Let \((P,{\mathcal L})\) be an incidence space. Following a definition of \textit{B. Reinmiedl} [`Verallgemeinerte kinematische Räume', Diss. TU München (1990; Zbl 0721.51018)] the authors call a map \(\delta:P\to P\) a dilatation if \(\delta(L)\cap L=\emptyset\) or \(\delta(L)=L\) for any \(L\in{\mathfrak G}\) and \((P,{\mathfrak L},\cdot)\) a dilatation space if \(P\) is supplied with a binary operation such that \(x\to ax\), \(x\to xa\) are dilatations for any \(a\overline\in P\). For the nontrivial cases \(|{\mathfrak L}|\geq 2\), \(|L|\geq 3\) for each \(L\overline\in{\mathfrak L}\) they can show: \((P,\cdot)\) is a quasigroup, in particular a kinematic loop if it has an identity, the set \(P_{id}\) of idempotents of \((P,\cdot)\) is empty, \(=P\) or is of cardinality 1, if \(P_{id}=\varphi\) then \((P,{\mathcal F},\cdot)\) is a fibered quasigroup with fibration \({\mathcal F}=\{F\overline\in{\mathcal L};F\cdot F\subset F\}\), if \(P_{id}\neq\emptyset\) then \((P,{\mathcal L},\cdot)\) is a kinematic quasigroup. Furthermore, conditions and relevant examples are given to verify whether a dilatation space embedded into a projective space is a kinematic space in the sense of H. Karzel.