(a) The image on the right shows a sculpture located on the M4 motorway in Co - Leaving Cert DCG - Question C-4 - 2016
Question C-4
(a) The image on the right shows a sculpture located on the M4 motorway in Co. Kildare. The design is based on concentric circles and an Archimedean spiral.
A simi... show full transcript
Worked Solution & Example Answer:(a) The image on the right shows a sculpture located on the M4 motorway in Co - Leaving Cert DCG - Question C-4 - 2016
Step 1
Draw concentric circles (R100 & R40) as given
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Answer
Begin by drawing two concentric circles with radii of 100mm and 40mm, ensuring they are centered at the same point.
Step 2
Divide circles into 12 equal parts as shown
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Answer
Using a protractor, divide each circle into 12 equal sectors of 30° each, marking the division points clearly.
Step 3
Establish start point A and end point B for spiral
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Label the starting point A at the initial radius (60mm) on the outer circle and the endpoint B at a final radius of 90mm.
Step 4
Establish intermediate radii on angular division lines
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Calculate the intermediate radii at 10mm intervals between 60mm and 90mm. Label these points accordingly.
Step 5
Draw Archimedean spiral through required points (any = 1)
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Begin the spiral at point A and gradually draw the Archimedean spiral by connecting the established points, ensuring the distance between revolutions increases uniformly.
Step 6
Establish parallel lines 8mm from either side of angular division lines
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From each angular division line, measure 8mm outward to create parallel lines, aiding in the sculpture's overall design continuity.
Step 7
Completion of drawing
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Review the entire drawing to ensure clarity and precision, completing all necessary details and labels for the sculpture.
Step 8
Draw tipped truck body, tailgate and wheel in required relative positions
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Sketch the truck with its body tipped at an angle of 60°, depicting the tailgate T_T1 and the position of the wheel W accordingly.
Step 9
Division of 60° angle into equal parts (min. 6)
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Divide the 60° angle into six segments of 10° each, clearly marking these divisions on the truck's rotation path.
Step 10
Use of angular divisions to establish intermediate for bottom of Tailgate
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Establish the positions for the bottom edge of the tailgate at the marked angular divisions, to guide accurate portrayal in the drawing.
Step 11
Divide wheel into corresponding number of equal parts
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Calculate and mark divisions on the circumference of the wheel that correspond to the given number of rotations.
Step 12
Use of points established at (x) & (xi) above to determine points on locus
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Utilize the established points from previous steps to trace the locus of point T during the movement, ensuring it accurately reflects the truck's motion.
Step 13
Draw required locus (any = 1)
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Sketch the final path or locus that point T traces as the truck moves, completing the combined movement representation.
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