DRW 102 – Drawing II – week 5

Complicated geometrical shapes – spiral shapes

You are asked to draw the following spiral shapes by using the guidelines next to each exercise

scale: 1:100

Complicated geometrical shapes – spiral shapes

EXERCISE 1 - (ADVANCED AND/OR EXPANSION OF A) CIRCLE

• circumference of circle – divide into 12 equal parts• from the division parts expand the radiuses and the tangents • on the tangent (point 0) expand a line equal with length of circumference (Δ x 3.14) – divide the expanded line in 12 parts• on the tangent (point 1) expand section 1A equal with arc 01 so equal with distance 01’• on the tangent (point 2) expand section 2B equal with arc 02 so equal with distance 02’• use the same way to find the rest of the points Γ,Δ,Ε,Ζ,Η,Θ,Ι,Κ,Λ and Μ• join the points by using curvilinear ruler

Diameter Δ= 30 mm

EXERCISE 2 - (ADVANCED AND/OR EXPANSION OF A) TRIANGLE

• equilateral triangle ΑΒΓ• expand sides ΑΒ, ΒΓ, ΓΑ• as a centre point A (of triangle) and radius equal with the side of the arc, expand BA and break to point Δ• as a centre point B (of triangle) and radius double the size of the side of arc, expand ΒΓ and break to point E• as a centre point Γ (of triangle) and radius triple the size of the side of arc, expand AΓ and break to point Z• use the same way and alternatively change the centres, to shape the expansion

Side AB= 25 mm

EXERCISE 3 – spiral / rectangle method

• pitch of spiral – by using the ¼ of the total length of the pitch, shape rectangle ΑΒΓΔ• expand each of the sides of the rectangle ΑΒ, ΓΒ, ΔΓ, ΑΔ• draw arc ΔΕ by using as a centre the point A and radius equal with ΑΔ (meaning the ¼ of the pitch)• draw arc EZ by using as a centre the point B and radius equal with BE (meaning the ½ of the pitch)• draw arc ZH by using as a centre the point Γ and radius equal with ΓZ (meaning the ¾ of the pitch)• draw arc ΗΘ by using as a centre the point Δ and radius equal with ΔH (meaning the pitch)

Pitch B= 80 mm

EXERCISE 4 – Archimedes spiral

• pitch of spiral equal with KA • divide KA into 12 parts – numbered the parts from 1-12• divide point K ( use angle of 360 degrees) into 12 parts and expand the lines • as a centre point K and radiuses equal with K11, K10… K1 draw arcs and break lines into points 11, 10… 1• join the points 1, 2… 12 (by using curvilinear ruler) to make the spiral• for another spiral – use distance equal to KA and on each line draw points 1’, 2’, 3’… 12’• using the same way draw another spiral, etc.

Pitch B= 36 mm