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The 3D graphic on the right shows a pull along toy - Leaving Cert DCG - Question C-4 - 2010
Question C-4
The 3D graphic on the right shows a pull along toy. A cam and in-line knife-edge follower are used inside the toy to move the head up and down as the toy rolls. The... show full transcript
Worked Solution & Example Answer:The 3D graphic on the right shows a pull along toy - Leaving Cert DCG - Question C-4 - 2010
Step 1
Displacement Diagram
Answer
To draw the displacement diagram for the cam:
- 360° Division: Start by dividing the diagram into 360° sections to accommodate each motion phase.
- Follower Positions: Mark the positions of the follower at 0°, 120°, 180°, and 360° on the horizontal axis.
- 0° to 120° (Uniform Velocity): For the rise from 0° to 120°, draw a straight line representing a displacement of 40mm, as the motion is uniform.
- 120° to 180° (Dwell): Indicate a horizontal section from 120° to 180°, representing the dwell with no movement.
- 180° to 360° (Simple Harmonic Motion): From 180° to 360°, the displacement will follow a simple harmonic motion profile, which typically resembles a smooth curve back to the original horizontal position at 360°.
- Direction of Rotation: Ensure to label the direction of cam rotation as anti-clockwise, which impacts the follower's movement.
Step 2
Cam Profile
Answer
Next, draw the cam profile based on the displacement diagram:
- Minimum Radius: Identify the smallest radius; for a rise of 40mm from the reference axis, this will be at the starting point.
- Camshaft Diameter: The diameter is given as 20mm. Ensure the cam profile starts from this radius.
- Maximum Radius: The maximum radius can be determined as the sum of the minimum radius and the maximum displacement (40mm), leading to a maximum radius of 70mm.
- 0° to 120° (Uniform Velocity): The profile from 0° to 120° rises linearly, marking 40mm at 120°.
- 120° to 180° (Dwell): Maintain the profile at this maximum radius until the 180° mark.
- 180° to 360° (Simple Harmonic Motion): Draw a curve back to the original radius at the 360° mark, ensuring the characteristics of simple harmonic motion are followed, which often looks like a wave.
- Final Draft: Clearly label each section of the cam profile including all measurements and ensure the transitions are smooth.
Step 3
Cycloid Locus
Answer
For the trundle wheel, to plot the locus of point P:
- Setup Line AB, Circle C, and Point P: Begin by drawing a horizontal line AB in the diagram, marking points A and B. Draw circle C centered at the initial position of the wheel.
- Division of Circle: Segment circle C into equal parts corresponding to the rotations it will make. The circumference can be calculated by the formula:
- Set Centers on AB: As the wheel rolls, mark the positions of the center of circle C along line AB for each division calculated.
- Swung Arcs: For each center you marked, swing arcs to find point P, which will trace the locus of that point as the wheel rolls.
- Constructing the Locus: Finally, plot each locus point from circle C's rolling motion to complete the trajectory of point P.