How to Make a Paper Cutout Travel in an Arc Between Two Card Windows

A point attached to a rotating wheel stays the same distance from its center. That fixed distance determines its circular path. Placing two windows on that path lets the same cutout appear at both positions without a sliding track.

Rotating wheels are an established paper mechanism. The BMCC Makerspace’s Paper Pop-Ups Workshop describes using them for changing illustrations and adapting the location and number of openings. Channin Pelletier’s Hero Arts rotating-wheel tutorial demonstrates a wheel mounted with a brad, a viewing window, and a raised front panel.

The dimensions below are an original worked layout derived from that mechanism, rather than a reproduction of either source’s template. Use a scrap-card prototype to check the fit of your particular cardstock, fastener, and adhesive before making the finished version.

Prepare these materials:

• Two cardstock squares, each 160 × 160 mm: one front panel and one backing panel.
• One cardstock wheel, 124 mm in diameter.
• One paper cutout that fits entirely within a 12 mm diameter circle.
• One small brad, also called a split pin.
• Foam mounting tape or cardstock spacer strips.
• Paper adhesive and removable tape.
• A ruler, compass, pencil, scissors, and suitable tools for cutting windows and making pivot holes.

BMCC suggests paper around 160–220 gsm for its paper-engineering projects and lists split pins for rotating wheels. That range is a useful starting point here; check that your assembled panels remain flat. See its workshop materials list.

Choose a simple cutout, such as a small sun or colored circle. A shape without a strong upright direction suits this construction because the cutout turns roughly 74 degrees between the two windows. Use a plain wheel in the background color you want visible through the empty window.

Measure every position from the top-left corner of each square, with horizontal measurements running rightward and vertical measurements running downward. Mark the following layout on the front panel and transfer the pivot position to the backing panel.

Feature	Position or size
Pivot	80 mm from the left, 90 mm from the top
Left window center	50 mm from the left, 50 mm from the top
Right window center	110 mm from the left, 50 mm from the top
Each window	24 × 24 mm, centered on its marked point
Wheel	124 mm diameter, centered on the pivot
Finger notch	An inward semicircle of 15 mm radius, centered on the front panel’s bottom edge

Both window centers are 50 mm from the pivot: each is horizontally offset by 30 mm and vertically offset by 40 mm, giving a radius of √(30² + 40²) = 50 mm. The upper arc passes through a point 80 mm from the left and 40 mm from the top. Its center therefore rises 10 mm above the window centers during the journey.

These calculated dimensions also leave a 36 mm solid bridge between the square windows. The 12 mm cutout can disappear completely behind that bridge. The wheel extends from 18 to 142 mm horizontally and from 28 to 152 mm vertically, leaving room around it for mounting spacers.

For a different layout, draw the desired window centers first. The pivot must be equally distant from both. For windows at the same height, place it on their vertical centerline. Moving the pivot farther below the windows produces a shallower upper arc; moving it closer produces a more pronounced rise. Recheck the wheel size and panel boundaries whenever you change the geometry.

Cut the windows, wheel, and finger notch

Cut the two 24 mm square windows in the front panel. Their edges should be at 38–62 mm and 98–122 mm horizontally, with both extending from 38 to 62 mm vertically. Cut the semicircular finger notch into the bottom edge of the front panel only.

Cut the wheel and mark its exact center. Make a small central hole in the wheel and a matching hole at the backing panel’s pivot mark. Keep the holes close to the brad shaft’s size: a visibly oversized opening allows the wheel to shift away from its intended path.

Fit the pivot before adding the cutout

Place the wheel on top of the backing panel, aligning the holes. Insert the brad from the wheel side through both layers, then spread its legs behind the backing. Adjust the fastening so the wheel turns while remaining centered.

Temporarily position the front panel over the assembly with removable tape and loose spacer pieces. The bottom notch should expose enough of the wheel edge to turn it. Keep the front panel clear of the brad head.

Pelletier’s rotating-wheel construction similarly combines a central brad, an access notch, and foam tape beneath the front panel. Here, the brad passes directly through the backing panel, so establish that pivot before closing the assembly.

Attach the single traveling cutout

With the front panel aligned, mark the center of the left window lightly on the wheel. Remove the front panel without turning the wheel. Glue the cutout flat onto the wheel, centered on that mark, and allow the adhesive to dry.

Replace the front panel temporarily. Turn the wheel clockwise as viewed from the front. The cutout should move upward and rightward, disappear beneath the bridge, then enter the right window. Reverse the turn to bring it back. Do not attach a second cutout at the destination: the same piece makes the journey.

The cavity between the backing and front panel must accommodate the wheel, the attached cutout, and the brad head without pressing them together. There is no universal spacer thickness because those materials vary. Begin with removable spacer pieces and add height until the wheel turns without lifting or bowing the front.

Position permanent spacers outside the wheel’s entire circular footprint. For this layout, narrow strips near the left and right panel edges and along the top edge provide possible mounting areas. Keep the bottom access notch open. Avoid placing spacers merely outside the cutout’s short travel arc: the rest of the wheel still rotates through the cavity.

Test while holding the panels together lightly at their intended mounting points. If the wheel turns when the front is lifted but sticks when it is lowered, increase the cavity height or flatten a raised attachment. If it sticks with the front removed, inspect the pivot instead.

Rotate the wheel until the cutout is centered in the left window. Make a small registration mark on the exposed wheel rim and a corresponding mark beside the finger notch. Repeat with the cutout centered in the right window. Distinct labels such as A and B make the two positions easy to find.

Marking image positions through a temporarily fitted front panel follows the alignment approach shown in Pelletier’s original tutorial. Here, the two rim marks indicate the endpoints of one image’s movement.

Before fixing the front permanently, turn the wheel through several complete return journeys. Confirm that the cutout clears both window edges, disappears beneath the bridge, and returns to both centers. Then adhere the spacers and front panel without letting adhesive enter the wheel cavity.

The registration marks guide positioning; they do not mechanically limit rotation. Turning beyond either mark takes the cutout farther around the concealed circle. For this simple version, add a short curved arrow beside the notch and use the two marks to indicate the intended travel range.

If you want a folded greeting card, attach the completed backing panel to a separate folded base. This covers the brad legs while leaving the wheel accessible through the front notch.

Symptom	What to inspect	Adjustment
The wheel resists turning everywhere	Pivot tension or front-panel pressure	Ease the brad fastening or increase spacer height.
It catches at one window	Raised cutout edges or uneven window cuts	Flatten the cutout and trim the opening cleanly.
The cutout reaches one center but misses the other	Unequal pivot-to-window distances or misplaced cutout	Recheck both 50 mm radii and the cutout’s attachment point.
The wheel shifts sideways	Pivot hole size	Replace the loose wheel or reinforce and remake its central hole.
The cutout remains visible between windows	Cutout size relative to the bridge	Reduce the cutout or increase the solid separation between openings.
The cutout arrives tilted	Rotation inherent in the mechanism	Choose an orientation-neutral shape or accept the changing angle.

If continuous visibility matters, two separate windows will conceal part of the journey. A connecting curved opening would reveal the intermediate movement, but it changes the front-panel design. Decide whether you want a hidden transfer or a visibly traced arc before decorating the panel.

A construction made entirely from paper is also possible: Duncan Birmingham’s Hub Turning Wheel Mechanism specifically presents a paper hub for rotating images behind a window without hardware. That hub is an alternative pivot construction; it needs its own assembly method and clearance checks.

Finish the decoration after the mechanism works. Keep embellishments clear of the window edges and finger notch, then use the endpoint marks to demonstrate the motion. The completed card carries one physical cutout along a defined upper arc, hiding it beneath the bridge before revealing it in the second window.

• Paper Pop-Ups Workshop — BMCC Makerspace
• Video: Interactive Rotating Wheel Card + Introducing Channin! — Hero Arts, hosted by Spellbinders
• Hub Turning Wheel Mechanism — Make Pop Up Cards