---
jupyter:
  description: 'A bell crank as a 2D CAD exercise: a dimensioned drawing with an angle to model in planex2d or any CAD
    system, a solution as one chain of lines and tangent arcs with mirrored flanks, and the area and centroid to check a
    model against.'
---

# Bell crank

A bell crank turns a pull in one direction into a pull in another. It pivots on its hub, and its two arms, at an angle
to each other, carry the rods at their bosses. As a sketch, it is one chain of lines and tangent arcs around the
hub, the two bosses and the corner between the arms. Model the bell crank from the drawing in planex2d or in any CAD
system, then check its area and centroid against the values at the end of the page. A solution in planex2d follows.

![The bell crank exercise: a dimensioned drawing of a bell crank with a hub, two arms at 105 degrees and a boss with a hole at the end of each arm](../_static/gallery/bell-crank.png){.result}

```python
import math
import planex as px
```

```python nbsphinx="hidden"
from docs_figures import Row
```

## The outline

The outline is one chain, drawn roughly from the start at the origin. It runs a quarter arc around the hub, a line out
along the first arm, a half circle around its boss, a line back, a small arc the other way for the corner between the
arms, a line out along the second arm and a half circle around its boss. `Close()` closes the chain with a line back to
the start. With `auto_constraint=True`, every joint of the chain becomes a tangency, the closing line's included, so the
outline keeps its shape when the dimensions move it.

The pieces get their ids in the order they are drawn, the arcs `Arc.1` to `Arc.4` (the hub, the first boss, the corner
and the second boss) and the lines `Line.1` to `Line.4`. The interactive plot below shows a piece's id when the mouse is
over it:

```python
crank = px.Sketch(auto_constraint=True)
crank.Move((0, 0), dir=(0, -1)).Arc(10, 90).Line(30).Arc(10, 180).Line(15).Arc(5, -90).Line(10).Arc(10, 180).Close()
crank.Plot(backend="plotly")
```

## The holes and the center lines

The holes go into the centers of the hub and the bosses, with `concentric=`. The hub's bore is fixed with `px.Fix` where
it is drawn, its center at (10, 0) and its diameter 12, and it holds the sketch in place. The arms' center lines are
construction lines from the hub's center to the center of each boss, the first one horizontal. `crank("left.center")` is
the bore's center as a point (Figure 1).

```python
crank.Circle(6 / 2, concentric="Arc.4", id="top")
crank.Circle(8 / 2, concentric="Arc.2", id="right")
crank.Circle(12 / 2, px.Fix, concentric="Arc.1", id="left")
crank.Line(crank("left.center"), crank("right.center"), px.Horizontal, construction=True, id="c_bottom")
crank.Line(crank("left.center"), crank("top.center"), construction=True, id="c_left");
```

```python nbsphinx="hide-input"
Row((crank, "The rough outline, the holes and the arms' center lines, dashed", {"fill": False}),
    caption="The outline and the holes")
```

## The dimensions

The arms are 60 and 45 long from center to center, and their center lines make an angle of 105°, set with `px.Angle`.
The flanks of each arm are mirrored about its center line with `px.SymmetricCarriers`, which mirrors their lines, not
their ends. The radii of the hub, the bosses and the corner and the diameters of the holes complete the sketch. Nothing
in it is left free (Figure 2):

```python
crank.Constrain("c_bottom", "c_left", px.Angle, 105, id="arm_angle")  # in degrees
crank.Constrain("Arc.1", px.Radius, 16, id="hub_r")
crank.Constrain("Arc.2", px.Radius, 10, id="boss_1_r")
crank.Constrain("Arc.3", px.Radius, 8, id="corner_r")
crank.Constrain("Arc.4", px.Radius, 9, id="boss_2_r")
crank.Constrain("Line.3", "Line.4", "c_left", px.SymmetricCarriers)
crank.Constrain("Line.1", "Line.2", "c_bottom", px.SymmetricCarriers)
crank.Constrain("c_bottom", px.Distance, 60, id="arm_1")
crank.Constrain("c_left", px.Distance, 45, id="arm_2")
crank.Constrain("top", px.Diameter, 6, id="top_d")
crank.Constrain("right", px.Diameter, 8, id="right_d")
print("status", crank.status, "| degrees of freedom", crank.dof)
```

```python nbsphinx="hide-input"
Row((crank, "Every dimension and tie of the sketch", {"constraints": True}), caption="The fully constrained sketch")
```

## The checks

These are the area and the centroid of the bell crank, measured from the hub's center with the first arm along x, to
compare with your own model (Figure 3):

```python
face = crank.Face()
hub = crank.Location("left.center")
c = face.center
print("area", round(face.mass, 2), "mm²")
print("centroid from the hub's center", tuple(round(v, 2) for v in (c[0] - hub[0], c[1] - hub[1])))
```

```python nbsphinx="hide-input"
Row((face, "The bell crank, its centroid marked", {"marks": [c[:2]]}), caption="The bell crank")
```

The bell crank as DXF in millimeters, for another CAD system or a laser cutter:

```python
crank.WriteDXF("bell_crank.dxf", unit=px.mm, scale=1)  # scale=1: the numbers as they are
```

The bell crank as DXF: [bell_crank.dxf](bell_crank.dxf)

```python nbsphinx="hidden"
import sys
sys.path.insert(0, "..")
import matplotlib.pyplot as plt
import numpy as np
from drawings import SheetFigure, View
from gallery import save_figure

# the arms' center lines, from the hub's center past each boss; the fixed bore's diameter from its geometry
hub, b1, b2 = (np.array(crank.Location(c + ".center")) for c in ("left", "right", "top"))
u1, u2 = (b1 - hub) / 60, (b2 - hub) / 45
view = View([(crank, {"arm_1": hub[1] - 24, "arm_2": 26, "arm_angle": 30, "hub_r": (225, "outside"),
                      "boss_1_r": (300, "outside"), "boss_2_r": (150, "outside"), "corner_r": (234, "inside"),
                      "right_d": (60, "leader"), "top_d": (60, "leader")})],
            axes=[(hub - 8 * u1, b1 + 14 * u1, hub), (hub - 8 * u2, b2 + 13 * u2, hub)],
            diameters=[(hub, 6, (300, "leader"))])
drawing = SheetFigure([view], margin=22, notes=("planex2d.org", "2D exercise 08"))
print("scale", drawing.planex_scale, "| paper", [round(v * 25.4) for v in drawing.get_size_inches()], "mm")
save_figure(drawing, "bell-crank", dpi=200)
plt.close(drawing)
```