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Tangent Constraint

In one sentence: Force a line and a curve (or two curves) to touch smoothly at a shared point, with no visible corner or kink at the junction.

Overview

Workbench: Sketcher · Menu: Sketch → Sketcher constraints → Tangent/Collinear Constraint
Toolbar: Sketcher Constraints · Shortcut: T

Tangent removes 1 degree of freedom — the relative angle at the junction between two edges. When applied between a line and an arc (or two arcs), it forces the edges to share the same tangent direction at their meeting point, eliminating the angle discontinuity (kink).

When applied to two lines that share a point, Tangent enforces collinearity (they become part of the same straight line). This is noted in the UI as "Tangent/Collinear".

Intuition

Imagine two railway tracks — a straight section and a curved section — meeting at a junction. If the curve does not align with the straight section at the join point, there is a visible kink and trains would feel a jolt. Tangent removes that jolt by forcing the curved track to arrive at exactly the same angle as the straight track leaves it.

For a line-to-arc junction this means the line is tangent to the circle (the line touches the circle at exactly one point and is perpendicular to the radius at that point). For arc-to-arc it means the two circles share the same tangent line at the meeting point.

When to use it

  • You are drawing a blended outline (straight sections transitioning smoothly into arcs) and need smooth, G1-continuous joins.
  • You want a circle to be tangent to a line (the classic tangent-line construction).
  • You drew a Polyline with the arc mode toggled on (M key) and want to ensure the auto-generated Tangent constraints are still correct after editing.
  • You need two arcs to blend smoothly (e.g. an S-curve).

When NOT to use it

  • You just want the edges to meet without a smooth join — use Coincident alone at the junction.
  • You want two lines to form one straight line — use Collinear (same constraint, different selection: two lines give collinearity).
  • You need a circle centred on a line — use Point on Object for the centre.

Step-by-step walkthrough

  1. Select two adjacent edges (a line and an arc, two arcs, or two lines). For a line-arc join, click near the shared endpoint for the best result.
  2. Press T or activate Sketch → Tangent/Collinear Constraint.
  3. The edges adjust to be tangent at their meeting point. If they were not already connected, add Coincident to join the endpoints.

Tip

The Polyline tool (with M toggled) applies Tangent automatically at each line-to-arc junction. Manual Tangent is needed when you draw the elements separately.

Parameters

No numeric parameters. Removes 1 DoF.

Advanced usage

Tangent at a specific point

If two curves share a common point but you want to specify which point is the tangency point (e.g. two arcs that cross at multiple locations), select the shared endpoint explicitly before applying Tangent.

Collinear lines

When Tangent is applied to two lines that share an endpoint, it forces them to be collinear — they become two segments of the same infinite line. This is useful for modelling a line interrupted by a boss or slot: draw the two segments, join their adjacent endpoints with Coincident, and then apply Tangent to make them perfectly collinear.

Common mistakes and pitfalls

Tangent applied but kink still visible

Cause: The two edges are tangent but their shared endpoint is not formally Coincident — they look joined but are not. The Tangent constraint only aligns directions, not positions.
Fix: Add Coincident between the shared endpoints.

Tangent makes the sketch over-constrained

Cause: The angle at the junction was already forced by other constraints (e.g. both a horizontal line and a circle with a coincident centre imply a specific tangent at their meeting point).
Fix: Check if tangency is already implied; if so, the extra Tangent is redundant and should be removed.

Python API

Minimal example

import FreeCAD as App
import Sketcher
import Part

doc = App.activeDocument()
sketch = doc.getObject("Sketch")

# A line ending at (10, 0) and an arc starting there
line = sketch.addGeometry(
    Part.LineSegment(App.Vector(0, 0, 0), App.Vector(10, 0, 0)), False)

import math
arc = sketch.addGeometry(
    Part.ArcOfCircle(
        Part.Circle(App.Vector(10, 5, 0), App.Vector(0, 0, 1), 5),
        -math.pi / 2, 0), False)

# Join them
sketch.addConstraint(Sketcher.Constraint("Coincident", line, 2, arc, 1))
# Make them tangent
sketch.addConstraint(Sketcher.Constraint("Tangent", line, arc))
doc.recompute()

See also