A core end engagement assembly is provided for a rewinding machine. The core end engagement assembly is configured to engage an end of the core and transmit rotational movement to the core during winding of the web material about the core. The assembly may include a drive housing. A chuck may project from a first end of the drive housing and may be configured to engage the end of the core. A first actuator may reciprocate the drive housing along a central axis of the core between an engagement and disengagement position of the chuck relative to the core. A second actuator may be mounted on the drive housing. The second actuator may be configured and adapted to move the chuck between release and hold positions. A flexible drive shaft operatively connects with and rotationally drives the chuck.