DNA has been used to construct a wide variety of nanoscale molecular devices. Inspiration for such synthetic molecular machines is frequently drawn from protein motors, which are naturally occurring and ubiquitous. However, despite the fact that rotary motors such as ATP synthase and the bacterial flagellar motor play extremely important roles in nature, very few rotary devices have been constructed using DNA. This paper describes an experimental study of the putative mechanism of a rotary DNA nanomotor, which is based on strand displacement, the phenomenon that powers many synthetic linear DNA motors. Unlike other examples of rotary DNA machines, the device described here is designed to be capable of autonomous operation after it is triggered. The experimental results are consistent with operation of the motor as expected, and future work on an enhanced motor design may allow rotation to be observed at the single-molecule level. The rotary motor concept presented here has potential applications in molecular processing, DNA computing, biosensing and photonics.