Loci of Points on a Mechanism

Loci of Points on a Mechanism

A locus is the path traced by a moving point. In a linkage, different points trace very different paths, and predicting them is what tells a designer whether a mechanism will foul its housing.

The method is sampling. Divide the driving crank's rotation into twelve equal positions. For each position, draw the whole mechanism in that position, and mark where the point of interest lies. Join the twelve marks in order.

The controlling constraint is that link lengths never change. So for each crank position, the connecting rod is swung as an arc of its own fixed length from the crank pin, and where that arc meets the slider's path fixes the mechanism. The links determine the positions — you do not place them by eye.

Worked example. In a crank and connecting rod, the crank pin traces a circle and the piston moves in a straight line. A point at the middle of the connecting rod traces neither — it draws a flattened oval, because it shares in both motions. That is exactly why it must be plotted rather than guessed.

Core checkpoint: Redraw the whole mechanism at each position. A locus is a set of sampled positions, not a curve you can sketch from the end points.