%cycloid
len=0.75; %length of line connected to centre of rolling circle
r=0.5; %radius of rolling circle
%if len=r then it becomes cycloid
n=0;
roughx=[];
roughy=[];
dtheta=pi/20;
t=linspace(0,2*pi,50);
[x,y]=pol2cart(t,r);
h1=patch(x,y,'r');%draw the circle
xl=[-len 0];yl=[0 0];%coordinates of line
h2=line(0,0);%draw line connected to centre of rolling circle
axis equal
axis([0 5*pi -1 1.5+(r+len)]);
set(gca,'position',[0.01 0.01 0.98 0.98])
set(gcf,'position',[10 40 1200 500])
line([-2 17],[0 0])%base line
upto=2*5*pi+dtheta;
while n<upto && ishandle(h2)
set(h1,'xdata',x+n*r,'ydata',y-min(y));%move circle forward by
[x3,y3]=transform2d(xl,yl,n*r,r,-n,0,0);%rotate and translate line
set(h2,'xdata',x3,'ydata',y3);
line([roughx x3(1)],[roughy y3(1)])
roughx=x3(1);
roughy=y3(1);
pause(0.025)
n=n+dtheta;
end
