with(plots):

animate({[cos(s),sin(s),s=0..2*Pi],
[cos(t)+s*t*sin(t),sin(t)-s*t*cos(t),s=0..1]},
t=0..3*Pi,scaling=constrained,frames=64,color=black);

animate({[cos(s),sin(s),s=0..2*Pi],
[cos(t)+s*t*sin(t),sin(t)-s*t*cos(t),s=0..1],
[cos(s*t)+s*t*sin(s*t),sin(s*t)-s*t*cos(s*t),s=0..1]},
t=0..3*Pi,scaling=constrained,frames=64,color=black);