A multi-stage fin deployment assembly includes a rotary actuator configured to release a first spring-loaded stage that, when deployed, releases a second spring-loaded stage to deploy a set of deployable member or fins. By chaining these spring-loaded stages together, a relatively small input force, as provided by the rotary actuator, causes the second spring-loaded stage to generate a relatively large output force on the fins. This multistage force magnification makes it possible for the deployment assembly to utilize smaller actuators that require less power and take up less space, compared to conventional locking mechanisms.