Design & Drawing for Production

Geometric Shapes & Solids

Shapes - The two-dimensional contour that characterizes an object or area, in contrast to three-dimensional form.

Solids - A three-dimensional body or geometric figure.

Figures & Polygons

Shapes:

Acute triangle - A triangle that contains only angles that are less than 90 degrees.

Obtuse triangle - A triangle with one angle that is greater than 90 degrees.

Circumscribe - 1. A triangle located round a polygon such as a circle. 2 To draw a figure around another, touching it at points but not cutting it.

Inscribe - To draw a figure within another so that their boundaries touch but do not intersect.

• Properties of Geometric Shapes - 2D:

Solids:

2D - Sketching Tools

line, spline, circle, ellipse, arc, fillet, , chamfer, polygon, mirror, circular pattern, rectangular pattern, offset, dimension, trim, extend, move, rotate, project, geometry, text, insert image

• Properties of Geometric Solids - 3D:
  • Area

    • Circle:  A = πr²

    • Ellipses: A = π(.5a)(.5b)  a = major axis,  b = minor axis

    • Triangle:  A =  .5(bh)

    • Rectangle:  A = LW or A = bh

    • Parallelogram:  A = bh

    • Multisided Polygons:  A = n ^{s(.5f)
                                                2}
           s = side length
           f = distance between flats or diameter of inscribed circle
           n = number of sides
       

    • Cone:  A =  π x Diameter x Length ÷ 2

    • Sphere:  A = π x Diameter²

    • Total Surface Area = Sum of the areas of all sides

     
  • Volume (V):  amount of space occupied by an object
    • Metric System:  Cubic Centimeter (cc)
    • English System:  Cubic Inch (in³)
       

    • Cube:  V = S³  or V = wdh

    • Rectangular Prism:  V = wdh

    • Cylinder: V = πr²h

    • Pyramid: V = 1/3 x (Area of Base) x (Height)

    • Cone: V = π x radius² x Height  / 3

    • Sphere: V = 4π x radius³  / 3

    • Right Tri. Prism: V = 1/2 Base x Height (Length)

Properties

• Mass (M):  quantity of matter in an object
  • Metric System:  Gram (g)
  • English System:  Slug
  • Mass (M) = Volume x Density
     
• Weight (W):  force of gravity acting on an object
  • Metric System:  Newton (N)
  • English System:  Pound (lb)

  • Weight = Mass x acceleration due to gravity

    • M = Mg

    • lbs = slugs x ft/sec²

    • Gravity (g) = 32.16 ft/sec²
       

• Density Weight (D_W):  an objects weight per unit volume
  • English System:  Pounds per cubic inch (lbs/in³)

  • Weight = Volume x Weight Density

  • W = VD_W
     

• Surface Area (SA):  the sum of all the areas of the faces of a 3D solid 

  • Cube:  SA = 6A

  • Rectangular Prism:  SA = 2(wd + wh + dh)

  • Cylinder:  SA = (2πr)h + 2(πr²)

3D Model Features

extrusions, midplane extrusion, intersect extrusion, tapered extrusion, revolve, hole, loft, circular pattern, rectangular pattern, rectangular pattern along a path, shell, rib, sweep, coil, thread, fillet, chamfer, mirror, emboss, decal

• Additive & Subtractive Solid Modeling
  • Additive - A three dimensional object can be viewed as the combination of two or more simple forms.

  

  • Subtractive - An object can be viewed as the remainder of a solid block that has had the geometry of one or more forms sequentially removed.

  

2D Constraints: