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The image on the right shows a toy which uses a series of cams and inline flat followers to create linear vertical movement - Leaving Cert DCG - Question C-4 - 2019
Question C-4
The image on the right shows a toy which uses a series of cams and inline flat followers to create linear vertical movement. Draw the displacement diagram for a sim... show full transcript
Worked Solution & Example Answer:The image on the right shows a toy which uses a series of cams and inline flat followers to create linear vertical movement - Leaving Cert DCG - Question C-4 - 2019
Step 1
Draw the displacement diagram.
Answer
- Create horizontal divisions at 15mm increments to represent each 30° interval.
- At the 0° to 60° interval, draw a line rising to 90mm, indicating uniform velocity.
- Draw a horizontal line from 60° to 90° to represent the dwell period.
- For the 90° to 270° interval, create a curve that falls 60mm, noting the necessary acceleration and retardation.
- Use the formula for UAR to determine the curvature:
,
where
Sis the distance fallen,uis the initial velocity (0), andais the uniform acceleration.
- Use the formula for UAR to determine the curvature:
,
where
- Finally, for the 270° to 360° interval, draw a line returning to the initial position (0mm) with uniform velocity.
Step 2
Draw required trochoid.
Answer
- Begin by drawing a circle with a radius of 350mm for the front wheel.
- Mark a line AB on the horizontal axis.
- Draw 12 equally spaced points on the circumference of the circle, which correspond to the spokes (at 30° intervals).
- Reference the position of the reflector at 220mm above the ground to plot its locus.
- Based on the wheel’s roll, trace the path of the reflector as the wheel completes a full rotation, forming the trochoid pattern accordingly.