The figure illustrates a device that flexes to allow rotation about a single axis through a total range of ±12°. This device was designed to offer the following advantages over commercial flexural pivots:
- Greater ratios of radial to rotational and axial to rotational stiffness for a given load capability;
- Higher load capabilities for a given rotational stiffness;
- No shift in the center of rotation assuming flexures are uniform in thickness;
- Theoretical unlimited fatigue life at ±10° excursion;
- Monolithic construction for higher reliability and greater likelihood of attaining the theoretical fatigue life; and
- No global buckling modes.
The device is called a "trefoil rotary flexure" because its flexible members are three radial, equally spaced thin plates that extend from an outer cylinder to the inner tri-lobed support. The distance from the inner terminus of the flexures to the rotational axis is made as small as possible to minimize rotational stiffness. The three lobes of the inner support are joined at the rotation axis to provide an extremely rigid attachment for the flexure elements, allowing high radial and axial stiffnesses. The tri-lobed support rotates relative to the outer cylinder on the flexures to create the flexural pivot motion. The total rotational range of ±12° is defined by hard stops in the lobes and the outer cylinder.
The lobes, fins, and outer cylinder are integral parts of the monolithic device, which was fabricated by electrical-discharge machining of a solid metal rod. To reduce concentrations of stresses and thereby ensure long fatigue life, generous fillet radii were incorporated at the inner and outer ends of the fins.
This work was done by Robert J. Calvet of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com under the Mechanics category.
In accordance with Public Law 96-517, the contractor has elected to retain title to this invention. Inquiries concerning rights for its commercial use should be addressed to
Technology Reporting Office
JPL
Mail Stop 122-116
4800 Oak Grove Drive
Pasadena, CA 91109
(818) 354-2240
Refer to NPO-20228, volume and number of this NASA Tech Briefs issue, and the page number.
This Brief includes a Technical Support Package (TSP).

Trefoil rotary flexure
(reference NPO20228) is currently available for download from the TSP library.
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Overview
The document presents a technical report on the Trefoil Rotary Flexure, an innovative device designed for rotary actuation, particularly in applications requiring precise motion control, such as inertial shakers. Developed by Robert J. Calvet at NASA's Jet Propulsion Laboratory, the Trefoil Rotary Flexure addresses specific engineering challenges associated with traditional flexural pivots.
Key features of the Trefoil Rotary Flexure include its superior stiffness ratios, which are significantly higher than those of current commercial flexural pivots. The device boasts a radial stiffness to torsional stiffness ratio of 3200 and an axial stiffness to torsional stiffness ratio of 7400. This results in higher load capabilities while maintaining similar torsional stiffness. Additionally, the design ensures virtually no shift in the center of rotation, which is critical for precision applications.
The flexure is constructed monolithically, enhancing its reliability and increasing the likelihood of achieving a theoretical infinite fatigue life at ±10° excursions. This construction method also eliminates global buckling modes, a common failure point in traditional designs. The device is capable of flexing to allow rotation about a single axis through a total range of ±12°, making it versatile for various applications.
The report outlines the technical problem addressed by the Trefoil Rotary Flexure: the need for a rotary actuator with a low rotary break frequency (5-10 Hz) and no internal resonances below 1000 Hz. The solution involves designing a rotor with high rotary inertia and sufficient rigidity to avoid these resonances. The flexure elements consist of three thin plates arranged radially, with their inboard edges positioned close to the rotation axis to minimize rotational stiffness.
Finite element analysis confirms the flexure's high lateral and axial stiffness, low rotational stiffness, and stress levels well below endurance limits at 100° deflection. This analysis supports the device's design goals of achieving precise rotary motion while ensuring durability and reliability.
Overall, the Trefoil Rotary Flexure represents a significant advancement in rotary motion technology, offering enhanced performance characteristics that can benefit various aerospace and engineering applications. The report serves as a technical disclosure of this innovative design, highlighting its potential impact on future technologies.

