Advanced Mechanism Design: Analysis and Synthesis Vol. II by Sandor, Arthur G. Erdman

By Sandor, Arthur G. Erdman

Sr/grad point textual content for a moment direction in mechanisms, kinematics or laptop dynamics.

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15. , 1979, Mathematical Principles of Mechanics and Electromagnetism. Part A: Analytical and Continuum Mechanics, Plenum Press, New York and London. Fundamentals of Rigid-Body Mechanics 55 16. Huston, R. L. sserello, C. E .. 1974. ch", ASl\JE J. Applied ]'vfechanics, Vol. 41. pp. 1130~1131. 17. " and Weimcr, F. , 1981. ions", ASME J. Applied Mechanics. Vol. 48. pp. 177 ~ 182. 18. , and Nash. , 1989. , Engelwood Cliffs. 19. vridis, J. , 1990, ·' i\Iaggi 's equations of motion and t he determina t ion of constraint reactions".

What we shall do in this sectiou is deri vc the Newton-EulET equations. eqs. 206a & b), using a Lagrangian formulation. First. sumption t hat tlwse coordinates arenot independent. hut subject to p < n indcpendcnt. s. 2. For our purposes in this subsection. o bc algcbrnir in the generalized coordinates. frec of thcir tinw-dcrivativcs. Morcovcr. 218) wlwrc vcctors fand 0 arc both {J-dinwnsional. alter rcprcscnt ing thc p-dimensional zcro vector. Iw forcgoing constraint equations. wc obtain thc differential constraints •)jl)· ) ( ·) -·- 'd whcrc A is a I' X 'II rnatrix and b is a 7'-dinH'nsional vector, as ddincd lwlow: (df, I iJq,) r(iJf2~ih{l) (iJf, I iJq2 l (iJfd iJq2) (iJfl'l iJq,) b i)f = -- = iJ!

Let the body at band be acted upon by a wrench of force f applied at its mass center, and a torque nc. 206a) 48 J. Angelesand A. 206b) The momentum p and the angular momentum he of a rigid body moving with an angular velocity w are defined below, the angular momentum being taken with respect to the mass center. 206b) are known as the Newton-Eu/er equations. 210) where 0 and 1 denote, again, the 3 X 3 zero and identity matrices. A similar 6 x 6 matrix was defined by von Mises, who called it the inertia dyad [13].

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