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Four-bar Linkage Demonstration

Four-bar Linkage Demonstration
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2022-03-02 23:51
Coordinate GeometryTransformationGeometric Construction
In collections Linkages
This example demonstrates the motion and geometric relationships of a four-bar linkage. It involves core mathematical concepts such as geometric constructions, transformations, and coordinate geometry. GeoGebra commands and objects used include Segment, Circle, Point, Intersect, Midpoint, and Line. Suitable for high school students and mathematics enthusiasts learning about mechanism motion principles.

GeoGebra Commands & Parameters

  1. Segment(O, U) → f
  2. Circle(U, O) → c_{2}
  3. Point(c_{2}) → E
  4. Segment(U, E) → g
  5. Circle(O, U) → d_{2}
  6. Circle(E, U) → e
  7. Intersect(e, d_{2}) → D_{1}, F, ,
  8. Segment(E, F) → h
  9. Segment(F, O) → i
  10. Segment(K, L) → r
  11. Midpoint(r) → N
  12. Circle(N, r) → c
  13. Point(c) → O_{1}
  14. Line(O_{1}, r) → a
  15. Circle(O_{1}, r / 2) → d
  16. Intersect(d, a, 1) → P
  17. Intersect(d, a, 2) → Q
  18. Segment(P, K) → b
  19. Segment(Q, L) → f_1
  20. Segment(P, Q) → j

AI Drawing Prompt Reference

On a plane, start with two given points O and U. Draw the circle centered at O passing through U and the circle centered at U passing through O. Use the intersections to define an endpoint E so that the segment U–E forms one link, then continue the linkage construction by drawing the corresponding circle through U centered at E and intersecting it with the other circle to obtain intersection points D1 and F. Connect E–F and F–O to complete the key geometric relationships of a four-bar linkage. After that, construct auxiliary points P and Q from intersections of a line through O1 with circles based on the same reference radius r, and draw segments P–K, Q–L, and P–Q to show the remaining connections.
The prompt above was compiled from the original drawing commands and is for reference only.