Notes can be found as interactive webpage at

1: Fundamentals of Graphical Communication & Subtractive Processes

01-25: Fundamentals of graphical communication #

Evolution of graphical visualization #

  • Hand drawing
  • Instrument drawing (using mechanical things to measure distances)
  • 2D CAD (initially only able to draw side views)
  • 3D CAD (solid modeling)
    • Automatic generation of 2D working drawings
    • Enable easy communication of measurements between designer and manufacturer
    • Created with the assumption that manufactured objects are made up of elementary objects, geons?
    • Now we have the ability to run algos to analyze models, removing unnecessary bits
    • We’re moving towards computer-generated geometry that’s contained by human input


  • Increasingly complex geometries
  • New interfaces
    • Virtual and augmented reality for visualizing designs

Why bother sketching by hand? #

  • Why not go straight to CAD?
  • Some possible reasons:
    • There is a connection between drawing and your own creativity; a feedback loop of sorts
    • CAD bottlenecks you to designing a certain way
    • Find one’s own distinctive style
    • Avoid making detailed decisions too early
    • Keep geometries more freeform
    • Ideas may come to mind anywhere, anytime
    • Potentially quicker
Sketch Examples
  • Leonardo da Vinci: “helicopter” (c. 1489)
  • Charles and Ray Eames: chair
  • Renzo Piano + Richard Rogers: Pompidou Center
  • Philippe Starck: lemon squeezer
    • Aside: how is it made?


  • Jonathan Ive/Apple design team: iPhone
  • Burj Khalifa: Adrian Smith
  • Tesla Model 3: Franz Holzhausen
  • Concept drawing for Berkeley Engineering

Essentials of 2D sketching #

  • Line types matters
    • Solid: edges
    • Dashed: hidden detail
    • Chain: centerline.
      • - . - .
    • Faint: construction
      • Align, but don’t touch, features
    • Dimension lines:
      • Fainter than edges, and not connected.
      • Long, thin arrows.
      • Lots of differing standards, just be consistent

3D pictorial approaches #

Isometric drawing #

  • ‘iso’ = same, ‘metric’ = measure
    • Any lines parallel .$x,y,z$ on the lines are equal length
  • Orthogonal edges of a 3D object map to:
    • Vertical lines
    • Lines at .$\pm 30^\circ$ to horizontal
  • Enables creating reasonably realistic drawings fairly easily
  • Dimensions in these orthogonal directions are preserved on page
  • Dimensions in other directions are not preserved on page

  • Circles in isometric
    • Use construction lines for bounding box
    • Mark midpoints
    • Draw longer quadrants first
    • Through holes: use construction lines for obscured circle; darken later
    • What if circle is not on an orthogonal face?

Coded plans for practicing isometric sketching #

  • Principle: number in cell gives height of column to be drawn
  • Codes could be given on isometric or square grid ( plan view)
  • Square grid: viewpoint explicitly specified

  • Different views / perspectives may obscure different features. Chose the one that minimizes information loss / ambiguity
  • You can shade certain surface to convey shadow (and thus depth, 3D information)
    Plan View Draw Example

Axonometric drawing #

  • Orthogonal edges are represented by:
    • Vertical lines
    • Lines at .$\pm 45^\circ$ to horizontal
  • Advantage:
    • Floorplans are not skewed/distorted
  • Disadvantage:
    • Areas of equal orthogonal faces are not equal on drawing
    • Can look more “distorted”


Example of axonometric drawing

  • Sometimes called “planometric”
  • Popular in architecture to preserve floorplans

Oblique drawings #

  • Front view is undistorted
  • Conveys lots of information of a single face
  • Angles are arbitrary (here they’re ~45)
  • Receding lines drawn at a constant angle
  • Judgement needed to select scale for receding direction

Perspective drawing #

  • Simulates how the eye sees 3D objects: further away objects/details are smaller
  • Much more challenging than other methods
    • Receding lines not parallel
    • But CAD software can generate
  • Horizon line
  • Vanishing point(s)
    • One point: dimensions referenced from closest surface
    • Two points: dimensions referenced from closest edge


Introduction to sketching tools #

Digital sketching tools #

  • Autodesk Sketchbook
    • Now discontinued! :(
      • OneNote is an alright alternative
    • Import isometric grid on Layer 2
    • Draw on Layer 1
  • Google Jamboard
  • Adobe Photoshop, Illustrator
  • Software resource page in bCourses

Analog sketching tools #

  • Set square/drawing triangle
  • Pencils:
    • Various hardness/softness
    • Mechanical vs traditional
  • Pens
    • Ballpoint
    • Felt tip
    • Technical

Possible ways of enhancing 3D sketches #

  • Shading – simulate the effect of light falling on object
    • e.x shadows, glare,
  • Visual clarity – edges bolder: example of how it clears confusion
  • Suggesting motion, sound, texture, etc.


01-27: Subtractive processes: types of subtractive process; mechanics of cutting #

Subtractive manufacturing processes #

  • Subtractive processes are those that begin with standard stock material (in rod, bar, sheet, plate form etc) and remove material to impart shape

Types of subtractive process #

  • Material comes in range of mediums: billet (below, left), sheet, foil, wire, pellets, etc.
  • A subtractive process removes material from a larger piece of material to define the geometry needed
    • Subtractive processes therefore generate waste material
    • How we deal with this is important
  • Take 5 minutes to brainstorm all the ways you can think of to remove material in a controlled way from a solid piece of stock to create a geometry
    • Also think about what could happen to the waste material What are some ways of removing material? Can we re-use the extra material?

How can we cut away material? Some possibilities: #

  • Cutting – taking a sharp edge to material
    • Drilling, boring, reaming
    • Milling
    • Lathe operations: turning, facing, tapping
    • Shearing/punching/puncturing
    • Sawing
    • Chiseling
    • Collectively: “machining”
  • Electric field
    • Electrical discharge machining (EDM): electrode, wire
  • Localized melting or vaporization
    • Laser cutting, laser ablation
    • Flame, plasma cutting
    • Hot wire (typically used for plastics)
    • Aside: is melting really subtractive?
  • Misc
    • Chemical methods ( Etching)
    • Explosives (think mining)
    • Forcing apart (using physical force)
  • Abrasion – rough, abrasive wheels rotate at high speed across the surface of the component, removing particles of the workpiece. This approach is well suited even to the hardest of materials, although control of geometry is not as great as in cutting operations, for example.
    • Grinding, sanding, lapping, polishing, filing
    • Abrasive jet (water jet)
    • Sand blasting

Why would we choose a subtractive process #

  • Instead of an additive process? Instead of a forming process, e.g. casting?

Some possible reasons to: #

  • Stock materials tend to be readily available (and inexpensive compared with the specialist powders that are used in some additive processes such as selective laser melting
  • Precision and finish are exceptionally good – probably better than any other family of processes
  • Need strength / structure
  • Material cannot be molded (it’s the only feasible process)
  • Doesn’t alter heat treatment (if feed and speed isn’t too high)
  • Short runs – no specialized tooling costs
  • Easy customization & More control for iterative product development – every component produced can be different if needed
    • All you need is to generate new .gcode; versus a whole mold

Why not choose subtractive? #

  • Slow for large run sizes compared to forming processes
    • Most processes are “serial”, meaning that each feature on the component needs to be produced sequentially, making the processes slow. This is in contrast, for example, to molding/casting operations where the entire component is produced in approximately one step.
  • Fairly costly in comparison
    • Large amount of waste generated (low efficiency)
    • High operator skill is often demanded, raising processing costs
  • Cuts across metal grains – not as strong as forged or possibly cast components focus on material cutting Cutting operations rely on wedge-shaped teeth

Mechanics of lathe turning of metals #

  • To understand the key concepts of metal cutting, we focus specifically on lathe turning
    • i.e. a reduction in the diameter of a cylindrical component using a cutting tool.
  • We focus on the turning of metals and their alloys, although turning is also widely used to process polymeric materials and even composite materials (wood being one “composite” that is regularly turned).
  • Cutting operations rely on wedge-shaped teeth

    Lectures 4 and 5 will focus on cutting-based operations; Lecture 6 will look at some of the others A close look at a metal cutting operation

Terminology #

  • The workpiece (or simply work — the solid material that is to be reduced in diameter) is held firmly at one end in a chuck, whose jaws are tightened against the workpiece enough that the friction between the work and the chuck is always enough to resist the torques experienced by the work during cutting.
  • The work is rotated, using an electric motor, at angular velocity .$\omega$, which is typically hundreds or even thousands of revolutions per minute. Let us call the axis of rotation z. If the radius of the workpiece is a at the location of cutting, then the linear, tangential velocity of the work relative to the tool is .$V_\text{cut} = \omega a$, provided that .$\omega$ is expressed in radians/second (to convert from rev/min to rad/sec multiply by .$2\pi/50$).
  • The cutting tool is mounted on a cross-slide/carriage assembly, which enables precise control of the cutting edge along the z axis and also radially outwards from the z axis (let us call this radial direction the x axis). The carriage and cross-slide could be moved by manual screws or by computer-controlled motors with positional feedback.
  • Once the work is rotating at its target speed, the tool is positioned slightly to the right of the end of the work and the tool is moved inwards in the x direction (towards the rotational z axis) by a distance .$d$, called the depth of cut. The tool is then moved from right to left along the workpiece at a velocity called the feed rate given by .$V_\text{feed} = f\omega$, where .$f$ is the feed, or the distance moved by the tool along the z axis in one revolution of the work.
    • Feed rate is a velocity, while feed is a distance per revolution — this subtlety of terminology is important to note. Note that in almost any turning process, .$V_\text{cut} » V_\text{feed}$

A close look at a metal cutting operation #

High-speed video: cutting tool moves across surface

  • Teeth are at a specific, optimal wedge angle wrt the material to shave away stock
  • Material is sheared off the workpiece (like butter and knife)
  • Quality of cut depends on rake angle (front angle), .$\alpha$, of tool
    • Rake angle vertical (.$\alpha = 0$): material piles up and lot of heat is generated
    • Rake angle too large: tool is fragile, can dig into material
    • Rake angle just right: cutting happens close to tool
    • What is “just right” for the rake angle .$\alpha$?
      • .$30^\circ$ is a good magic starting value
    • Clearance angle should be non-zero
      • Allows you to run the tool in reverse over the material without cutting

Material Removed #

  • The metal that is cut, or shaved, away from the workpiece is called the chip, and depending on (1) how brittle or ductile the work material is, (2) the shape of the cutting tool, and (3) the speed of cutting, the chip may be either a fairly continuous spiral or a series of small chips that regularly fracture.
  • Many small chips are desirable from a practical perspective because, unlike very long continuous chips, they do not tend to become tangled around the work and potentially scratch it.
  • Cutting tools will often have protrusions on their front surface that are designed to break up a chip as it comes off the workpiece.
  • So in turning, a spiral of material is being removed from the work that has initial cross-section .$d \times f$ and with the tool sweeping through the material with velocity .$V$. Thus, the volumetric removal rate of material is .$R_\text{MR} = Vdf$.

Cutting depends on material properties #

  • More ductile materials (aluminum, mild steel, copper etc): long, spiral-shaped chips of material
  • More brittle materials (e.g. cast iron): comes off in short chips

    Basic types of chips produced in metal cutting and their micrographs:
    (a) continuous chip with narrow, straight primary shear zone;
    (b) secondary shear zone at the tool-chip interface;
    (c) continuous chip with built-up edge;
    (d) segmented or nonhomogeneous chip; and
    (e) discontinuous chip.