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Three-dimensional perception is a key technology for many robotics applications, including obstacle detection, mapping, and localization. There exist a number of sensors and techniques for acquiring 3-D data, many of which have particular utility for various robotic tasks. We introduce a new design for a 3-D sensor system, constructed from a 2-D range scanner coupled with a passive linkage mechanism, such as a spring. By mounting the other end of the passive linkage mechanism to a moving body, disturbances resulting from accelerations and vibrations of the body propel the 2-D scanner in an irregular fashion, thereby extending the device's field of view outside of its standard scanning plane. The proposed 3-D sensor system is advantageous due to its mechanical simplicity, mobility, low weight, and relatively low cost. We analyze a particular implementation of the proposed device, which we call Zebedee, consisting of a 2-D time-of-flight laser range scanner rigidly coupled to an inertial measurement unit and mounted on a spring. The unique configuration of the sensor system motivates unconventional and specialized algorithms to be developed for data processing. As an example application, we describe a novel 3-D simultaneous localization and mapping solution in which Zebedee is mounted on a moving platform. Using a motion capture system, we have verified the positional accuracy of the sensor trajectory. The results demonstrate that the six-degree-of-freedom trajectory of a passive spring-mounted range sensor can be accurately estimated from laser range data and industrial-grade inertial measurements in real time and that a quality 3-D point cloud map can be generated concurrently using the same data.