Lesson 7: Parametric Transforms and the Phone Stand Project

Estimated time: 75-90 minutes

Learning Objectives

• Use parametric transforms (rotate(), translate(), scale()) to position and orient sub-assemblies¹
• Apply the Minkowski operation as a method for creating filleted edges²
• Create multi-part assemblies where each component serves a distinct structural function³
• Test and validate parametric variations before printing¹

Materials

• 3dMake project scaffold with src/main.scad
• Access to a printer or slicing software
• Measuring tools (calipers) for post-print validation

Related Project: Study phone_stand.scad for an advanced example combining multiple transforms and Minkowski operations in a real-world assembly.

Understanding Parametric Transforms

Transforms are the foundation of positioning objects in 3D space. Unlike drag-and-drop interfaces, OpenSCAD requires you to explicitly specify every position and rotation. This precision is what enables parametric design-once defined mathematically, a model can be infinitely reconfigured.

Core Transform Operations

Translating Objects: Moving in 3D Space

translate([x, y, z]) moves an object in three-dimensional space. The key insight is that you specify the movement before creating or referencing the object:

// Move a cube 30 mm to the right
translate([30, 0, 0]) cube([20, 20, 20]);

// Move it up by 10 mm
translate([0, 0, 10]) cube([20, 20, 20]);

// Move it diagonally (right and forward)
translate([30, 20, 0]) cube([20, 20, 20]);

A critical concept: When you use translate(), OpenSCAD moves the coordinate system, not just the object. The object is then created in the new coordinate system. This means:

// These are functionally equivalent:
translate([10, 0, 0]) cube([20, 20, 20]);

cube([20, 20, 20]);
translate([10, 0, 0]) cube([20, 20, 20]);  // Second cube shifted right

For multi-part assemblies, you typically nest translate() calls within modules:

module phone_stand() {
  // Base stays at origin
  base();
  
  // Back support is translated up and back
  translate([0, -30, base_thickness])
    rotate([65, 0, 0])
      back_support();
}

Rotating Objects: Orientation Around Axes

rotate([x_deg, y_deg, z_deg]) rotates an object around the X, Y, and Z axes (in degrees):

// Rotate 45 around X axis (tilts forward/back)
rotate([45, 0, 0]) cube([10, 10, 10]);

// Rotate 90 around Y axis (rotates left/right)
rotate([0, 90, 0]) cube([10, 10, 10]);

// Rotate 45 around Z axis (spins in place)
rotate([0, 0, 45]) cube([10, 10, 10]);

// Rotate around all three axes
rotate([45, 30, 15]) cube([10, 10, 10]);

Order matters: When you specify multiple rotations, they are applied in sequence (X, then Y, then Z). This can produce unexpected results:

// These produce different final orientations:
rotate([45, 90, 0]) cube([10, 10, 10]);
rotate([90, 45, 0]) cube([10, 10, 10]);

Combining Transforms: The Order of Operations

You can nest transforms to build complex positions. Remember: OpenSCAD applies transforms from the inside out:

// Example: Position a cylinder so it sticks up from the back of a base

// Step 1: Create a cylinder at the origin
cylinder(r=5, h=20, $fn=32);

// Step 2: Translate it to the right spot
translate([0, 0, base_thickness])
  cylinder(r=5, h=20, $fn=32);

// Step 3: In a module, combine positioning
module mounting_peg() {
  translate([base_width/2, base_depth - 10, base_thickness])
    cylinder(r=5, h=20, $fn=32);
}

// Inside a phone_stand() assembly:
mounting_peg();

Practical Tip: Coordinate System Visualization

When working with complex assemblies, it helps to visualize the coordinate system:

// Small axes indicator (add to your design temporarily for debugging):
module axes() {
  color("red") cube([20, 1, 1]);     // X axis (red)
  color("green") cube([1, 20, 1]);   // Y axis (green)
  color("blue") cube([1, 1, 20]);    // Z axis (blue)
}

// Place it at key points to verify positioning:
axes();
translate([100, 0, 0]) axes();  // Check alignment at offset

Step-by-step Tasks

Task 1: Build a Simple Phone Stand Base

Create a parametric base plate that can be adjusted for different phone weights and sizes:

// Phone Stand - Base Component
// Adjustable platform for holding phones and tablets

// === TOP-LEVEL PARAMETERS (customize these) ===
base_width = 70;    // mm - front-to-back width
base_depth = 90;    // mm - side-to-side depth
base_thickness = 4; // mm - thickness of base

angle = 65;         // degrees - tilt angle
lip_height = 12;    // mm - height of friction lip
fillet_r = 6;       // mm - edge rounding radius

// === MODULES ===

// Simple rectangular plate
module plate(w, d, t) {
  cube([w, d, t], center=false);
}

// Fillet edges using Minkowski sum (approximation)
module filleted_plate(w, d, t, r) {
  minkowski() {
    plate(w, d, t);
    cylinder(h=0.01, r=r, $fn=40);
  }
}

// Base of the stand
module base() {
  translate([0, 0, 0])
    filleted_plate(base_width, base_depth, base_thickness, fillet_r);
}

// Back support angled for viewing
module back() {
  // Rotate the plate to create the angle
  rotate([angle, 0, 0])
    filleted_plate(base_width, base_depth, base_thickness, fillet_r);
}

// Friction lip to prevent phone from sliding
module lip() {
  translate([0, base_depth - 8, base_thickness])
    cube([base_width, 8, lip_height], center=false);
}

// === ASSEMBLE ===
union() {
  base();
  back();
  lip();
}

Task 2: Test Parameter Variations

Save your file and test each variant by modifying the parameters and running 3dm build:

# Build the base version
3dm build

# Then try modifying angle in main.scad and rebuild
# angle = 45;  // Shallow angle for viewing documents
# 3dm build

# Or try a steep angle for portrait viewing
# angle = 75;  // Steep for reading
# 3dm build

Document the impact:

Task 3: Run 3dm orient to Optimize Orientation

3dm orient src/main.scad

This command analyzes your model and suggests:

• Optimal rotation for minimal support material
• Estimated support volume that will need to be removed
• Print time savings from better orientation

Task 4: Generate Variants for Different Devices

Modify your main.scad to create three configurations (tablet, phone, document holder):

// At the bottom of main.scad, uncomment one configuration:

// Configuration 1: Phone (narrow, shallow angle)
// base_width = 60;
// angle = 55;

// Configuration 2: Tablet (wide, moderate angle)
base_width = 120;
angle = 40;

// Configuration 3: Document (wide, steep angle)
// base_width = 200;
// angle = 20;

Task 5: Validate and Document

After printing (or slicing), record:

• Actual dimensions (measure with calipers)
• Angle accuracy (verify tilt angle with protractor or phone measurement app)
• Friction resistance (does phone stay in place?)
• Print quality (note any support marks, layer quality)

Advanced: Adding Snap-Fit Connectors

To join the base and back without fasteners, you can add interlocking features:

// Optional: Add snap-fit connectors

// Slot in base plate (where back plate slides in)
module base_slot() {
  slot_width = base_thickness + 0.5;  // Slight clearance
  slot_depth = 20;
  translate([base_width/2 - slot_width/2, 0, base_thickness])
    cube([slot_width, slot_depth, lip_height]);
}

// Tab on back plate (fits into base slot)
module back_tab() {
  tab_width = base_thickness;
  tab_height = lip_height;
  translate([base_width/2 - tab_width/2, 0, 0])
    cube([tab_width, 20, tab_height]);
}

Checkpoint

• After task 1, you have a working 3-part stand (base, back, lip)
• After task 2, you’ve tested at least 2 parameter variations
• After task 4, you have 3 different configurations ready to print

Quiz - Lesson 3dMake.7 (10 questions)

1. What does the rotate() function do, and how does it differ from physical rotation¹?
2. Why is parametric positioning important for design iteration¹?
3. Explain the Minkowski sum operation and why it’s useful for filleting².
4. How would you position a second component relative to the first using translate()¹?
5. What parameter would you change to make a phone stand suitable for tablets³?
6. True or False: You can rotate an object around multiple axes in a single rotate() call.
7. Describe how $fn affects the appearance of rounded edges created by Minkowski².
8. What advantage does parametric design have over manually modeling each variant¹?
9. How would you verify that your stand’s angle matches your design intent after printing³?
10. What design considerations should you account for when adding a lip to prevent phone slippage³?

Extension Problems (10)

1. Create five stand variants (for phones, tablets, documents, laptops, and books) by parameterizing width, angle, and lip height³.
2. Add parametric feet (small cylinders) to the base to improve stability; test with and without feet¹.
3. Use 3dm describe to document each variant’s key geometric properties¹.
4. Design and test a snap-fit connector system that joins the base and back without fasteners³.
5. Create a comparison table showing print time, material weight, and assembly complexity for each variant³.
6. Build a complete phone stand product family: define naming convention, parameter ranges, and assembly instructions.
7. Develop a stress analysis guide: identify high-stress areas in your stand and propose reinforcement strategies.
8. Create a customization guide for end users: how to modify angle, width, and lip height for different devices.
9. Design an accessibility-focused stand: include tactile angle markers and clear, non-visual assembly instructions.
10. Write a comprehensive stand design documentation: CAD parameters, material recommendations, print settings, assembly, troubleshooting, and accessible design notes.

References

1. OpenSCAD Manual - Transformations - https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Transformations ↩ ↩2 ↩3 ↩4 ↩5 ↩6 ↩7 ↩8

2. OpenSCAD Manual - Minkowski - https://en.wikibooks.org/wiki/OpenSCAD_User_Manual/Transformations#minkowski ↩ ↩2 ↩3

3. 3DMake GitHub - Phone Stand Example - https://github.com/tdeck/3dmake/blob/main/docs/examples.md ↩ ↩2 ↩3 ↩4 ↩5 ↩6 ↩7