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Sphere development

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Sharmaine de Jesus
Sharmaine de Jesus

The document describes two methods for approximately developing a sphere: 1. The polycylindric/gore method which divides a quadrant into equal central angles and measures arcs and chords to form gores which are assembled to approximate the sphere. 2. The polyconic/zone method which draws concentric circles and arcs, dividing the sphere into equal sectors. Tangent lines and arcs are drawn to form zones which are assembled to approximate the sphere.

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Ex. 15 Approximate Development of a Sphere
SPHERE is a closed surface all points of which are equidistant from a fixed point called the center TOP VIEW TOP VIEW P P A B C 5 1  A A 4 B  2 B 3 C C  3 2 D D 1   5 E 4  P P A 1 2 3 4 5 P B A C B D C E E Quarter Development Half Development FRONT VIEW FRONT VIEW Construction by the Polycylindric/Gore method Construction by the Polyconic/Zone method Title SAMPLE Approximate Development of the Spheres Name Activity No. Marifa S. Torralba, PhD Sec. Student No. Date Station No.
Instructions • Sizes of the figures are at your own discretion • Apply the alphabet of lines & ink the figures based on the character of the lines of the top, front, & lateral area. • Use leader lines for its dimensions • Retain the construction lines or do not erase the pencil sketches totally • Height of letters = 0.5 cm including that of the title block • Use 0.2 pen for all letterings Prepared by: Marifa Torralba,PhD
SPHERE • closed surface all points of which are equidistant from a fixed point called the center • a radius of the sphere is a line segment from the center to any point on the its surface • a diameter of the sphere is a line segment whose endpoints are on the surface that passes through its center Prepared by MARIFA S TORRALBA, PhD
TOP VIEW Construction by the Polycylindric/Gore method- quarter development 1. Draw concentric circles in the top (letters) – lines in front are diameters of these circles 2. divide a quadrant to equal central angles 3. measure arcs 1-2, 2-3, 3-4, 4-5 and draw line at the midpt 4. measure circumferential arc from great circle (E )to the nxt P 5 circle in the front view ( D ) 5. measure the chord P of circle D in top A 6. Repeat steps 4 and 5 until P 4 B A 7. Trace a curve at each endpoints to form a gore C 3 D B 8. Using the developed gore E 2 1 as template, lay out other C gores to complete the D approximate development P of the sphere A B 1 2 3 4 5 C D E FRONT VIEW Prepared by: MARIFA S. TORRALBA, PhD
TOP VIEW Construction by the Polyconic/Zone method 1. Draw circle A and draw chord in the front view 2. With P as vertex/pivot, draw arc whose radius = chord 3. Divide one quarter of the sphere to equal sectors 4. Measure arc in A (top) & lay it off in arc (16 parts) 5. Draw line tangent to the sphere at circle A (front) 6. With that line tangent as radius, draw the arc tangent to arc P A B C 5 7. Draw circle B  8. In the front view, measure line tangent + arc bet. A& B. This becomes the Radius of another arc 4 9. Measure arc in B (top) & lay it off in arc (16 parts) 3 10. Repeat step 5 to finsih half the sphere  2 development 1    P  P A B C E FRONT VIEW Prepared by: MARIFA S. TORRALBA, PhD

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Sphere development

  • 2. SPHERE is a closed surface all points of which are equidistant from a fixed point called the center TOP VIEW TOP VIEW P P A B C 5 1  A A 4 B  2 B 3 C C  3 2 D D 1   5 E 4  P P A 1 2 3 4 5 P B A C B D C E E Quarter Development Half Development FRONT VIEW FRONT VIEW Construction by the Polycylindric/Gore method Construction by the Polyconic/Zone method Title SAMPLE Approximate Development of the Spheres Name Activity No. Marifa S. Torralba, PhD Sec. Student No. Date Station No.
  • 3. Instructions • Sizes of the figures are at your own discretion • Apply the alphabet of lines & ink the figures based on the character of the lines of the top, front, & lateral area. • Use leader lines for its dimensions • Retain the construction lines or do not erase the pencil sketches totally • Height of letters = 0.5 cm including that of the title block • Use 0.2 pen for all letterings Prepared by: Marifa Torralba,PhD
  • 4. SPHERE • closed surface all points of which are equidistant from a fixed point called the center • a radius of the sphere is a line segment from the center to any point on the its surface • a diameter of the sphere is a line segment whose endpoints are on the surface that passes through its center Prepared by MARIFA S TORRALBA, PhD
  • 5. TOP VIEW Construction by the Polycylindric/Gore method- quarter development 1. Draw concentric circles in the top (letters) – lines in front are diameters of these circles 2. divide a quadrant to equal central angles 3. measure arcs 1-2, 2-3, 3-4, 4-5 and draw line at the midpt 4. measure circumferential arc from great circle (E )to the nxt P 5 circle in the front view ( D ) 5. measure the chord P of circle D in top A 6. Repeat steps 4 and 5 until P 4 B A 7. Trace a curve at each endpoints to form a gore C 3 D B 8. Using the developed gore E 2 1 as template, lay out other C gores to complete the D approximate development P of the sphere A B 1 2 3 4 5 C D E FRONT VIEW Prepared by: MARIFA S. TORRALBA, PhD
  • 6. TOP VIEW Construction by the Polyconic/Zone method 1. Draw circle A and draw chord in the front view 2. With P as vertex/pivot, draw arc whose radius = chord 3. Divide one quarter of the sphere to equal sectors 4. Measure arc in A (top) & lay it off in arc (16 parts) 5. Draw line tangent to the sphere at circle A (front) 6. With that line tangent as radius, draw the arc tangent to arc P A B C 5 7. Draw circle B  8. In the front view, measure line tangent + arc bet. A& B. This becomes the Radius of another arc 4 9. Measure arc in B (top) & lay it off in arc (16 parts) 3 10. Repeat step 5 to finsih half the sphere  2 development 1    P  P A B C E FRONT VIEW Prepared by: MARIFA S. TORRALBA, PhD