Abstract
In this present paper, we will take three affine Cayley-Klein planes into consideration: A e , P e and P e ' . The plane P e ' is a fixed plane relative to two other moving affine Cayley-Klein (CK)-planes. We will describe one-parameter motions A e / P e , A e / P' e and P e / P' e and discuss the relation between the motions A e / P e , A e / P' e and P e / P' e and by evaluating their derivative formulae, velocity vectors and pole points. Also, we will observe moving coordinate system and after that we willl examine canonical relative system for one-parameter planar motions in the affine CK-planes by using the notions of moving coordinate system. Moreover, Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, will be obtained with the help of canonical relative system for one-parameter motions in affine CK-planes planes by using the method given by H. R. Muller in 1956 [1].
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