Properties of Twofold Tape Loops: The Influence of the Subtended Angle

Tape springs are thin-walled structures with zero longitudinal and constant transverse curvature. Folding them twice and connecting both ends creates a tape loop which acts as a linear guide. At this time, there is insufficient understanding of the influence of the tape spring's cross section on its behavior. This study investigates the influence of the subtended angle on the tape spring's behavior, especially the energy distribution and the fold radius. First, some key aspects in the design of a twofold tape loop are discussed. By performing a curvature analysis of this folded geometry, the different regions within a tape spring are identified. This information is used to identify the influence of the subtended angle on the geometry and energy state of the tape loop. The fold radius and fold angle are determined by analyzing the geometry of the fold region. The analysis showed that the energy within the transition regions cannot be neglected. The energy within these regions and the length of the transition regions both increase with the subtended angle. It is also shown that the fold radius is not constant when the subtended angle is small. The subtended angle should be above 100 deg to ensure a constant radius.