Peaucellier-Lipkin Linkage: Straight-Line Generator

① This example demonstrates the classic Peaucellier-Lipkin linkage, a mechanical linkage that converts circular motion into exact straight-line motion through a series of hinged rods. ② Core mathematical concepts include inversion transformation, properties of rhombi and parallelograms, circle geometry, and locus generation, involving segment lengths, angles, and symmetry. ③ Construction highlights: Based on the construction summary, GeoGebra commands such as Line, Distance, Segment, Midpoint, Circle, Intersect, CircleArc, Point, and Ray are used to build multiple points (O, Q, P, C, D, E, F, I, J, G, H, etc.), circles (c, k, r), segments (l_1, l_2, b, e, a, q, d, m, n, j, l, s, t, i), and auxiliary objects. Intersections and midpoints drive the linkage, and tracing point L reveals a straight-line locus. ④ Suitable for high school and above, this example is ideal for exploring geometric construction, transformations, and loci, as well as for mathematical modeling or mechanism design, helping students understand inversion and linkage mathematics.