By M. F. Hassan
The foreign convention on Mechanical layout and creation has through the years demonstrated itself as a great discussion board for the alternate of rules in those verified fields. the 1st of those meetings was once held in 1979. The 7th, and newest, convention within the sequence used to be held in Cairo in the course of February 15-17, 2000.International engineers and scientists accumulated to switch stories and spotlight the state of the art learn within the fields of mechanical layout and construction. moreover a heavy emphasis used to be put on the problem of know-how transfer.Over a hundred papers have been authorised for presentation on the convention. present Advances in Mechanical layout & construction VII doesn't, although, try to submit the entire paintings offered yet as a substitute deals a pattern that represents the standard and breadth of either the paintings and the conference.Ten invited papers and fifty four traditional papers were chosen for inclusion in those lawsuits. They conceal a variety of uncomplicated and utilized themes that may be labeled into six major different types: method Dynamics, sturdy Mechanics, fabric technological know-how, production techniques, layout and Tribology, and business Engineering and its purposes.
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The stiffness forces due to this element at nodes i and j are first computed in the direction of element axis ui and vi then transformed to the direction of the global axes. These forces are given by: Fu i -- Fvi = Mzi -Fuj -F~j Mzj = = = = Ka du KbjdV - Kb2d0 -Kb2dv + Kb3 dO -Mzi - FviLo (2) Current Advances in Mechanical Design and Production, MDP-7 29 with: EA Ka = ' 6EI K b 2 = - -L2o 12EI Kbl = ' - L To ' du : c , ( x , - x,)+ s , ( y j - y , ) - L o & , 4EI Kb3 = - - ~ , dO = Oj -0 i -x,)+ c,(yj-y,) - - o d v : -si(x i where Ka is the axial stiffness constant, Kbl, Kb2, Kb3 are bending stiffness constants, du, dv, dO are the axial, transverse and angular deflection of the element respectively, E is the modulus of elasticity, A is the link cross sectional area and I is its second moment of area.
Among the previous four mDH parameters three are constants (ai-1, a i - 1 , ri) and one is variable (0i = qi). The geometry of a particular manipulator is then defined by the table of the twenty four mDH parameters among whose eighteen are constants and six variables. For example the table corresponding to the RMS 6R type manipulator is indicated hereafter: i 1 2 3 4 ai-1 o 0 0 o as a3 Oi ri ql 0 q2 0 q3 0 q4 0 . 5 . . 6 a4 0 q5 0 q6 0 , , 4. DEFINITION OF THE MANIPULATOR CONFIGURATION AND OF THE END E F F E C T O R LOCATION The manipulator configuration q is defined by six generalized coordinates: q = (ql q2 .
Because of the impossibility to express these roots literally our method will be only numeric, although it allows the literal writing of this equation coeffcients. Nevertheless this literal writing is generally too complicated to be of any use. For a particular 6R type manipulator, the algorithm we have developed allows to compute numerically all the complex configurations corresponding to a particular given end effector location. Among these configurations, we extract the real ones. Finally, we give an example of a very simple, but non academic, particular 6R type manipulator- the RMS of the American shuttle - for which we obtain sixteen real configurations corresponding to a particular given end effector location.