A yarn winding spindle is disclosed which is characterized by the ability to grip the interior of a tubular bobbin during the winding of the yarn thereon and then release the bobbin to facilitate doffing. The spindle comprises a cylindrical support member which is composed of a plurality of axially spaced apart annular entrainment members and a plurality of annular, elastic clamping members mounted between adjacent entrainment members. The elastic members are configured and internally self-biased so as to assume a radially extended position to engage the bobbin in the absence of an external force being applied thereto, and to assume a radially retracted position to release the bobbin upon a biasing force being applied thereto.