# 🔱 Pendants and Charms: Bails, Volumes and Thickness

## Learning Objectives

- Size a bail from a real chain measurement, including clearance for movement.
- Build a pendant body as a three-dimensional form with a controlled front, edge, and back.
- Set and verify even wall thickness so the piece can be printed or cast without thin, weak spots.
- Join a bail to the body with enough overlap and a stress-relieving fillet.
- Run a basic manifold and thickness check before the model leaves your desk.

## Quick Review

In the ring lesson you turned a ring size into a diameter, shaped a five-point profile, and spun that profile into a symmetric band. You also checked diameter and symmetry before moving on.

Keep that habit here: decide the important numbers first, then model. For a pendant, the important numbers are the chain size, the bail opening, and the wall thickness.

## Theory

### A pendant is a volume, not a flat shape

A pendant body has a front surface, a side or edge, and a back. If you start from a flat outline and extrude it, the result often looks like a cookie cutter. It may render acceptably from the front, but it looks thin and cheap from the side.

Build volume early. A domed front, a tapered edge, and a back with a slight curve will catch light and read as metal. The back does not need to be decorative, but it does need enough thickness to survive wear.

For this course, use **1.2 mm** as the default minimum wall for a silver pendant. Small decorative details can go to about 1.0 mm, but 1.2 mm is safer. If your caster or printer recommends more, follow their number. These are studio rules of thumb, not universal law.

### The bail is a load-bearing part

The bail is the loop at the top of the pendant. The chain passes through it, and it carries the pendant's weight. A pretty bail with a tight hole or a thin wall is a failure waiting to happen.

==Measure the chain first, then size the bail.== Use the chain's maximum cross-section, not its nominal size. A 2 mm chain may have links or a clasp that are wider than 2 mm.

| Part | Rule of thumb | Why it matters |
| --- | --- | --- |
| Bail inner diameter | Chain maximum width + 2 x clearance | The chain must pass through and move freely |
| Side clearance | 1.0 to 1.5 mm per side | Allows movement and casting tolerance |
| Bail radial wall | 1.2 mm minimum | Carries load and resists wear |
| Bail overlap into body | At least 1 mm | Creates a strong joint |
| Joint fillet | 0.8 to 1.5 mm | Spreads stress and removes a sharp inside corner |
| Pendant wall | 1.2 mm default for silver | Avoids thin spots that can fail |

The bail's {{c1::inner diameter}} must be larger than the chain's maximum cross-section.

A safe studio default for silver pendant walls is {{c2::1.2 mm}} at the thinnest point.

Use the Solidify modifier's {{c3::Even Thickness}} option to keep walls uniform.

For a pendant that hangs flat, the bail plane is usually {{c4::perpendicular}} to the pendant face, so the chain exits left and right.

### Even wall thickness

Even thickness means the metal is roughly the same depth everywhere, not just at the center. Thin edges, sharp inside corners, and paper-thin backs are where prints tear and castings fail.

In Blender, the Solidify modifier is your main tool. Set the thickness to 1.2 mm, enable Even Thickness, and check the result. Do not trust the viewport alone. Use a section cut, wireframe view, or a temporary clipping plane to inspect the thinnest area.

Bevel sharp inside corners. A sharp corner concentrates stress. A small fillet at the bail joint does more for strength than adding bulk everywhere.

### Topology and print checks

A printable or castable mesh should be manifold: no holes, no flipped normals, and no self-intersections. Keep curved surfaces mostly quad based, and place support loops around the bail joint. Avoid n-gons on visible curved areas.

If you use a Boolean to join the bail, apply it and inspect the seam. Booleans can create messy topology. Clean the result before you call the model finished.

## Worked Examples

### Example 1: Size a bail for a 1.8 mm chain

Start with the chain. Let the maximum cross-section be 1.8 mm. Choose 1.2 mm clearance on each side.

Inner diameter = chain width + 2 x clearance  
Inner diameter = 1.8 + 2(1.2) = 4.2 mm

Round up to 4.5 mm. Rounding up is safer than rounding down because it leaves room for chain movement and small casting tolerances.

Now add the bail wall. Use a 1.2 mm radial wall.

Outer diameter = inner diameter + 2 x wall  
Outer diameter = 4.5 + 2(1.2) = 6.9 mm

If you build the bail from a torus, the major radius is:

Major radius = (inner diameter + outer diameter) / 4  
Major radius = (4.5 + 6.9) / 4 = 2.85 mm

The minor radius is half the radial wall:

Minor radius = 1.2 / 2 = 0.6 mm

That gives you a clean starting point. Scale the bail along the chain axis if you want a wider band, but keep the radial wall intact.

### Example 2: Estimate metal weight before you commit

You are planning a pendant about 20 mm tall, 15 mm wide, and 2.5 mm thick. The shape fills roughly 60 percent of that bounding box.

Bounding volume = 20 x 15 x 2.5 = 750 mm³  
Filled volume = 750 x 0.60 = 450 mm³  
Convert to cm³: 450 / 1000 = 0.45 cm³

Silver weighs about 10.5 g/cm³.

Estimated mass = 0.45 x 10.5 = 4.7 g

This is a rough check, not a final weight. If 4.7 g feels heavy for the design, reduce the thickness, shrink the outline, or hollow the back with even walls. Do the math before you spend time on details.

## Guided Practice

Your capstone pendant will become the centerpiece of the final render. Use this sequence.

```steps
1. Sketch the silhouette at real size. Write down height, width, and maximum thickness.
2. Block out the body as a simple volume. Add a domed front and a controlled back.
3. Set the wall thickness to 1.2 mm with Solidify and Even Thickness.
4. Build the bail from your chain measurement. Keep the inner opening clear.
5. Overlap the bail into the body by at least 1 mm, then union and clean the seam.
6. Add a 0.8 to 1.5 mm fillet at the joint.
7. Check for manifold geometry, thin spots, and a clear chain path.
```

Now try these three exercises.

1. A chain measures 2.4 mm at its widest point. You want 1.0 mm clearance per side and a 1.2 mm bail wall. What inner and outer diameters do you choose?
2. A pendant is 18 mm tall, 12 mm wide, and 2.8 mm thick. It fills about 60 percent of its bounding box. Using silver at 10.5 g/cm³, estimate the mass.
3. Critique this bail: inner diameterof 3.0 mm, a 0.5 mm wall, and the bail sitting on the very top edge of the body with no overlap, touching the surface only.

Check your answers and reasoning below.

1. Inner diameter = 2.4 + (2 x 1.0) = 4.4 mm. Outer diameter = 4.4 + (2 x 1.2) = 6.8 mm. Round the inner opening up if you want extra clearance, but never down.
2. Bounding volume = 18 x 12 x 2.8 = 604.8 mm³. Filled volume = 604.8 x 0.60 = 362.9 mm³, which is 0.363 cm³. Mass = 0.363 x 10.5 = about 3.8 g. That is a believable weight for a small silver pendant, so the design passes this check.
3. Three problems. The 0.5 mm wall is too thin for most casting workflows, so raise it to 1.0 to 1.2 mm. The inner diameter of 3.0 mm leaves only 0.3 mm per side for a 2.4 mm chain, which is too tight for the chain to swing, so go to at least 4.4 mm inner. And a bail that only touches the body creates a weak joint, so push it 1 mm or more into the body, union the two, and add a fillet.

> [!TIP]
> Every number you write down in the blockout stage saves a rebuild later. Blockout dimensions, bail opening, wall thickness, and estimated mass are the four numbers worth recording.

## Expert Corner

Common mistakes and rules of thumb:

- **Thin walls everywhere.** Beginners often build a pendant at 0.4 mm because it looks delicate on screen. It will not cast and it will not survive wear. Keep walls at 1.0 to 1.2 mm and reserve thinness for surface detail only.
- **A bail as an afterthought.** The bail carries the chain and takes real load. Model it with the same care as the body, with a proper cross-section and a smooth joint.
- **Inconsistent thickness on curved forms.** Solidify with Even Thickness handles most cases, but tight corners and deep domes still pinch. Check thickness visually in an orthographic front view.
- **Sharp internal corners.** Add fillets everywhere metal meets metal. Sharp corners become stress risers and casting defects.
- **Unverified chain path.** Rotate a small cylinder along the bail path to prove the chain can move freely.

```cloze
A minimum safe wall thickness for cast jewelry is around {{c1::1.0 to 1.2 mm}}.
The bail inner diameter equals chain width plus {{c2::clearance}} on each side.
Solidify's {{c3::Even Thickness}} option keeps wall thickness constant on curved surfaces.
A bail should overlap the body by at least {{c4::1 mm}} before the union.
An estimated mass comes from filled volume multiplied by the {{c5::density}} of the metal.
```

## Summary and Next Steps

You now have the full pendant workflow:

1. Translate the sketch into real millimeter numbers for height, width, and maximum thickness.
2. Block out the volume with a domed front and a controlled, slightly flatter back.
3. Set even walls of 1.0 to 1.2 mm with Solidify and Even Thickness.
4. Build the bail from the chain width plus clearance per side, with 1.0 to 1.2 mm walls.
5. Overlap, union, fillet the joint, then verify manifold geometry and a clear chain path.
6. Sanity-check the mass before adding detail.

```flashcard
[
  { "front": "What information do you need before sizing a bail?", "back": "The widest measurement of the chain that will pass through it." },
  { "front": "How do you calculate bail inner diameter?", "back": "Chain width plus clearance on each side, typically 0.5 to 1.0 mm per side." },
  { "front": "How do you calculate bail outer diameter?", "back": "Inner diameter plus two times the bail wall thickness." },
  { "front": "What is a typical safe wall thickness for cast jewelry?", "back": "About 1.0 to 1.2 mm for silver or gold." },
  { "front": "Which Solidify option keeps wall thickness uniform on curves?", "back": "Even Thickness." },
  { "front": "Why must a bail overlap the pendant body?", "back": "To create reliable contact and a strong joint instead of a surface touch." },
  { "front": "How much should a bail overlap the body before union?", "back": "At least 1 mm, often 1 to 2 mm." },
  { "front": "Why add a fillet at the bail-to-body joint?", "back": "It removes sharp internal corners that cause stress and casting defects." },
  { "front": "What does manifold geometry mean for a pendant?", "back": "The mesh is closed with no holes, so it can be 3D printed and cast." },
  { "front": "How do you estimate pendant mass?", "back": "Bounding box volume times fill percentage, converted to cm³, times metal density." },
  { "front": "What is the density of silver used for quick estimates?", "back": "About 10.5 g/cm³." },
  { "front": "What three checks close out a pendant model?", "back": "Manifold mesh, no thin spots, and a clear chain path." },
  { "front": "Why keep the back of a pendant slightly flatter than the front?", "back": "It sits comfortably against the body and keeps wall thickness predictable." }
]
```

In the next lesson, **Earrings: Mirroring, Posts and Matched Pairs**, you will reuse this thickness discipline but build pairs, so both ears get an identical, mirrored result.