Abstract: A machine for fining/polishing ophthalmic lenses has a horizontal and vertical plates rigidly fixed in an inverted T. Eccentric shafts journalled 180 degrees out of phase on the horizontal plate orbit tools on one side of the vertical plate. A swing frame pivotally mounted on the other side of the vertical plate has a horizontal shaft parallel to the vertical plate. Shafts orthogonal to the horizontal shaft are journalled for see-saw motion about the horizontal shaft, for rotational motion about their own longitudinal axes and for sliding motion along the horizontal shaft. Block adapters on the orthogonal shafts hold lenses in vertical alignment above the tools. Separate linkages reciprocate the horizontal shaft in parallel relationship to the vertical plate and the orthogonal shafts in orthogonal relationship to the vertical plate. The shaft linkages have a timing ratio such that the block adapters travel in laterally reciprocating horizontal figure eight patterns.