The image below shows the booms of two cranes - Leaving Cert DCG - Question A-1 - 2022
Question A-1
The image below shows the booms of two cranes.
The crane booms are represented by the skew lines AB and CD on the right.
(a) Determine the projections of the shorte... show full transcript
Worked Solution & Example Answer:The image below shows the booms of two cranes - Leaving Cert DCG - Question A-1 - 2022
Step 1
Draw line from A parallel to CD (or C parallel to AB) in elevation
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From point A, draw a line parallel to the line CD in the elevation view. This line will indicate how the boom AB projects in the vertical plane.
Step 2
Draw line from A parallel to CD (or C parallel to AB) in plan
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On the plan view, draw a line from point A that is parallel to the line CD. This represents the top view projection of the crane boom.
Step 3
Determine plane of horizontal line in either plane
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Identify the horizontal line joining the two projections of the lines AB and CD. This line will be horizontal in both elevation and plan views.
Step 4
X_Y perpendicular to plan of horizontal line
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Establish a horizontal reference line X_Y that is perpendicular to the horizontal line found in the previous step.
Step 5
Projections of AB and CD on X_Y
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Project the ends of lines AB and CD onto the line X_Y. This gives the projections needed to find the shortest distance.
Step 6
Y_Y perpendicular to X_Y line
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Draw a vertical line Y_Y that is perpendicular to the line X_Y, indicating the height difference between the booms at their respective projections.
Step 7
Projections of AB and CD on X_Y
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Repeat the projection process for lines AB and CD onto the perpendicular Y_Y, ensuring the correct distances are marked.
Step 8
Projections of required shortest horizontal distance to plan and elevation
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Mark the distance between the two projections on Y_Y indicating the shortest horizontal distance between the skew lines. This can be measured on both the plan and elevation.
Step 9
Correct length of shortest horizontal distance indicated in millimetres
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Measure the shortest horizontal distance using a ruler or scale to find its length in millimeters, ensuring accurate representation.
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