Computer-aided mechanism design: A symbolic-computing approach (Q1802270)

Single degree of freedom plane linkages (formed of rigid bars with unfettered joints) must consist of \(\geq 4\) bars. There are a few linkages of 5 and 6 bars that allow motions not executable by the 4-bar linkage. The condition of one degree of freedom imposes a determinant condition on the motions of these linkages. The authors note that modern symbolic computation programs can solve these equations in closed form: the condition that given 5 or 6 dimensional determinants with complex coefficients vanish splits into two real polynomial equations whose common root can be found by Sylvester's dialytical method from a linear equation. The corresponding computations are quite hopeless for hand calculation. Sylvester's resultant naturally still has to be solved numerically as polynomial equation of high degree (with the accompanying danger of ill conditioning, making a big question whether practical engineering can really gain from these computations as compared to the usual trial and error approximations).