An ideal constant-force spring is a spring for which the force it exerts over its range of motion is a constant, that is, it does not obey Hooke's law. In reality, "constant-force springs" do not provide a truly constant force and are constructed from materials which do obey Hooke's law. Generally constant-force springs are constructed as a rolled ribbon of spring steel such that the spring is in a rolled up form when relaxed.
The approximation of "constant force" comes from a long travel and a pre-loaded rest position, so that the initial force does not start from zero but a finite value. For relatively small variations around this initial position the force is approximately constant.
References
- Ansel C. Ugural, Mechanical Design of Machine Components, Second Edition, page 683, CRC Press, 2015 ISBN 1439887810.