  We study period doublings in $N$ $(N=2,3,4, \dots)$ coupled parametrically
forced damped pendulums by varying $A$ (the amplitude of the external driving
force) and $c$ (the strength of coupling). With increasing $A$, the stationary
point undergoes multiple period-doubling transitions to chaos. We first
investigate the two-coupled case with $N=2$. For each period-doubling
transition to chaos, the critical set consists of an infinity of critical line
segments and the zero-coupling critical point lying on the line $A=A^*_i$ in
the $A-c$ plane, where $A^*_i$ is the $i$th transition point for the uncoupled
case. We find three kinds of critical behaviors, depending on the position on
the critical set. They are the same as those for the coupled one-dimensional
maps. Finally, the results of the $N=2$ case are extended to many-coupled cases
with $N \geq 3$, in which the critical behaviors depend on the range of
coupling.
