The handhold of an exercise handgrip turns freely while seated between the open ends of the upwardly extending prongs. It can be easily removed by moving the specially formed end part of the handhold into an access opening wide enough to slip the end part through. In positioning the handhold's end part for this removal, it must be forcibly snapped through a narrow opening. By reversing the procedure, the handhold can easily be returned to its place of rotation. The specially formed end part of the handhold must, therefore, have a narrow neck-like portion to fit through the narrow opening but the end part must also be enlarged to keep it in place for rotation. Preferably, there is also a stem and ball unit in one of the prongs which swings into place to trap exercise sheeting, cord or other media within an opening at the handgrip's bottom portion.