO,'Position',[x.coordO,y.coordO],...
'String',sprintf('(%.2f,%.2f)',XO,YO));
set(h.coordA,'Position',[x.coordA,y.coordA],...
'String',sprintf('(%.2f,%.2f)',XA,YA));
set(h.coordB,'Position',[x.coordB,y.coordB],...
'String',sprintf('(%.2f,%.2f)',XB,YB));
set(h.coordE,'Position',[x.coordE,y.coordE],...
'String',sprintf('(%.2f,%.2f)',XE,YE));
set(h.angleO,'position',[x.angleO,y.angleO],'string',sprintf('%.1f^o',a.angleO));
set(h.angleA,'position',[x.angleA,y.angleA],'string',sprintf('%.1f^o',a.angleA));
set(h.angleB,'position',[x.angleB,y.angleB],'string',sprintf('%.1f^o',a.angleB));
set(h.angleE,'position',[x.angleE,y.angleE],'string',sprintf('%.1f^o',a.angleE));
set(h.MovingPolode,'XData',x.MovingPolode,'YData',y.MovingPolode);
set(h.PositionSlider,'value',h.dtheta1(h.cstep));
set(h.PositionEdit,'string',sprintf('%.1f',h.dtheta1(h.cstep)));
if h.switched
rotTheta=atan2(YE-YO,XE-XO);
CurrentFixedIC=TMAT2D(XO,YO,rotTheta)*h.FixedICMatrix;
set(h.FixedPolode,'xdata',CurrentFixedIC(1,:),...
'ydata',CurrentFixedIC(2,:));
end
drawnow
end
function ANIMATE
while h.animate
h.cstep = h.cstep+h.increment;
REDRAW;
pause(h.pause)
end
end
function STARTSTOP(src,event,c)
if h.animate
h.animate = false;
set(h.StartButton,'string','START','foregroundcolor',1/200*[42 121 17]);
else
h.animate = true;
set(h.StartButton,'string','STOP','foregroundcolor',1/255*[230 0 0]);
ANIMATE;
end
end
function INVERT(src,event,c)
if h.switched
direction = sign(h.rstep-h.cstep);
if direction
set(h.InvertButton,'string','Inverting...');
h.increment = direction*abs(h.increment);
while sign(h.rstep-h.cstep) == direction
h.cstep = h.cstep+h.increment;
REDRAW;
end
h.cstep = h.rstep;
set(h.InvertButton,'string','Invert Mechanism');
end
h.switched = false;
set(h.FixedPolode,'xdata',h.FixedICMatrix(1,:),...
'ydata',h.FixedICMatrix(2,:));
REDRAW;
JointPathX1=[]; JointPathX2=[];
JointPathY2=[]; JointPathY2=[];
for k=1:numel(h.xa)
JointPathX1(k)=h.PosArray(1,2,k,k);
JointPathX2(k)=h.PosArray(1,3,k,k);
JointPathY1(k)=h.PosArray(2,2,k,k);
JointPathY2(k)=h.PosArray(2,3,k,k);
end
set(h.JointPath1,'xdata',JointPathX1,'ydata',JointPathY1);
set(h.JointPath2,'xdata',JointPathX2,'ydata',JointPathY2);
else
h.switched = true;
REDRAW;
set(h.JointPath1,'xdata',squeeze(h.PosArray(1,1,h.rstep,:)),...
'ydata',squeeze(h.PosArray(2,1,h.rstep,:)));
set(h.JointPath2,'xdata',squeeze(h.PosArray(1,4,h.rstep,:)),...
'ydata',squeeze(h.PosArray(2,4,h.rstep,:)));
end
end
function REVERSE(src,event,c)
h.increment=-h.increment;
end
function SPEED_SLIDER(src,event)
val=round(get(h.SpeedSlider,'value'));
set(h.SpeedSlider,'value',val);
h.pause=.5/2^val;
if val==h.maxSpeed
pause off;
else
pause on;
end
end
function POSITION_SLIDER(src,event)
val=get(h.PositionSlider,'value');
[minVal,minPos]=min(abs(h.dtheta1-val));
set(h.PositionSlider,'value',minVal);
set(h.PositionEdit,'string',num2str(minVal));
h.cstep = minPos;
REDRAW;
end
function POSITION_EDIT(src,event)
val=str2num(get(h.PositionEdit,'string'));
[minVal,minPos]=min(abs(h.dtheta1-val));
set(h.PositionEdit,'string',minVal);
set(h.PositionSlider,'value',minVal);
h.cstep = minPos;
REDRAW;
end
function POLODES_CHECKBOX(src,event)
checked=get(h.PolodesCheckbox,'value');
if checked
set([h.FixedPolode h.MovingPolode h.ic],'visible','on');
else
set([h.FixedPolode h.MovingPolode h.ic],'visible','off');
end
end
function JOINTPATHS_CHECKBOX(src,event)
checked=get(h.JointPathsCheckbox,'value');
if checked
set([h.JointPath1 h.JointPath2],'visible','on');
else
set([h.JointPath1 h.JointPath2],'visible','off');
end
end
function ANGLES_CHECKBOX(src,event)
checked=get(h.AnglesCheckbox,'value');
if checked
set([h.angleO,h.angleA,h.angleB,h.angleE],'visible','on');
else
set([h.angleO,h.angleA,h.angleB,h.angleE],'visible','off');
end
end
function COORDS_CHECKBOX(src,event)
checked=get(h.CoordsCheckbox,'value');
if checked
set([h.coordO,h.coordA,h.coordB,h.coordE],'visible','on');
else
set([h.coordO,h.coordA,h.coordB,h.coordE],'visible','off');
end
end
function OPTIONS(src,event)
val=get(h.Popup,'value');
switch val
case 2 %Revert to Current
rNew=h.r;
case 3 %Previous
rNew=h.rOld;
case 4 %GCCC Example
rNew=[ 3 4 3 1.5];
case 5 %GCRR Example
rNew=[ 1.5 3 4 3];
case 6 %GRCR Example
rNew=[ 3 1.5 3 4];
case 7 %GRRC Example
rNew=[ 4 3 1.5 3];
case 8 %RRR1 Example
rNew=[ 2 4 2 1];
case 9 %RRR2 Example
rNew=[ 1 2 4 2];
case 10 %RRR3 Example
rNew=[ 2 1 2 4];
case 11 %RRR4 Example
rNew=[ 4 2 1 2];
case 12 %SCCC Example
rNew=[ 3 4 3 2];
case 13 %SCRR Example
rNew=[ 2 3 4 3];
case 14 %SRCR Example
rNew=[ 3 2 3 4];
case 15 %SRRC Example
rNew=[ 4 3 2 3];
case 16 %Parallelogram
rNew=[ 2 3 2 3];
case 17 %Deltoid
rNew=[ 2 2 3 3];
case 18 %Square
rNew=[ 2 2 2 2];
end
if val>1
for k=1:4
set(h.LinkSlider(k),'value',rNew(k));
set(h.LinkEdit(k),'string',num2str(rNew(k)));
end
end
end
function LINK_SLIDER(src,event)
index=find(h.LinkSlider==src);
set(h.LinkEdit(index),'string',num2str(get(h.LinkSlider(index),'value')));
set(h.Popup,'value',1);
end
function LINK_EDIT(src,event)
index=find(h.LinkEdit==src);
val=str2num(get(h.LinkEdit(index),'string'));
if val>10
val=10;
elseif val<=0
val=.001;
end
set(h.LinkSlider(index),'value',val);
set(h.LinkEdit(index),'string',num2str(val));
set(h.Popup,'value',1);
end
function CHANGELINKS(src,event,c)
animatestatus=h.animate;
tempLinks=transpose(cell2mat(get(h.LinkSlider,'value')));
if isequal(tempLinks,h.r)
return;
else
rOld=h.r;
h.r=tempLinks;
end
GRASHOFTEST;
if ~h.isconstructible
h.r=rOld;
errordlg('Desired mechanism is not constructible or does not move.')
return
else
h.rOld=rOld;
end
set(h.ChangeLinksButton,'string','Calculating...');
drawnow;
CALCULATIONS;
FixedXIC=[];
FixedYIC=[];
JointPathX1=[]; JointPathX2=[];
JointPathY2=[]; JointPathY2=[];
for k=1:numel(h.xa)
FixedXIC(k)=h.PosArray(1,5,k,k);
FixedYIC(k)=h.PosArray(2,5,k,k);
JointPathX1(k)=h.PosArray(1,2,k,k);
JointPathX2(k)=h.PosArray(1,3,k,k);
JointPathY1(k)=h.PosArray(2,2,k,k);
JointPathY2(k)=h.PosArray(2,3,k,k);
end
h.FixedICMatrix=[FixedXIC;FixedYIC;ones(1,numel(FixedXIC))];
set(h.FixedPolode,'xdata',FixedXIC,'ydata',FixedYIC);
if ~h.switched
set(h.JointPath1,'xdata',JointPathX1,'ydata',JointPathY1);
set(h.JointPath2,'xdata',JointPathX2,'ydata',JointPathY2);
else
set(h.JointPath1,'xdata',squeeze(h.PosArray(1,1,h.rstep,:)),...
'ydata',squeeze(h.PosArray(2,1,h.rstep,:)));
set(h.JointPath2,'xdata',squeeze(h.PosArray(1,4,h.rstep,:)),...
'ydata',squeeze(h.PosArray(2,4,h.rstep,:)));
end
set(h.base,'xdata',[0,h.r(4)]);
REDRAW;
set(h.FigTitle,'string',h.mechType);
set(h.ChangeLinksButton,'string','Change Links');
set(h.PositionSlider,'min',min(h.dtheta1),'max',max(h.dtheta1));
AUTOZOOM(0,0,0);
h.animate=animatestatus;
end
function AUTOZOOM(src,event,c)
maxlink=max(h.r);
xmin=-1.5*maxlink; xmax=1.5*maxlink+h.r(4);
ymin=xmin; ymax=-ymin;
LocHWratio=(ymax-ymin)/(xmax-xmin);
if LocHWratio < h.HWratio
Height=h.HWratio*(xmax-xmin);
ymax=1/2*Height; ymin=-1/2*Height;
elseif LocHWratio > h.HWratio
Width=(ymax-ymin)/h.HWratio;
xmax=1/2*h.r(4)+1/2*Width; xmin=1/2*h.r(4)-1/2*Width;
end
axis([xmin xmax ymin ymax]);
end
function ZOOMALL(src,event,c)
numpoints=numel(h.PosArray(1,:,:,:));
xPoints=reshape(h.PosArray(1,:,:,:),1,numpoints);
yPoints=reshape(h.PosArray(2,:,:,:),1,numpoints);
xPoints(xPoints==Inf)=[];
yPoints(yPoints==Inf)=[];
xmin=min(xPoints);
xmax=max(xPoints);
ymin=min(yPoints);
ymax=max(yPoints);
LocHWratio=(ymax-ymin)/(xmax-xmin);
if LocHWratio < h.HWratio
Height=h.HWratio*(xmax-xmin);
ymax=1/2*Height+1/2*(ymax+ymin); ymin=-1/2*Height+1/2*(ymax+ymin);
elseif LocHWratio > h.HWratio
Width=(ymax-ymin)/h.HWratio;
xmax=1/2*(xmax+xmin)+1/2*Width; xmin=1/2*(xmax+xmin)-1/2*Width;
end
axis([xmin xmax ymin ymax]);
end
function HELPDIALOG(src,event,c)
dlgname = 'Instructions';
helpstring = {...
'For a quick start, just press "START."' ;...
' ' ;...
'To change mechanisms: ' ;...
' ' ;...
' 1) use the drop down box for "Link Length" options, ' ;...
' or ' ;...
' 2) use the length slider bars, ' ;...
' and ' ;...
' 3) hit "Change Links" button.' ;...
' ' ;...
'Interesting mechanisms to try: GCCC, GRCR, & SRCR examples.' ; ...
' ' ;...
'You may change link lengths, during the animation, if you press' ;...
'the "Change Links" button ' ;...
' ' ;...
'The 4-bar is in red, the polodes are in blue and black.';...
' ' ;...
'What is this all about? ' ;...
' ' ;...
'The two polodes are the plots of the coupler link''s instant center (IC).' ; ...
'The IC is where the input link and output link intersect.' ;...
'The polode plot is shown for the mechanism and its inversion.' ; ...
'The inversion changes the moving coupler link to be the ground' ;...
'The IC is where the coupler link ''instantly'' rotates around.' ;...
'The two polode curves, when they roll on each other, ' ; ...
'produce the same motion as the 4-bar.' ; ...
' ' ;...
'The 4-bar may be easily seen by unchecking all boxes under "display." ' ;...
' ' ;...
'The notation follows Barker''s classification of planar 4-bar mechanisms:' ;...
'Gxxx = Grashof, RRRx = non-Grashof, Sxx = special case ' ;...
'C = crank, R = rocker, thus a GRCR is a Grashof rocker-crank-rocker.' ;...
' ' ;...
'See Norton''s Design of Machinery (4th ed, pg 61) for more details.' ; ...
};
helpdlg(helpstring,dlgname)
end
function close_fig(src,event,c)
if isappdata(0,'base_unit')
set(0,'Units',getappdata(0,'base_unit')); % Units set to original value
rmappdata(0,'base_unit'); % remove the knowledge of org value
end
h.animate = false; % Hit "stop" if running, for a clean exit.
delete(gcbf)
end
end
