Load–Displacement Characterization in Three Degrees-of-Freedom for General Lamina Emergent Torsion Arrays

Abstract

Lamina emergent torsion (LET) joints for use in origami-based applications enables folding of panels. Placing LET joints in series and parallel (formulating LET arrays) opens the design space to provide for tunable stiffness characteristics in other directions while maintaining the ability to fold. Analytical equations characterizing the elastic load–displacement for general serial–parallel formulations of LET arrays for three degrees-of-freedom are presented: rotation about the desired axis, in-plane rotation, and extension/compression. These equations enable the design of LET arrays for a variety of applications, including origami-based mechanisms. These general equations are verified using finite element analysis, and to show variability of the LET array design space, several verification plots over a range of parameters are provided.

A Foldable and Reconfigurable Monolithic Reflectarray for Space Applications

“…Many types of surrogate folds have been developed and designed for various motion and loading conditions [15]. Work has been done to characterize surrogate folds [15]- [16]. In most applications it is desired that a surrogate fold has motion similar to a traditional pin-joint hinge, allowing rotation around one axis and restricting all other motion.…”

“…This enables origami-based folding of patterned panels by allowing the needed rotation along the joint while minimizing the joint footprint on the panels. LET joints have been used in space applications [16], antennas arrays [17]- [18], parabolic antenna design [19], precision adjustment target shrouds [20], and robotic surgical instrument design [21]. LET joint surrogate hinges can also be used to maintain electrical continuity across joints.…”

“…where kT is the stiffness of the torsional sections, kB is the stiffness of the bending sections, and where P and S are the amount of LETs in parallel and series, respectively [16]. The in-plane rotational stiffness (y-direction) is given by…”

“…While the desired motion of the LET joint is an out-of-plane rotation, other undesirable "parasitic" motions can also occur as the joint has 6 degrees of freedom (DOF). Researchers have characterized LET joints according to many of these DOF [16], [22], [24]. The surrogate joint is used to simulate a pin-joint and precise motion of the joint is important.…”

“…7. This was quantified by using the ratio of the stiffnesses (ky/kx) as defined in [16]. The optimization was constrained to design a LET array that would not fail due to stresses when folded as defined in [22].…”