A device that measures both translational acceleration and rotation exploits the dynamics of a vibratory structure that resembles a clover leaf. This device is related to other vibratory accelerometers and vibratory gyroscopes in which vibrations in suitably shaped structures are excited electrostatically and measured either capacitively or piezoresistively. The basic principle of this device could also be applied to a different structure, provided that, like the clover-leaf structure, it vibrates in substantially degenerate modes and provided further that it has a small mass imbalance.
The figure depicts the clover-leaf structure in the present device. This structure vibrates in two degenerate modes. A small mass imbalance defines the shape of the modes in that it causes the node lines of the vibrational pattern to lie along (1) a line that runs through the geometric center of the structure and the location of the mass imbalance and (2) a line perpendicular to the aforementioned line. In the presence of a nominal constant (e.g., zero) rotation or constant translational acceleration, it is possible to rotate the node lines to make them coincide with the Cartesian axes of symmetry of the structure; this is accomplished by applying an electrostatic force of such a magnitude as to contribute a negative spring-stiffness component that compensates for the mass imbalance.
The vibrational dynamics are such that a change in the translational acceleration perturbs the compensation, causing the node lines to rotate back toward alignment with the mass unbalance. In operation in an open-loop mode, the rotation of the node lines can be deduced from the amplitude and phase relationships among the outputs of the capacitive vibration sensors. Alternatively, the device can be operated in a closed-loop mode in which the signals are processed into feedback control signals that adjust the electrostatic force to keep the node lines from rotating; in this case, the feedback control signal serves as an indication of the angular velocity or translational acceleration. It is possible to measure rotation and translational acceleration simultaneously and separately because the translation- and rotation-related capacitive-sensor outputs come out in quadrature with each other.
This work was done by Roman Gutierrez and Tony K. Tang of Caltech for NASA's Jet Propulsion Laboratory.
This invention is owned by NASA, and a patent application has been filed. Inquiries concerning nonexclusive or exclusive license for its commercial development should be addressed to
the Patent Counsel
NASA Resident Office - JPL; (818) 354-5179
Refer to NPO-20620
This Brief includes a Technical Support Package (TSP).

Vibratory accelerometer and gyroscope
(reference NPO20620) is currently available for download from the TSP library.
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Overview
The document presents a technical support package from NASA detailing a novel vibratory accelerometer and gyroscope developed by Roman Gutierrez and Tony K. Tang at the Jet Propulsion Laboratory (JPL). This device is designed to measure both translational acceleration and rotation by exploiting the dynamics of a clover-leaf-shaped vibratory structure that operates in substantially degenerate modes.
The core innovation lies in the device's ability to utilize a small mass imbalance within the structure, which affects the vibrational modes. When the device is subjected to acceleration, the node lines of the vibrational pattern rotate back toward alignment with the mass imbalance. This rotation can be monitored in two operational modes: an open-loop mode, where the rotation is deduced from the outputs of capacitive vibration sensors, and a closed-loop mode, where feedback control signals adjust the electrostatic force to maintain alignment of the node lines.
The document highlights that the device can measure rotation and translational acceleration simultaneously due to the quadrature relationship between the outputs related to translation and rotation. This capability is significant as it allows for precise motion sensing using the same electronic system.
The invention is distinct from traditional accelerometers, which typically rely on a stationary mass suspended by cantilevers. Instead, this device employs a vibrating structure, making it more sensitive to changes in acceleration. The introduction of a mass imbalance is a key factor that enables the rotation of the vibrational modes, which serves as an indication of acceleration.
The technical disclosure also outlines the problem the inventors aimed to solve: the unexpected relationship between mode rotation and acceleration, which was discovered during experiments. The solution involves using electrostatic forces to compensate for the mass imbalance, allowing for accurate measurements of acceleration and rotation.
Overall, this vibratory accelerometer and gyroscope represents a significant advancement in sensor technology, with potential applications in various fields, including aerospace and robotics. The document concludes with a note on the patent status of the invention and invites inquiries for commercial development.

