I am plotting parametric curves. The plots look smooth and continuous for plots with fewer, more loosely spaced "arms". However, for plots with more arms, more densely spaced, the plot looks jagged and inaccurate. Remedy?

xcoordinate[a_, b_, t_] := (a + b)*Cos[t] - b*Cos[(a + b)/b*t]

ycoordinate[a_, b_, t_] := (a + b)*Sin[t] - b*Sin[(a + b)/b*t]

ParametricPlot[{xcoordinate[1/4, 41/(4*4), t], ycoordinate[1/4, 41/(4*4), t]}, {t, 0, 82 Pi}, AspectRatio -> Automatic]

ParametricPlot[{xcoordinate[1/8, 359/(8*18), t], ycoordinate[1/8, 359/(8*18), t]}, {t, 0, 718 Pi}, AspectRatio -> Automatic]