The last set of hinge tests that I showed used a cut out a rectangle of material to form the links. By re-arranging a formula that calculates the required inter-link clearance, it’s possible to find the minimum number of links to make a bend using only a single cut with the laser if the width of the cut (laser kerf) is known. Its then also possible to calculate what the radius of that minimum bend is from the length of the lattice cut area.
For a 90 degree bend in a 3mm thick sheet and 3mm wide links, 23 torsional links are needed if the laser kerf is 0.2mm. This will form a bend with a 44mm internal radius.
Lattice hinges are formed when a set of parallel, overlapping cuts divide a flat sheet into thinner, linked sections that can deform more easily than the solid sheet. By dividing the sheet into an array of parallel columns, each column can twist along its own length to let the sheet form a bend by twisting around the axis of these torsional links. Flexibility of the joint is determined by the material properties of the plate and the geometry (length of the overlapping cuts and cross sectional area) of the torsional links. For simplicity I’m only considering links where the width of the link is equal to the plate thickness.