---
jupyter:
  description: 'Slots, arc slots, keyholes, polygons and hexagons in a planex2d sketch: one call each, with named
    parts. A motor mounting plate with all of them, checked against its exact area.'
---

# Slots, keyholes and polygons

Some outlines come up in almost every part: a slot for an adjustable screw, an arc slot for an angle adjustment, a
keyhole for hanging a part on a screw head, and a hexagon for a nut. Each of them is one call in a sketch:

| Call | Draws |
|---|---|
| `Slot(l, w)` | A straight slot of width w along a spine of length l, with round ends |
| `ArcSlot(r, sweep, w)` | A slot of width w along an arc of radius r and the angle sweep, in degrees |
| `Keyhole(l, w, r)` | A slot of width w that starts in a round hole of radius r |
| `Polygon(r, n)` | A regular polygon with n corners on a circle of radius r |
| `Hexagon(af)` | A regular hexagon with the width across flats af, as for a nut |

The spine of a slot or a keyhole is placed like a line, so `Slot` takes every form of `Line` and `ArcSlot` every form
of `Arc`, with the width as the last number. `Polygon` and `Hexagon` are placed like a circle. The spine and the
polygon's circle are construction elements.

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

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

## A motor mounting plate

The example is a mounting plate of 120 × 80 for a small motor, with every one of these shapes (Figure 1):

- a pivot hole of 8.5 at (30, 40), about which the motor turns;
- an arc slot 6.6 wide around the pivot, on a radius of 40, from −30° to 30°, for the screw that holds the motor;
- two slots 6.6 wide and 20 long for the screws of a belt tensioner;
- a keyhole, so that the plate can hang on a screw head;
- a hexagonal opening that holds an M6 nut, 10 across flats.

The spine of each straight slot and of the keyhole starts at the pen and runs along the direction given to `Move`.
The arc slot uses the keyword form of `Arc`: its start point, the width, and the center and sweep of its spine. The
hexagon takes its center as the first two numbers, like a circle.

```python
sk = px.QuickSketch().Rectangle(120, 80, id="plate")
sk.Circle(30, 40, 4.25, id="pivot")
a = math.radians(-30)
sk.ArcSlot((30 + 40 * math.cos(a), 40 + 40 * math.sin(a)), 6.6, center=(30, 40), sweep=60, id="tilt")
for k, y in enumerate((12, 68)):
    sk.Move((80, y), dir=(1, 0)).Slot(20, 6.6, id=f"tension {k + 1}")
sk.Move((100, 32), dir=(0, 1)).Keyhole(10, 5, 5, id="hanger")
sk.Hexagon(12, 68, 10, id="nut")
plate = sk.Face()
```

```python nbsphinx="hide-input"
Row((sk, "A motor mounting plate, the spines dashed"), caption="Slots, a keyhole and a hexagon in one sketch")
```

Each opening has a closed form for its area. A slot is a rectangle with two half discs, and an arc slot the band
along its arc with two half discs. A keyhole is the hole and the slot with its end cap, less the strip of the slot
inside the hole. A hexagon with the width across flats af has the area √3/2 af².

```python
def slot(length, width):
    return length * width + math.pi * (width / 2) ** 2


def keyhole(length, width, radius):
    inside = width / 2 * math.sqrt(radius**2 - width**2 / 4) + radius**2 * math.asin(width / (2 * radius))
    return math.pi * radius**2 + length * width + math.pi * (width / 2) ** 2 / 2 - inside


openings = math.pi * 4.25**2 + slot(math.radians(60) * 40, 6.6) + 2 * slot(20, 6.6)
openings += keyhole(10, 5, 5) + math.sqrt(3) / 2 * 10**2
print("area", plate.mass, "exact", 120 * 80 - openings)
```

## The parts of a shape

Every opening is a wire of its own, `tilt`, `tension 1` and so on, and its parts have ids of their own: the sides
`left` and `right`, the caps `startcap` and `endcap`, and for a keyhole the `hole`. The spine is the construction line
`spine`. The parts can be measured, selected and referred to like any other element:

```python
for part in ("left", "right", "startcap", "endcap", "spine"):
    print("tension 1." + part, "length", sk.Measure("tension 1." + part)["length"])
```

In a constraint sketch, the width of a slot, the radius of a keyhole's hole and the size of a polygon are dimensions
that can change later. See [Offsets and profiles revisited](../constraints/offsets-profiles.md) for details. See
[Circles and rectangles](circles-and-rectangles.md) for rectangles from corners and around a center, and
[Fillets and chamfers](fillets-chamfers.md) for rounding the corners of a part.