The graphic on the right shows a crank and slider mechanism in a steam engine - Leaving Cert DCG - Question C-4 - 2014

Divide the circumference of the circle into 12 equal segments, marking each point clearly. These segments will represent the positions at every 30° of rotation.

For each of the 12 positions marked on the circle, draw the link AB so that it is always 140mm long and pivots around point A. Draw these arms sequentially for each 30° increment.

Connect the endpoints of link AB drawn from each position to form a smooth curve. Highlight any turning points where the arm changes direction, indicating the locus of point B's movement throughout the crank's rotation.

Draw the profile of the camshaft based on the information provided, ensuring to represent the archimedian spiral accurately.

Draw line AB horizontally to represent the displacement of the follower as the cam rotates.

Similar to the crank mechanism, divide the circle representing the cam in 12 equal segments corresponding to each 30° increment.

Using the appropriate formula for the archimedian spiral, calculate and plot points to create the accurate cam profile.

Plot the spiral according to the points determined using the spiral equation, ensuring it accurately represents the rapid fall of the follower.

Add horizontal grid lines on the displacement diagram to facilitate measurement of the follower's movement in relation to the cam's rotation.

From the plotted cam profile, measure the vertical heights at each incremental position and transfer these heights onto the displacement diagram.

Finally, join the transferred points on the displacement diagram to create a smooth curve that represents the follower's movement during one full rotation of the cam.