FORWARD POSITION ANALYSIS OF THE SP-PS-RS ARCHITECTURES

R. Di Gregorio

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  37. [37] R. Di Gregorio, Analytic form solution of the forward position analysis of three-legged parallel mechanisms generating SRPS-RS structures, Mechanism and Machine Theory, 2005, in press. Appendix If n0 and n1 simultaneously vanish, then (10) yield: p1 = (g2 + j2 1 )(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 p1 and p0, respectively, into (7) yields: p4(a2 )2 + p3(a2 )a + p2(a2 ) + a[(g2 + j1 2 )(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 equations coincide): [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-hand side of (A.4) is equated to zero, an equation that coincides with (3c) is obtained, which proves that, if n0 and n1 simultaneously vanish, (3c) is contained in (7).

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