  The general solution of the graded contraction equations for a
$\zz_2^{\otimes N}$ grading of the real compact simple Lie algebra $so(N+1)$ is
presented in an explicit way. It turns out to depend on $2^N-1$ independent
real parameters. The structure of the general graded contractions is displayed
for the low dimensional cases, and kinematical algebras are shown to appear
straightforwardly. The geometrical (or physical) meaning of the contraction
parameters as curvatures is also analysed; in particular, for kinematical
algebras these curvatures are directly linked to geometrical properties of
possible homogeneous space-times.
