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Drafting – Product Design & Architecture

Drafting – Product Design & Architecture. Geometric Terms & Construction. Geometry. The study of the size and shape of things The relationship of straight and curved lines in drawing shapes

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Drafting – Product Design & Architecture

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  1. Drafting – Product Design & Architecture Geometric Terms & Construction

  2. Geometry • The study of the size and shape of things • The relationship of straight and curved lines in drawing shapes • It is essential to recognize geometry that exists within objects for the purpose of creating solid models or multiview drawings

  3. Vertex Angles • Acute Angle • Measures less than 90° • Obtuse Angle • Measures more than 90° • Right Angle • Measures exactly 90° • Vertex • Point at which two lines of an angle intersect

  4. Circle • Radius • Distance from the center of a circle to its edge • Diameter • Distance across a circle through its center • Circumference • Distance around the edge of a circle • Chord • Line across a circle that does not pass at the circle’s center

  5. 90° 90° 90° 90° Circle • Has 360° • Quadrant • One fourth (quarter) of a circle • Measures 90° • Concentric • Two or more circles of different sizes that share the same center point

  6. Triangles • Equilateral • All three sides are of equal length and all three angles are equal • Isosceles • Two sides are of equal length • Scalene • Sides of three different lengths and angles with three different values

  7. HYPOTENUSE Triangles • Right Triangle • One of the angles equals 90° • Hypotenuse • The side of a right triangle that is opposite the 90° angle

  8. Quadrilaterals • Square • Four equal sides and all angles equal 90° • Rectangle • Two sides equal lengths and all angles equal 90° • Trapezoid • Only two sides are equal length

  9. Quadrilaterals • Rhombus • All sides are equal length and opposite angles are equal • Rhomboid • Opposite sides are equal length and opposite angles are equal

  10. Regular Polygons • Pentagon • Five sided polygon • Hexagon • Six sided polygon • Octagon • Eight sided polygon

  11. Regular Polygons • Distance across flats • Measurement across the parallel sides of a polygon • Distance across corners • Measurement across adjacent corners of a polygon

  12. Solids • Prism • Right Rectangular • Right Triangular

  13. Solids • Cylinder • Cone • Sphere

  14. Solids • Pyramid • Torus

  15. Geometric Terms • Circumscribe • Process of creating a polygon that fully encloses a circle and is tangent to all of the polygons sides • Inscribe • Process of creating a polygon that is fully enclosed by a circle at its corners

  16. Geometric Terms • Bisect • Divide into two equal parts • Tangent • A line and arc, or two arcs that touch each other at one point only

  17. Geometric Terms • Parallel • Two or more lines that are always the same distance apart • Perpendicular • Two lines that are at a 90° angle

  18. Angle Triangle Radius Diameter Parallel Perpendicular Square Centerline C L Geometric Symbols R

  19. Bisect a Line w/ a Compass • Given line AB • With points A & B as centers and any radius greater than ½ of AB, draw arcs to intersect, creating points C & D • Draw line EF through points C and D

  20. H D F C E A B G Bisect a Line w/ a Triangle • Given line AB • Draw line CD from endpoint A • Draw line EF from endpoint B • Draw line GH through intersection

  21. Bisect an Arc • Given arc AB • With points A & B as centers and any radius greater than ½ of AB, draw arcs to intersect, creating points C & D • Draw line EF through points C and D

  22. Bisect an Angle • Given angle AOB • With point O as the center and any convenient radius R, draw an arc to intersect AO and OB to located points C and D • With C and D as centers and any radius R2 greater than ½ the radius of arc CD, draw two arcs to intersect, locating point E • Draw a line through points O and E to bisect angle AOB

  23. B A C Divide a Line into Equal Parts • Given line AB • Draw a line from endpoint A perpendicular to line AB • Position scale, placing zero on line AC at an angle so that the scale touches point B • Keeping zero on line AC, adjust the angle of the scale until any of the desired number of divisions are included between line AC and point B • Mark the divisions • Draw lines parallel to AC through the division marks to intersect line AB

  24. Construct a Hexagon:given distance Across Flats (Circumscribed) • Given distance across the flats of a hexagon, draw centerlines and a circle with a diameter equal to the distance across flats • With parallel edge and 30° – 60 ° triangle, draw the tangents

  25. C D A B F E Construct a Hexagongiven distance Across Corners (Inscribed) • Given distance AB across the corners, draw a circle with AB as the diameter • With A and B as centers and the same radius, draw arcs to intersect the circle at points C, D, E, and F • Connect the points to complete the hexagon

  26. Construct an OctagonAcross Flats (Circumscribed) 1 • Given the distance across the flats, draw centerlines and a circle with a diameter equal to the distance across flats 5 7 3 4 • With a parallel edge and 45 triangle, draw lines tangent to the circle in the order shown to complete the octagon 8 6 2

  27. C G E B A H F D Construct an OctagonAcross Corners (Inscribed) • Given the distance across the corners, draw centerlines AB and CD and a circle with a diameter equal to the distance across corners • With the T-square and 45° triangle, draw diagonals EF and GH • Connect the points to complete the octagon

  28. A R B R C D Construct an Arc Tangent to Two Lines at an Acute Angle • Given lines AB and CD • Construct parallel lines at distance R O • Construct the perpendiculars to locate points of tangency • With O as the point, construct the tangent arc using distance R

  29. A R C B R D Construct an Arc Tangent to Two Lines at an Obtuse Angle • Given lines AB and CD • Construct parallel lines at distance R O • Construct the perpendiculars to locate points of tangency • With O as the point, construct the tangent arc using distance R

  30. A D R2 R2 R1 B C E Construct an Arc Tangent to Two Lines at Right Angles • Given angle ABC • With B as the point, strike arc R1 equal to given radius O • With D and E as the points, strike arcs R2 equal to given radius • With O as the point, strike arc R equal to given radius

  31. C R1 R1 A B O D Construct an Arc Tangent to a Line and an Arc • Given line AB and arc CD • Strike arcs R1 (given radius) E • Draw construction arc parallel to given arc, with center O T1 • Draw construction line parallel to given line AB • From intersection E, draw EO to get tangent point T1, and drop perpendicular to given line to get point of tangency T2 T2 • Draw tangent arc R from T1 to T2with center E

  32. A R1 R O B C R1 D S Construct an Arc Tangent to Two Arcs • Given arc AB with center O and arc CD with center S • Strike arcs R1 = radius R E T • Draw construction arcs parallel to given arcs, using centers O and S T • Join E to O and E to S to get tangent points T • Draw tangent arc R from T to T, with center E

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