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The image on the right shows a machine from the popular TV game show "Tipping Point" - Leaving Cert DCG - Question C-4 - 2015

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Question C-4

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The image on the right shows a machine from the popular TV game show "Tipping Point". The machine is similar to those found in amusement centres. The forward and ba... show full transcript

Worked Solution & Example Answer:The image on the right shows a machine from the popular TV game show "Tipping Point" - Leaving Cert DCG - Question C-4 - 2015

Step 1

Draw circular path, link OA, line CD and point B as given

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Answer

Begin by drawing the circular path representing crank OA with a radius of 35 mm centered at point O. Then, draw the line segments for link CD and identify point B based on the given lengths for AB and BC (both 112 mm). Ensure that the dimensions are accurately depicted to maintain the proportions.

Step 2

Divide circle into equal parts (min 12)

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Answer

Next, divide the circumference of the drawn circle into a minimum of 12 equal sections. This can be achieved by calculating the angle for each segment, which is 30° (360°/12). Use a protractor to mark these segments accurately around the circle.

Step 3

Divide CD into 6 equal parts as shown

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Take the line segment CD and divide it into 6 equal parts. Measure the total length of CD and mark the divisions at intervals of the calculated length using a ruler. Clear markings are essential for later steps.

Step 4

Draw arm AB in all positions

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Answer

For each of the segments marked on the circle, draw the arm AB at the respective angles. Start from the center O and extend to point A, ensuring to maintain the length of 112 mm. Repeat this for each of the 12 angles marked.

Step 5

Draw required locus of point B

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Answer

Finally, connect the endpoints of arm AB for each position to sketch the locus of point B. This should smoothly illustrate the path traced by point B as the crank OA makes one full revolution.

Step 6

Establish ‘nearest approach’ on diagram of cam

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Answer

Begin by identifying the nearest approach of the knife edge follower to the cam centre, estimated at 42 mm. This should be marked clearly on the cam diagram.

Step 7

Divide circle into 12 equal parts

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Answer

Take the circle representing the cam and divide it into 12 equal sections, similar to the previous step with crank OA. This defines the intervals for the displacement diagram.

Step 8

Horizontal divisions on displacement diagram

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Answer

Draw horizontal divisions to represent each section of the 12-part division established earlier. These lines will be critical in measuring the rise, dwell, and return movements of the follower.

Step 9

Construction to determine U.A.R. on displacement diagram

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Answer

Using the established parameters, construct the Unidirectional Angle Ratio (U.A.R.) for the cam profile. The rise of 54 mm must be represented within the relevant interval.

Step 10

Show dwell on displacement diagram

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Answer

Indicate the dwell period clearly on the displacement diagram, marking the segment between 180° to 240° where the follower remains stationary.

Step 11

Transfer of heights from displacement diagram to cam diagram

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Answer

Carefully transfer the heights at each division from the displacement diagram onto the cam diagram, representing how the follower moves at each point in the rotation.

Step 12

Complete cam diagram

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Answer

Draw the entire cam outline as influenced by the follower’s movement, ensuring that all parts are connected smoothly and accurately reflecting the distances determined.

Step 13

Transfer of heights to displacement diagram

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Answer

Reconfirm the heights established on the cam diagram and ensure they are transcribed correctly onto the displacement diagram for clarity.

Step 14

Complete displacement diagram

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Answer

Finish by refining the displacement diagram to include all necessary elements for clarity, ensuring it aligns with your previously established measurements and the parameters of movement.

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