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The 3D graphic on the right shows part of an automated packaging machine - Leaving Cert DCG - Question C-4 - 2010
Question C-4
The 3D graphic on the right shows part of an automated packaging machine. The mechanism is shown in line-diagram format in Fig. C-4(a). Below in the diagram, crank O... show full transcript
Worked Solution & Example Answer:The 3D graphic on the right shows part of an automated packaging machine - Leaving Cert DCG - Question C-4 - 2010
Step 1
Plot the locus of point B for one revolution of the crank OA.
Answer
To plot the locus of point B:
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Identify the Rotation: The crank OA rotates clockwise, which means we start from an initial position encoded by the angle.
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Calculate Positions: Using the angles from 0° to 360° in increments (for a smooth curve), calculate the coordinates for point B using the position of A and the defined radius for circle R.
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Draw the Circle: Construct the circle with radius 40 mm centered at point O, which dictates the path point A travels.
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Locate Point B: At each angle, find point B's location by considering the tangent from point A to circle R.
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Sketch the Locus: Connect the calculated positions of point B to form the locus over one full revolution, ensuring that the curve visually represents the tangential motions described.
Step 2
Draw the cam profile and the displacement diagram given the following data:
Answer
To create the cam profile and displacement diagram:
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Segment the Motion: Divide the total rotation of the cam into three segments:
- 0° to 180°: During this phase, the rise of 40mm follows simple harmonic motion. The arc can be plotted using the sine function to model this rise:
- Arc length, s = R (1 - rac{1}{2} imes (1 - ext{cos}( heta))).
- 180° to 270°: The cam remains stationary, indicated by a horizontal line segment in the displacement diagram.
- 270° to 360°: The return phase back to the original position, plotted as a descending curve returning to the x-axis.
- 0° to 180°: During this phase, the rise of 40mm follows simple harmonic motion. The arc can be plotted using the sine function to model this rise:
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Draw the Cam Profile: Construct the profile corresponding to the calculated displacement for each section, ensuring proper curvature between the segments is maintained.
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Create the Displacement Diagram: Using the x-axis (angle) and y-axis (displacement), accurately reflect the rise, dwell, and return phases on the graph, clearly marking the transitions at each segment.