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The quantum commutations $RTT=TTR$ and the orthogonal (symplectic) conditionsfor the inhomogeneous multiparametric $q$-groups of the $B_n,C_n,D_n$ type arefound in terms of the $R$-matrix of $B_{n+1},C_{n+1},D_{n+1}$. A consistentHopf structure on these inhomogeneous $q$-groups is constructed by means of aprojection from $B_{n+1},C_{n+1},D_{n+1}$. Real forms are discussed: inparticular we obtain the $q$-groups $ISO_{q,r}(n+1,n-1)$, including the quantumPoincar\'e group.Comment: 14 pages, latex, no figure

R-matrix formulation of the quantum inhomogeneous groups ISO q,r (N) and ISp q,r (N)