---
jupyter:
  description: 'A guide block as a 3D CAD exercise: a dimensioned drawing to model in planex2d or any CAD system, a
    solution from a T-slot profile padded through and counterbored holes, and the volume, mass and center of mass to
    check a model against.'
---

# Guide block

A guide block carries a T-slot for the bolts or sliding nuts of a fixture and is screwed down through two counterbored
holes. As a solid, it is one profile with the T-slot, padded through, and two stepped holes pocketed from the top.
Model the block from the drawing in planex2d or in any CAD system, then check its volume, mass and center of mass
against the values at the end of the page. A solution in planex2d follows.

![The guide block exercise: a dimensioned drawing of a block with a T-slot and two counterbored holes in a front view, a top view and an isometric](../_static/gallery/guide-block.png){.result}

```python
import math
import netgen.occ as occ
import planex as px
```

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

## The profile

The profile is the front view, sketched in the front plane, the plane with its normal toward the viewer, $-y$, with $x$
to the right and $z$ up and the origin in the middle of the bottom. The outline runs from the bottom left corner around
the block and down into the T-slot, over its neck, the ledge out to the wide part, its flank and its bottom, and the
same back up on the other side. With `auto_constraint=True`, the flags `px.Horizontal` and `px.Vertical` in the drawing
calls become constraints.

The profile is symmetric about the vertical axis. The left neck, flank, ledge and top mirror the lines of the right
ones, and the mirror sets their directions too, so they carry no flags. With the sizes of the front view, nothing in the
sketch is left free (Figure 1):

```python
front = px.XZ
profile = px.Sketch(front, auto_constraint=True)
profile.Move((-50, 0)).Line(100, px.Horizontal, id="bottom")
profile.Turn(90).Line(40, px.Vertical, id="right_side")  # Turn(90) turns the pen left, Turn(-90) right
profile.Turn(90).Line(40, px.Horizontal, id="right_top")
profile.Turn(90).Line(12, px.Vertical, id="right_neck")
profile.Turn(90).Line(5, px.Horizontal, id="right_ledge")
profile.Turn(-90).Line(8, px.Vertical, id="right_flank")
profile.Turn(-90).Line(24, px.Horizontal, id="slot_bottom")
profile.Turn(-90).Line(8, id="left_flank")
profile.Turn(-90).Line(5, id="left_ledge")
profile.Turn(90).Line(12, id="left_neck")
profile.Turn(90).Line(40, id="left_top")
profile.Close(px.Vertical, id="left_side")
profile.Constrain("bottom.mid", "origin", px.Coincident)
profile.Constrain("bottom", px.Distance, 100, id="length")
profile.Constrain("right_side", px.Distance, 40, id="height")
profile.Constrain("right_neck", "left_neck", px.Distance, 14, id="opening")
profile.Constrain("right_neck", px.Distance, 12, id="neck")
profile.Constrain("right_flank", "left_flank", px.Distance, 24, id="slot_w")
profile.Constrain("right_flank", px.Distance, 8, id="slot_h")
profile.Constrain("left_neck", "right_neck", "V", px.SymmetricCarriers)
profile.Constrain("left_flank", "right_flank", "V", px.SymmetricCarriers)
profile.Constrain("left_ledge", "right_ledge", "V", px.SymmetricCarriers)
profile.Constrain("left_top", "right_top", "V", px.SymmetricCarriers)
print("status", profile.status, "| degrees of freedom", profile.dof)
```

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

## The block

`px.Pad` extrudes the profile 30 to both sides of the front plane, 60 in all, so that the T-slot runs through the
block from front to back. Its volume is the area of the profile times 60 (Figure 2):

```python
block = px.Pad(profile, 30, length2=30)
print("volume", block.mass, "area × 60", profile.Face().mass * 60)
```

```python nbsphinx="hide-input"
Views(("The profile extruded 60 deep", [(block, "shade"), (block, "ink")]), caption="The block")
```

## The holes

The counterbores, 15 across and 9 deep, are sketched on the top of the block, its face highest in $z$. The T-slot splits
the top in two, but both halves lie in the plane of the sketch. They are placed roughly, 60 apart, and the spacing of 70
moves them to their place (Figure 3a). The block shows them pocketed (Figure 3b):

```python
top = block.faces.Max(occ.Z)  # one half of the top; the sketch takes its whole plane
counterbores = px.Sketch(top)
counterbores.Circle(15 / 2, center=(-30, 0), id="left_counterbore")
counterbores.Circle(15 / 2, center=(30, 0), id="right_counterbore")
counterbores.Constrain("left_counterbore", px.Diameter, 15, id="counterbore_d")
counterbores.Constrain("left_counterbore", "right_counterbore", px.Equal)
counterbores.Constrain("left_counterbore.center", "right_counterbore.center", px.Distance, 70, id="spacing")
counterbores.Constrain("left_counterbore.center", "H", px.Coincident)
counterbores.Constrain("left_counterbore.center", "right_counterbore.center", "V", px.Symmetric)
block = px.Pocket(block, counterbores, 9)  # 9 deep, against the face's normal: down
```

```python nbsphinx="hide-input"
Row((counterbores, "The sketch on the top, the block under it", {"plot": {"show_parent": block, "show_constraints": True}}),
    (block, "Both counterbores in the top", {"views": [(block, "shade"), (block, "ink")], "angles": (-40, 0, 20)}),
    caption="The counterbores")
```

The through holes, 9 across, go through the counterbores' centers, sketched on the same top, and `until=px.last` cuts
them down through the bottom (Figure 4):

```python
holes = px.Sketch(top)
for side in ("left", "right"):
    holes.Circle(9 / 2, center=counterbores.Location(side + "_counterbore.center"), id=side + "_hole")  # the solved center
holes.Constrain("left_hole", px.Diameter, 9, id="hole_d")
holes.Constrain("left_hole", "right_hole", px.Equal)
block = px.Pocket(block, holes, until=px.last)  # through to the last flat face it crosses
```

```python nbsphinx="hide-input"
Row((holes, "The sketch of the holes on the top, the block under it", {"plot": {"show_parent": block, "show_constraints": True}}),
    (block, "The through holes from the counterbores down", {"views": [(block, "shade"), (block, "ink")],
                                                             "angles": (-40, 0, 20)}),
    caption="The through holes")
```

## The checks

These are the volume, the mass in steel S235 (7.85 g/cm³) and the center of mass, with the origin in the middle of the
bottom, to compare with your own model. The block is symmetric about two planes, so its center of mass lies on the
vertical axis:

```python
c = block.center
print("volume", round(block.mass, 1), "mm³")
print("mass", round(block.mass * 7.85e-6, 3), "kg")
print("center of mass", round(c.z, 2), "above the bottom, off the axis by", round(math.hypot(c.x, c.y), 6))
```

The block as STEP, for another CAD system:

```python
block.WriteStep("guide_block.step")
```

The block as STEP: [guide_block.step](guide_block.step)

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

# the views from the sketches and the block: the outline of the top view, the slot seen from above, the holes
x0, x1 = profile.Location("bottom.start")[0], profile.Location("bottom.end")[0]
y0, y1 = block.faces.Min(occ.Y).center.y, block.faces.Max(occ.Y).center.y
height = profile.Location("right_side.end")[1]
neck = profile.Location("right_neck.start")[0]
flank = profile.Location("right_flank.start")[0]
deep = height - 9
rows = [(counterbores.Location(s + "_counterbore.center")[0], counterbores.Measure(s + "_counterbore")["radius"],
         holes.Measure(s + "_hole")["radius"]) for s in ("left", "right")]
front_view = View(
    [(profile, {"length": -18, "slot_w": -32, "height": x1 + 30, "neck": x1 + 15, "slot_h": x1 + 15,
                "opening": height + 15}, {}, front)],
    hidden=[[(x - rc, height), (x - rc, deep), (x + rc, deep), (x + rc, height)] for x, rc, _ in rows]
    + [[(x + s * rh, deep), (x + s * rh, 0)] for x, _, rh in rows for s in (-1, 1)],
    axes=[((0, -5), (0, height + 5))] + [((x, -5), (x, height + 5)) for x, _, _ in rows],
    measures=[((rows[0][0] - rows[0][1], deep), (rows[0][0] - rows[0][1], height), x0 - 15, 9)])
top_view = View(
    [(counterbores, {"spacing": y0 - 15, "counterbore_d": (120, "leader", 2)}, {}),
     (holes, {"hole_d": (240, "leader", 2)}, {})],
    at=(0, -95),
    lines=[[(x0, y0), (x1, y0), (x1, y1), (x0, y1), (x0, y0)]] + [[(s * neck, y0), (s * neck, y1)] for s in (-1, 1)],
    hidden=[[(s * flank, y0), (s * flank, y1)] for s in (-1, 1)],
    axes=[((x0 - 5, 0), (x1 + 5, 0), (0, 0)), ((0, y0 - 5), (0, y1 + 5), (0, 0))]
    + [((x, y0 - 5), (x, y1 + 5), (x, 0)) for x, _, _ in rows],
    measures=[((x1, y0), (x1, y1), x1 + 15, y1 - y0)])
drawing = SheetFigure([front_view, top_view, Pictorial(block, at=(x1 + 100, 10), width=95)], margin=15,
                      notes=("planex2d.org", "3D exercise 02"), first_angle=True)
print("scale 1 :", round(1 / drawing.planex_scale), "| paper", [round(v * 25.4) for v in drawing.get_size_inches()], "mm")
save_figure(drawing, "guide-block", dpi=200)
plt.close(drawing)
```