Abstract: We propose to measure the quality of an affine motion by its steadiness, which we formulate as the inverse of its Average Relative Acceleration (ARA). Steady affine motions, for which $ARA=0$, include translations, rotations, screws, and the golden spiral. To facilitate the design of pleasing in-betweening motions that interpolate between an initial and a final pose (affine transformation), B and C, we propose the Steady Affine Morph (SAM), defined as $A^tcirc B$ with $A = C circ B^-1$. A SAM is affine-invariant and reversible. It preserves isometries (i.e., rigidity), similarities, and volume. Its velocity field is stationary both in the global and the local (moving) frames. Given a copy count, n, the series of uniformly sampled poses, $A^frac in circ B$, of a SAM form a regular pattern which may be easily controlled by changing B, C, or n, and where consecutive poses are related by the same affinity $A^frac 1n$. Although a real matrix $A^t$ does not always exist, we show that it does for a convex and large subset of orientation-preserving affinities A. Our fast and accurate Extraction of Affinity Roots (EAR) algorithm computes At, when it exists, using closed-form expressions in two or in three dimensions. We discuss SAM applications to pattern design and animation and to key-frame interpolation.