Homoclinic and Heteroclinic Orbits in Climbing Cucumber Tendrils

Many biomaterials utilize chiral growth to imitate biological functions. A prominent example can be found in growing cucumbers, which use tendrils as winding support for both fixation and climbing. A number of tendril-mimicking materials and artificial plant-like mechanical machines have been developed to imitate tendril deformation. However, tendrils tend to not only show spiral or parallel shapes, but also a combination of both configurations. It remains unclear whether these morphologies are regular and how they form mechanically. Here, the morphology of climbing tendrils as a complex nonlinear phenomenon is investigated via experimental and theoretical approaches. The results of the experiments clarify the relationship between tendril morphologies and actual tendril growth as well as relevant stress characteristics during the climbing of a support by the tendril, and their mechanical properties. On this basis, the three-dimensional configuration problem of a cylinder-constrained rod has been utilized to describe the phenomenon of a tendril climbing support. The phenomena of spiral and parallel configuration combinations in tendrils could be effectively explained by studying similar homoclinic and heteroclinic orbits. Applying these results accurately guides the development of mimicking material.