Trace loci of points under geometric constraints. Explore ellipse, parabola, and cardioid generation through linkage mechanisms.
Locus Tracer follows a marked point as an ellipse, parabola, or cardioid mechanism changes configuration. Instead of presenting only a finished curve, it relates the accumulated path to the linkage and geometric constraints that move the point. The key distinction is between one displayed position and the locus: the current marker is a single allowed position, while the locus is the complete set of positions allowed by the motion. A recognizable outline is therefore the result of the constraint, not an independently drawn graph.
Each configuration satisfies the mechanism's geometric constraints, such as fixed pivots, guide lines, or unchanged link lengths. The tracked point contributes one position for that configuration. Continuing the motion reveals the collection of allowable positions. A single configuration explains where the point is now; the accumulated trace answers where it can be while the same constraints remain in force.
The named results have standard geometric descriptions. An ellipse has a constant sum of distances to two foci. A parabola consists of points equidistant from a focus and a directrix. A cardioid can be generated by a point on a circle rolling around a fixed circle of equal radius. The displayed linkage is a construction of a curve, not its mathematical definition.
The linkage changes configuration, but its fixed geometric relationships remain in force. Those relationships restrict the tracked point to a particular set of possible locations. Each configuration supplies another location from that same set, so the marker moves while the accumulated locus retains its ellipse, parabola, or cardioid form.
No, not by itself. The trace is a visual account of positions produced by the mechanism. It can suggest the intended curve and clarify the construction, but an exact conclusion requires a derivation from the constraints, such as proving a focal-distance relation or obtaining coordinates that satisfy the relevant equation.
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