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The 3D graphic on the right shows a pedal-operated weaving machine - Leaving Cert DCG - Question C-4 - 2012

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Question C-4

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The 3D graphic on the right shows a pedal-operated weaving machine. A link mechanism in the machine is similar to the one shown in line diagram format in Fig. C-4(a... show full transcript

Worked Solution & Example Answer:The 3D graphic on the right shows a pedal-operated weaving machine - Leaving Cert DCG - Question C-4 - 2012

Step 1

Draw links and circular paths as given.

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Answer

To draw the links and paths, first sketch the links OA, BC, AD, and CP based on the provided lengths: OA = 32, BC = 42, AD = 80, CP = 165. Ensure the point O is designated at the center, and arms OA and BC are oriented correctly based on the anti-clockwise rotation.

Step 2

Divide semi-circle into equal parts.

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Construct a semi-circle with a radius determined by the arm lengths. Divide this semi-circle into equal parts, marking the subdivisions clearly.

Step 3

Divide circle line corresponding to no. of equal parts.

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Using the same radius as above, define the full circle's diameter and divide it into the same number of equal parts as the semi-circle, ensuring symmetry.

Step 4

Locate positions for point D.

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Calculate the position of point D considering the rotation of arm BC. Use geometric constructions to mark point D's position accurately.

Step 5

Extend arm CD to determine points on required locus (point P).

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From the determined position of point D, extend arm CD to plot the locus of point P. This should be traced accurately throughout the rotation.

Step 6

Draw required locus.

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Finalize the drawing by smoothly connecting the plotted points to form the continuous locus of point P. This should represent all positions of point P throughout its full movement.

Step 7

Draw the given elevation of the cylinder and project a plan.

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Begin by accurately sketching the elevation view of the cylinder as specified. Then project a horizontal plan view, ensuring alignment with the elevation.

Step 8

Draw the surface development of the front half of the cylinder, including points A and B.

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Unroll the front half of the cylinder to create a flat surface representation. Mark the positions of points A and B on this development, ensuring spatial orientation is preserved.

Step 9

Determine height and width for development.

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Measure the height and width of the cylinder. Use these dimensions to ensure the development is proportionate and accurately reflects the cylindrical shape.

Step 10

Locate points A and B on development.

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On the developed view, clearly mark points A and B, ensuring to reference their positions relative to the cylinder.

Step 11

Determine points on helix (min 4 incl. 'turning point').

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Calculate the coordinates for points along the helical slot. Include at least four distinct points, ensuring to mark the 'turning point' appropriately.

Step 12

Draw required helix.

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Using the determined points, sketch the helical path accurately on the surface development, ensuring smooth continuity through the calculated points.

Step 13

Indicate rotation angle as required.

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Measure and indicate the total angle of rotation needed for the cylinder to maintain the vertical cutting head position. This should be visually referenced on the diagram.

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