Simulate four-bar linkage mechanisms with adjustable link lengths. Trace coupler curves and classify Grashof type.
Enter the ground, input, coupler, and output lengths to inspect a planar four-bar linkage as its input angle changes. The simulator shows the linkage pose, traces the path of a point attached to the coupler, and classifies the length combination by its Grashof family and inversion. The main trap is reading "Grashof" as "all moving links rotate fully." It only guarantees a full relative rotation somewhere in the chain. With one link grounded, the shortest link's location determines which ground-connected link can act as a crank.
A concrete input and expected output from the current implementation.
Input
Ground link: 6 Input link: 2 Coupler link: 5 Output link: 4
Expected output
Classification: Grashof crank-rocker. The 2-unit input link can rotate continuously, while the 4-unit output link rocks.
The ordered lengths are 2, 4, 5, and 6. The shortest plus longest is 2 + 6 = 8, which is less than 4 + 5 = 9; because the shortest link is adjacent to the fixed ground and is the input, this inversion is a crank-rocker.
Order the four lengths as shortest s, longest l, and intermediate p and q. A strict s + l < p + q gives an ordinary Grashof linkage; equality is the change-point boundary; and s + l > p + q is non-Grashof. The inversion name then depends on the fixed link: grounding the shortest, an adjacent link, or the opposite link produces different motion classes.
For each input angle, the coupler-output joint must be one coupler length from the input joint and one output-link length from the fixed output pivot. Those constraints can have two assembly solutions, one tangent solution, or no real solution. Following one valid assembly branch over changing input angles produces the coupler-point curve. The curve records position only, not speed, force, or elapsed time.
No. The Grashof comparison establishes that continuous relative rotation is possible, but the grounded-link inversion decides which link has that motion. If the shortest link is adjacent to ground and used as the input, it is the crank. If the shortest link is opposite ground, both links connected directly to ground are rockers.
When the shortest plus longest length equals the sum of the other two, the linkage is at the change-point boundary. It can reach a collinear toggle configuration where the two assembly branches meet. Small length changes can move the design to either side of the Grashof boundary, so equality should not be treated as a mechanically robust continuous-rotation design.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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