Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscrib...Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.展开更多
A reprogrammable microactuator system is presented,consisting of antagonistic shape memory alloy(SMA)microactuators for bidirectional folding of miniature-scale tiles following the concept of origami.Additional integr...A reprogrammable microactuator system is presented,consisting of antagonistic shape memory alloy(SMA)microactuators for bidirectional folding of miniature-scale tiles following the concept of origami.Additional integrated heatable soft-magnetic pads with low ferromagnetic transition temperature allow for control of magnetic latching forces.The strongly coupled thermo-mechanical and thermo-magnetic properties of the microactuator and magnetic subsystems are taken into account in a model-based design to enable their selective control by Joule heating.A procedure for local shape setting of the SMA microactuators is presented to adjust their memory shape at either maximum or minimum bending angle and,thus,to functionalize their performance as protagonists or antagonists.A microfabrication process is developed that takes the specific requirements for processing the various materials and structures into account.A demonstrator system consisting of four triangular tiles with an edge length of 500μm and an angular range of about±100°is introduced that is programmed to adopt the shape of a pyramid and later on reprogrammed to self-unlatch,self-unfold,and subsequently to adopt the shape of a table.展开更多
文摘Ellipses can be constructed by folding disks. These folds are forming an envelope of tangents to the ellipse. In the paper of Gorkin and Shaffer, it was shown that the ellipse constructed by folding can be circumscribed by an arbitrary triangle of tangents, the vertices of which are lying on the circumference of the disk. They offered two non-elementary methods of proof, one using Poncelet’s Theorem, the other employing Blaschke products. In this paper, it is the intention to present an elementary proof by means of analytic geometry.
基金funded by the German Science Foundation within the Priority Program“Cooperative Multistage Multistable Microactuator Systems”(SPP2206)partly carried out with the support of the Karlsruhe Nano Micro Facility(KNMFi,www.knmf.kit.edu),a Helmholtz Research Infrastructure at Karlsruhe Institute of Technology(KIT,www.kit.edu)funding by the German Science Foundation(DFG)through the project 413288478.
文摘A reprogrammable microactuator system is presented,consisting of antagonistic shape memory alloy(SMA)microactuators for bidirectional folding of miniature-scale tiles following the concept of origami.Additional integrated heatable soft-magnetic pads with low ferromagnetic transition temperature allow for control of magnetic latching forces.The strongly coupled thermo-mechanical and thermo-magnetic properties of the microactuator and magnetic subsystems are taken into account in a model-based design to enable their selective control by Joule heating.A procedure for local shape setting of the SMA microactuators is presented to adjust their memory shape at either maximum or minimum bending angle and,thus,to functionalize their performance as protagonists or antagonists.A microfabrication process is developed that takes the specific requirements for processing the various materials and structures into account.A demonstrator system consisting of four triangular tiles with an edge length of 500μm and an angular range of about±100°is introduced that is programmed to adopt the shape of a pyramid and later on reprogrammed to self-unlatch,self-unfold,and subsequently to adopt the shape of a table.
