Loci of Up to Three Mechanism Points

≈ 42 min

Loci of Up to Three Mechanism Points

CAPS Grade 12 requires the loci of up to three points on one mechanism, plotted together. The method is unchanged; the discipline required is greater.

One pass, three marks. For each of the twelve crank positions, draw the mechanism once and mark all three points before moving on. Plotting one point through all twelve positions and then starting again is three times the work and risks the mechanism being reconstructed slightly differently each pass.

Label consistently. With three curves developing at once, an unlabelled point becomes ambiguous almost immediately. Number every mark with its position number and identify which point it belongs to.

Interpreting the result. The three loci usually differ completely: a point on the crank traces a circle, a point on the slider a straight line, and a point on the connecting rod some flattened oval between them. The family of curves is what shows a designer where the mechanism sweeps and whether it will foul its housing.

Worked example. A point one quarter along the connecting rod from the crank pin traces a path much closer to a circle than a mid-rod point does — it shares more of the crank's motion. Proportion along the link determines the shape.

Core checkpoint: One mechanism position, all three marks, then advance. Never plot one locus at a time.

When plotting three loci on one mechanism, what is the correct working order?

Draw the mechanism once per crank position and mark all three points, then advance.

Plot the first locus fully, then start again for the second.

Plot the extremes of each locus only.

Plot the three loci on three separate drawings.

Why does plotting each locus in a separate pass risk inconsistency?

Each pass reconstructs the mechanism independently, so small differences make the curves describe links of changing length.

Because the paper stretches between passes.

Because the crank divisions change each time.

It does not — separate passes are equally accurate.

A point one quarter along the connecting rod from the crank pin traces what kind of path compared with a mid-rod point?

Closer to a circle, because it shares more of the crank's motion.

Closer to a straight line, because it is nearer the slider.

Exactly the same oval.

A perfect circle.

Why must every plotted mark be labelled when three loci are drawn together?

With three curves developing at once, an unlabelled mark cannot be assigned to the right locus or position.

Because CAPS awards marks for labelling itself.

To show the order in which the drawing was made.

Labelling is optional when the curves are drawn together.