  The Ohnuki-Kitakado (O-K) scheme of quantum mechanics on $S^D$ embedded in
$R^{D+1}$ is investigated. Generators satisfying the O-K algebra are written
down explicitly in term of the induced gauge potential. A direct method is
developed to obtain the generators in covariant form. It is seen that there
exists an induced gauge configuration which is trivial on $S^D$ but might cause
a nontrivial physical effect in $R^{D+1}$. The relation of the O-K scheme to
extended objects such as the 't Hooft-Polyakov monopole is discussed.
