>

restart;

>	with(plots):

>

n:=10;

>	x:=cos(n*t)-n*cos(t);y:=sin(n*t)-n*sin(t);

>	x1:=diff(x,t); y1:=diff(y,t);

>	x2:=diff(x1,t); y2:=diff(y1,t);

>	w:=x1*y2-y1*x2; v:=x1^2+y1^2;

>	r:=v^(3/2)/abs(w);

>	xc:=x-v/w*y1; yc:=y+v/w*x1;

>	p1:=plot([x,y,t=0..2*Pi],scaling=constrained,color=yellow):

>	p2:=animate([xc+r*cos(s),yc+r*sin(s),s=0..2*Pi],t=0..2*Pi,scaling=constrained,color=red,frames=100):

>	p3:=animate([(1-s)*xc+s*x,(1-s)*yc+s*y,s=0..1],t=0..2*Pi,scaling=constrained,color=blue,frames=100):

>	p4:=plot([xc,yc,t=0..2*Pi],scaling=constrained,color=green):

>	display(p1,p2,p3,p4,thickness=3,axes=none);

>