This paper describes the design of a unique suite of mechanisms which make up the Deployment and Pointing System (DAPS) for the Neutron Star Interior Composition Explorer (NICER/SEXTANT) instrument, an X-Ray telescope, which will be mounted on the International Space Station (ISS). The DAPS system uses 4 stepper motor actuators to deploy the telescope box, latch it in the deployed position, and allow it to track sky targets. The DAPS gimbal architecture provides full-hemisphere coverage, and is fully re-stowable. The compact design of the mechanism allowed the majority of total instrument volume to be used for science. Override features allow DAPS to be stowed by ISS robotics.