Translations are transformations that are expected to be bijective and preserve connectedness, shape, perimeter, and area. In digital geometry, as we show here, this is not always obvious; we may need special conditions on the translation vector to have translations with these desired properties. In this paper, we use the Khalimsky grid, i.e., the semi-regular grid induced by the Khalimsky topology. This grid, also known as the truncated quadrille or truncated square tiling, is built up by regular octagons and squares with equal side length. We also generalize the case when the side lengths vary, but the neighborhood structure and, thus, the topology of the grid remains the same.