Smooth contour duplication tool

Chain-like models have been proposed to approximate various contours using a sequence of connected straight segments, instead of the step-like approximation used in traditional contour gauges.

The present model goes one step further by using an alignment of (roughly) circular arcs with adjustable radii, providing a smooth curve representation of a contour without any sharp points.

Despite the flexibility of the thin wall that is used to implement the curved line, the whole object becomes surprisingly rigid once all segments are locked.

This tool is has similarities with the Spline and whales technique, but has several differences. The constraints applied to the curves are not the same. Also, it is not used in the same way.

Using the tool

The tool is made of a sequence of identical elements which can be individually locked by tightening a nut. To pick the contour of an object:

• Unlock all nuts
• Press the flexible wall side against the object
• Tighten all nuts

Features

The model is largely customizable. The provided files gives a chain of 11 segments with a 2cm pitch. The total length is thus 22cm, which fits on many printers. Each segment has a theoretical minimum curvature radius of 8cm in both ways (convex and concave), though the actual radius may be slightly greater.

Printing

The “wall” part can be printed at 0.2mm layer height, with two perimeters, no infill, no top/bottom. You can customize the model to make it as long as your printer can handle. I recommend using PETG.

Other parts should be printed at 0.15mm layer height, with 2 perimeters and reasonable top/bottom infill settings (e.g. 0.6mm and 30%). Each part need to be printed once for each segments.

Assembly is straightforward, but you should assemble inner and outer links at the same time on a given beam, to avoid breaking something.

Design and customization

The principle of this design is that each individual element is made of

• One "flexible" wall
• Two “rigid” walls making a 90° angle with the ends of the flexible wall
• An adjustable link which fixes the distance between the other ends of the rigid walls

Without any external constraints, this results in a symmetric arc. However, shear constraints in particular will deform the arc.

Customizing the model can be done in OpenSCAD. Width, height, pitch, number of segments are easy to modify. Note that the minimum radius will be limited (depending on pitch and width) by the separation between links (rather than PETG flexibility).

The current version is functional, but it may be worth playing with parameters to improve it, for example making the hinges less fragile, or adding a way to combine several wall lengths…