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Four Bar Linkages
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One important application of four bar linkages is the generation of functions - relating the output of a mechanism with some functional relationship of the input. In the example shown here, the input (X) is proportional to the angular position of link AC with a travel of 60 degree of arc. The output (Y) is the angular position of link BD with a travel of 70 degrees of arc. The desired functional relationship between Y and X is Y = X^2. While X ranges from 1 to 6, Y ranges from 1 to 36. The graph in the lower left hand corner shows the positions of Y vs. X, compared to the desired functional relationship. [Ref 3, p 241]
As shown, the mechanism traces the desired output within about 3% based on full scale. A separate analysis of the linkage produces the track as follows:
The error as a function of X looks like:
The sensitivity of error to the connecting link and output link lengths shows that the geometry used in the animation (cd = 83, bd = 98) is right in the middle of a minimum error valley.
As shown, the mechanism traces the desired output within about 3% based on full scale. See the attached optimization calculations.