Tangent

tangent makes a line and a circle/arc, or two circles/arcs, touch smoothly — no corner where they meet. Together with coincident at the junction it produces the kink-free outlines of rounded profiles, belts and cams.

In the viewport

1. Click a line and an arc / circle, or two arcs / circles.
2. Click Tangent. The pair gets a T badge at the touching point.

The 2D Fillet tool writes coincident + tangent pairs for you when it rounds a corner.

At a junction

A line running into an arc: coincident joins them, tangent removes the kink.

A line and an arc picked: Tangent is enabled.

Before

The arc is joined to the line by coincident, but meets it at a corner.

Aftertangent(l, a)

The arc leaves the line without a kink.

The code behind it

coincident(l.end(), a.start()) joins the profile; tangent(l, a) forces the arc to leave the line without a corner (1 DOF). The radius then sizes the arc.

hook.part.js

import { sketch, line, arc } from 'fluidcad/core';
import { coincident, tangent, horizontal, fix, radius, distance } from "fluidcad/constraints";

sketch("xy", () => {
    const l = line([0, 0], [48, 2]);
    const a = arc([48, 2], [55.5, 20], [30, 20]);
    coincident(l.end(), a.start());
    tangent(l, a);
    horizontal(l);
    fix(l.start());
    distance(l.start(), l.end(), 50);
    radius(a, 20);
})

Touching somewhere along the line

For a line that touches a circle somewhere rather than at a shared end, pair tangent(l, c) with coincident(l.end(), c) — the point-on-circle form — so the line's end sits exactly at the tangency point. A belt around two pulleys is four of those:

The code behind it

belt.part.js

import { sketch, line, circle } from 'fluidcad/core';
import { tangent, coincident, fix, diameter } from "fluidcad/constraints";

sketch("xy", () => {
    const pulley1 = circle([0, 0], 100).guide();
    const pulley2 = circle([200, 0], 40).guide();
    // Guessing the lines above / below the pulleys picks the two
    // outer tangents — the belt run.
    const top = line([-7, 49], [197, 20]);
    const bottom = line([-7, -49], [197, -20]);
    fix(pulley1.center());
    fix(pulley2.center());
    diameter(pulley1, 100);
    diameter(pulley2, 40);
    tangent(top, pulley1);
    tangent(top, pulley2);
    coincident(top.start(), pulley1);
    coincident(top.end(), pulley2);
    tangent(bottom, pulley1);
    tangent(bottom, pulley2);
    coincident(bottom.start(), pulley1);
    coincident(bottom.end(), pulley2);
})

Which side? The guess decides

A circle tangent to a line can rest above or below it. Both circles here carry identical constraints; only the guessed centers differ, and the solver settles each on the side its guess was drawn.

The code behind it

branches.part.js

import { sketch, line, circle } from 'fluidcad/core';
import { tangent, horizontal, fix, diameter } from "fluidcad/constraints";

sketch("xy", () => {
    const l = line([0, 0], [120, 0]);
    // Same constraints on both circles — only the guesses differ.
    const above = circle([40, 18], 40);
    const below = circle([80, -23], 40);
    fix(l.start());
    fix(l.end());
    tangent(l, above);
    tangent(l, below);
    diameter(above, 40);
    diameter(below, 40);
})

In code

tangent(l, a)                    // line ↔ arc or circle: 1 DOF
tangent(c1, c2)                  // circle/arc ↔ circle/arc: 1 DOF
tangent(l, ref)                  // against a projected reference edge

Order does not matter. Two lines cannot be tangent — use collinear.

See also

• Radius — the dimension that usually completes a tangent arc
• Sketch tools → Fillet