Rigid origami models facets as rigid bodies joined by crease hinges. The selected calculator intentionally covers only one symmetric two-panel fold: two equal rigid panels meet at a zero-thickness center hinge while their projected span shortens as the hinge rises.
Rigid Origami Interactive Calculator
Explore exact projected span and center-hinge rise for one symmetric two-panel rigid fold.
Equation Used
- The unit contains two equal perfectly rigid panels joined by one ideal revolute crease.
- Fold angle is measured from the flat state and endpoints remain at equal elevation.
- Panels and hinge have zero thickness and cannot stretch or bend.
- Miura tessellation geometry, collision, force, stiffness, dynamics, actuation and reliability are excluded.
The secondary figure uses the same flat span and selected included fold angle.
How the selected rigid-fold unit works
Two equal panels of length L/2 are joined by a revolute crease. The endpoints remain at one elevation and move symmetrically as the center hinge rises. Because the panel lengths stay constant, one fold-angle input fixes the ideal configuration.
This is the smallest useful rigid-panel hinge model. It is not a Miura-ori tessellation: a Miura sheet has a degree-four crease vertex, coupled fold angles and additional cell dimensions.
What this calculator demonstrates
Select flat end-to-end span and included fold angle. The calculator returns ideal projected span, center-hinge rise, span shortening and remaining-span percentage for this symmetric two-panel unit.
It does not calculate a deployable solar array, stowed volume, deployed area, Miura cell geometry, panel thickness, collisions, hinge limits, actuator stroke, forces, stiffness, stability, dynamics or reliability.
Exact two-panel geometry
Let the flat span be L, so each rigid panel has length a = L/2. For included fold angle θ measured from the flat state, half-angle trigonometry gives projected span x = 2a cos(θ/2) = L cos(θ/2) and center-hinge rise h = a sin(θ/2) = (L/2)sin(θ/2).
Span shortening is Δx = L − x and remaining-span percentage is 100x/L = 100cos(θ/2). These relationships apply only to the illustrated zero-thickness symmetric fold.
Default selected example
For L = 1.000 m and θ = 90°, each panel is 0.500 m long. Projected span is 1.000cos45° = 0.707 m, hinge rise is 0.500sin45° = 0.354 m, shortening is 0.293 m and remaining span is 70.7%.
No stowed-volume or packing claim follows because panel thickness, width, collisions and any repeated crease pattern are outside the model.
Scope and correction boundary
The removed calculator presented an unsupported “folded length” equation as a general Miura-ori result using only flat length, one panel angle and one fold angle. Standard Miura analyses define a cell with multiple edge lengths and coupled geometric variables, so the page's three-input expression was not retained.
Tachi describes rigid origami as a constrained panel-and-hinge mechanism, while Wei and coauthors derive specific Miura unit-cell dimensions from explicit facet geometry and fold-state definitions. The replacement chooses a simpler geometry that is exact and visibly auditable.
Questions
Is this a Miura-ori calculator?
No. It is an exact symmetric two-panel fold. A Miura-ori unit needs additional facet and crease geometry.
What does zero-thickness mean?
The two panels may approach one another without their physical thickness causing contact. Real hinges and panels need clearance and offset design.
Is hinge rise an actuator stroke?
No. It is geometric center-hinge displacement for the selected constraint. An actuator's stroke depends on its attachment points and linkage.
Does foldability guarantee load capacity?
No. Kinematics alone does not provide hinge torque, stress, stiffness, stability, fatigue or deployment reliability.
Primary technical references
- Tachi, Generalization of Rigid-Foldable Quadrilateral-Mesh Origami — rigid-panel, crease-hinge and loop-closure kinematic framework.
- Wei et al., Geometric Mechanics of Periodic Pleated Origami — explicit Miura-ori unit-cell geometry and fold-state parameterization.
- Schenk and Guest, Geometry of Miura-folded metamaterials — Miura cell parameters, dimensions and rigid-fold geometry.
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