---
jupyter:
  description: 'A nut retainer as a 2D CAD exercise: a dimensioned drawing to model in planex2d or any CAD system, a
    solution from the profile tools Slot and Hexagon with holes in the centers of the slot''s ends, and the area to
    check a model against.'
---

# Nut retainer

A nut retainer holds a nut in its hexagonal opening so that a bolt can be screwed into it from the other side, and it is
fixed through the holes at its two ends. Its outline is a slot and its opening a hexagon, both profile tools of the
sketch, and the holes go into the centers of the slot's round ends. Model the retainer from the drawing in planex2d or
in any CAD system, then check its area against the value at the end of the page. A solution in planex2d follows.

![The nut retainer exercise: a dimensioned drawing of a plate with round ends, a hexagonal opening for a nut and two holes](../_static/gallery/nut-retainer.png){.result}

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

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

## The sketch

The outline is a `Slot` 60 long between the centers of its ends and 30 wide, drawn from the pen at $x = -30$ along $x$.
`Slot` makes its width a dimension, `plate.w`. The holes for the screws, 6.6 across, go into the centers of the slot's
ends, `plate.startcap` and `plate.endcap`, with `concentric=`. The opening for an M8 nut is a `Hexagon` 13 across its
flats, which makes that width a dimension too, `nut.af`, and keeps the hexagon regular (Figure 1):

```python
retainer = px.Sketch(auto_constraint={"horizontal": True, "vertical": True, "equal_radius": True})
retainer.Move((-30, 0)).Slot(60, 30, id="plate")  # 60 between the centers of its ends, 30 wide
retainer.Circle(6.6 / 2, concentric="plate.startcap", id="left_hole")
retainer.Circle(6.6 / 2, concentric="plate.endcap", id="right_hole")
retainer.Hexagon(13, center=(1, 1), id="nut");
```

```python nbsphinx="hide-input"
Row((retainer, "The slot, the holes and the hexagon, placed roughly", {"fill": False}), caption="The sketch")
```

## The dimensions

The slot's spine, the construction line between the centers of its ends, has its middle at the origin, 60 long. The
hexagon's center, the center of its construction circle `nut.circle`, is the origin too. The holes are 6.6 across.
The sketch was made with `auto_constraint={"horizontal": True, "vertical": True, "equal_radius": True}`, so the spine,
drawn level, stays level, and the hexagon's first side, drawn plumb, keeps two of its flats upright. The right hole,
drawn as large as the left one, stays equal to it. With these, nothing in the sketch is left free (Figure 2):

```python
retainer.Constrain("plate.spine.mid", "origin", px.Coincident)
retainer.Constrain("plate.spine", px.Distance, 60, id="plate_l")
retainer.Constrain("nut.circle.center", "origin", px.Coincident)
retainer.Constrain("left_hole", px.Diameter, 6.6, id="hole_d")
print("status", retainer.status, "| degrees of freedom", retainer.dof)
```

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

## The checks

This is the area, to compare with your own model. It is the slot, a rectangle 60 by 30 and a disc of 30, less the two
holes and the hexagon, $\sqrt{3} / 2$ times the square of its width across flats. The retainer is symmetric about both
axes, so its centroid is the origin (Figure 3):

```python
face = retainer.Face()
exact = 60 * 30 + math.pi * 15**2 - 2 * math.pi * 3.3**2 - math.sqrt(3) / 2 * 13**2
c = face.center
print("area", round(face.mass, 2), "mm², exact", round(exact, 2))
print("centroid", tuple(round(v, 6) for v in c[:2]))
```

```python nbsphinx="hide-input"
Row((face, "The nut retainer", {}), caption="The nut retainer")
```

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

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

The retainer as DXF: [nut_retainer.dxf](nut_retainer.dxf)

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

# the slot's width from its sides, the hexagon's width across its upright flats
w = retainer.dimensions["plate.w"]
view = View([(retainer, {"plate_l": -24, "nut.af": 12, "hole_d": (225, "leader", 2)},
              {"left_hole": "lines", "right_hole": "lines"})],
            axes=[((-50, 0), (50, 0), (0, 0)), ((0, -20), (0, 20), (0, 0))],
            measures=[((30, -w / 2), (30, w / 2), 54, w)])
drawing = SheetFigure([view], margin=20, notes=("planex2d.org", "2D exercise 11"))
print("scale", drawing.planex_scale, "| paper", [round(v * 25.4) for v in drawing.get_size_inches()], "mm")
save_figure(drawing, "nut-retainer", dpi=200)
plt.close(drawing)
```