Valentine's Hyperboloid Bouquet

Mathematics

This model takes advantage of a neat property of hyperboloid surfaces: they can be constructed entirely from straight lines! While not developable surfaces, like cylinders and cones, hyperboloids still see use in mechanical engineering in the forms of strong, lightweight architectural structures and towers, and specialty gears.

Assembly

To construct this model, print 2 rings, 12 flowers, and any combination of stems adding up to 12 (we printed 3 long, 6 medium, and 3 short, to form a triangular bouquet). The one constraint is that you cannot have a stem of one length next to another stem of the same length, so that the flowers have room for each other.

Also be sure to print all the parts flat-side down, including the stems. They have been flattened on one side to help with printing and assembly

To assemble, snap the upper ball joint of one stem into one ring, then the lower ball joint into the other ring. Then, go around both circles, adding the upper joint first for each stem, until all 12 are assembled (make sure that all of the stems are in the same order in both rings!). Then, snap the bottoms of the flowers onto the tops of each of the stems, and enjoy!

Learn More

This design was developed by the Compliant Mechanisms and Robotics Group (CMR) from Brigham Young University (BYU). Follow us at @byucmr on Instagram, @CompliantMechanismsResearchGroup on Facebook, or visit the BYU Compliant Mechanisms and Robotics (CMR) website to learn more about compliant mechanisms.

Intellectual Property

The downloadable 3D print files provided here may be used, modified, and enjoyed for noncommercial use. To license developable mechanism technology for commercial applications, contact:

BYU Technology Transfer Office
3760 Harold B. Lee Library
Brigham Young University
Provo, UT 84602
Phone: (801) 422-6266
https://techtransfer.byu.edu/contact