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By J. M. Skowronski

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X q ^ - ^ d t . 9) implies d fdL\ _dpi__ . 13), pi = Q? + Q( + dL/dq t Pt = Q? 14), SH/d . 24) proves difficult. Then T i s not an explicit function of t and so neither are L and H. 15) becomes the tautology 0 = 0 and we have . 16) ? 1). Technically, we proceed as follows. 10) becomes i which is the total energy of the system. 18) $ = A' (q)p. 18), we obtain T(q,p). 20) which yields T(q,p)=\YL^PiPr Z i 0-5-21) j Then we immediately have H(q,p) = T(q,p) + i^{q). {q p) Qf(q p u ). With the above, Eqs.


The primary work space is illustrated in Fig. 5 on a 3-joint ceiling-based RRP-manipulator working on a planar bench. It is of the type often met in the electronic assembly workshops. 0 in. 0 in. The suspension base 0 in 0 ^ , rj , ( is translated from the work space coordinates 0 ^ rj C by a constant vector r = const, which does not introduce any changes in our model since there is no motion between the base and the workbench. While the reference point reaches, the whole arm is confronted with obstacles which may disallow the reaching.

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