R. Di Gregorio
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Di Gregorio, Analytic form solution of the forward positionanalysis of three-legged parallel mechanisms generating SR-PS-RS structures, Mechanism and Machine Theory, 2005, inpress.AppendixIf n0 and n1 simultaneously vanish, then (10) yield:p1 = (g2 + j21 )(j1p4 − p3) + j1(g2p4 + p2) (A.1)p0 = −g2[j1(j1p4 − p3) + g2p4 + p2] (A.2)The substitution of expressions (A.1) and (A.2) for p1and p0, respectively, into (7) yields:p4(a2)2+ p3(a2)a + p2(a2) + a[(g2 + j12)(j1p4 − p3)+ j1(g2p4 + p2)] − g2[j1(j1p4 − p3) + g2p4 + p2] = 0(A.3)Equation (A.3) can be factorized as follows (note that,if we expand (A.3) and (A.4), the resulting equationscoincide):[p4a2+ (p3 − j1p4)a + g2p4 + p2 + j1(j1p4 − p3)]× (a2+ j1a − g2) = 0 (A.4)If the second factor of the expression at the left-handside of (A.4) is equated to zero, an equation that coincideswith (3c) is obtained, which proves that, if n0 and n1simultaneously vanish, (3c) is contained in (7).
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