Hexfoil rotary flexures have been proposed as pivots suitable for use in precise optical instruments. In the application that inspired the hexfoil concept, there is a requirement for a limited-rotation mirror gimbal that would maintain, with unprecedented accuracy, coincidence among the axes of rotation and a fiducial mark on the mirror, over the entire range of rotation. Theoretically, a hexfoil rotary flexure could satisfy this requirement.

A hexfoil rotary flexure would offer the following advantages over a nominally equivalent commercial rotary flexure:

- A hexfoil rotary flexure would maintain a static center of rotation; in other words, it would be subject to no more than negligible drift of the center of rotation.
- The ratio between lateral stiffness and rotational stiffness (this ratio is regarded as a figure of merit for a flexural pivot) would be much greater. Thus, a hexfoil would approximate an ideal pivot more closely.
- An optimized hexfoil rotary flexure could withstand a lateral load greater than that for any similarly sized commercial flexural pivot.
- A hexfoil rotary pivot would be made from a single piece of material. The monolithic nature of this device would ensure the highest reliability. The hexfoil rotary flexure is related to the device described in “Trefoil Rotary Flexure” (NPO-20228) NASA Tech Briefs, Vol. 22, No. 8 (August 1998), page 68. In comparison with a trefoil pivot, a hexfoil pivot would have twice the angular range,while sacrificing some lateral stiffness and load capability. A hexfoil pivot could be designed as a drop-in replacement for a standard Lucas (or equivalent) pivot, inas- much as it has the same type of interface.

A hexfoil pivot (see figure) would include two coaxial hollow circular cylinders that would constitute a rotor and stator, respectively. From each cylinder, three flexural elements in the form of thin plates spaced at equal circumferential intervals would extend radially inward, terminating at approximately the axis of rotation. More precisely, the plates attached to each cylinder would be parallelograms with bases equal to the length of the cylinder, radial heights approximately equal to the inner radius of the cylinder, and an axial slant distance of approximately half the length of the cylinder. Thus, in effect, the three flexural elements from each cylinder would terminate in a line segment of length equal to that of the cylinder, coincident with axis of rotation, dis- placed axially from the cylinder by half the length of the cylinder.

To complete the characterization, it should be mentioned that the on-axis flexure termination for each cylinder would be displaced axially toward the other cylinder, such that the flexure terminations for both cylinders would coincide. Furthermore, the flexural elements for the two cylinders would be “clocked” relative to each other such that each flexure from one cylinder would be coplanar (when not deflected) with one from the other cylinder. Hence, in essence, there would be three contiguous flexures connecting the two cylinders.

The advantages of this configuration are the following:

- The termination of the flexural elements would be brought as close as possible to the axis of rotation, thereby maximizing the rotational flexibility while maintaining lateral stiffness.
- Load paths through the device would be aligned such that all translational loads would be carried as tension or compression in the flexural elements (the stiffest and highest-load-bearing arrangement possible), while a torque applied about the axis of rotation would be reacted by simple bending (configuration of greatest compliance and least stress).

*This work was done by Donald Moore and Robert Calvet of Caltech for NASA’s Jet Propulsion Laboratory*.

##### NASA Tech Briefs Magazine

This article first appeared in the June, 2002 issue of *NASA Tech Briefs* Magazine.

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