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# lab6(1) - Chapter 6 Solving Algebraic Equations with C/C...

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Chapter 6 Solving Algebraic Equations with C/C++ Background , A 4-bar linkage is a complex mechanism that allows us to convert simple rota- tional input motions (say from a motor or water wheel) to a wide variety of output motions. The conﬁguration above is known as a rocker-crank where complete turns of the crank or input result in a rocking motion in the output link. But how do we determine what input angle maps to a desired output angle? Consider a general 4-bar linkage with the following geometries: Given the above link lengths and angles, we can derive the relationship between the input angle and output angle using vector analysis. Consider vectors deﬁned along each link such that: ~a + ~ b = ~ c + ~ d 71

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CHAPTER 6. SOLVING ALGEBRAIC EQUATIONS WITH C/C++ 72 Figure 6.1: A 4-bar linkage with input alpha, output beta, and link lengths a, b, c, and d. We can expand this relationship and ﬁnd that: a sin( α ) + b sin( γ ) = c sin( β ) a cos( α ) + b cos( γ ) = d + c cos( β ) Rearranging. ... b
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lab6(1) - Chapter 6 Solving Algebraic Equations with C/C...

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