A clamping device (01), for use on a lathe, includes a plurality of basic clamping supports (06), which can be moved in a star-shaped formation in relation to an axis of rotation and on each of which a clamping jaw (11) for clamping workpieces can be attached. The basic clamping supports (06) can be adjusted simultaneously by means of an adjusting drive (21, 36) of the clamping device (01). At least two basic clamping supports (06) are coupled directly or indirectly to one another by an outer rocker (15). At least in the middle of the adjusting path, a limited inward displacement of a basic clamping support (06a, 06c, and 06b, 06d, respectively) leads to a swiveling of the outer rocker (15a, 15c) and an outward displacement of the other coupled basic clamping support (06b, 06d, and 06a, 06c, respectively).