By R. Peierls

``Nuclear Physics'' offers with Bohr's paintings on nuclear physics which all started within the pre-1932 days together with his considering deeply, yet inconclusively in regards to the seeming contradictions then provided by means of the proof in regards to the nucleus. In 1936, Bohr recognized and defined the insights supplied via neutron scattering experiments; the thrill of this new realizing and its extension and consolidation occupied a lot of the following years. In 1939, he was once back first in realizing the basic positive aspects of the newly found phenomenon of fission, using effectively the viewpoint of nuclear reactions which he had built during the last 3 years. Later, in 1949-50, he was once inspired via the good fortune of the nuclear shell version, which at the face of it appeared tough to reconcile with the image of the heavily interacting nucleons which he had pioneered in 1936. Bohr placed a lot attempt into clarifying this paradox.

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Modeles des Robots Manipulateurs. Application a leur Commande", CEPADUES, Toulouse, France, (1984). *" * Professor, ** Graduate Student, Mechanical Design and Production Department Faculty of Engineering, Cairo University, Giza 12316- Egypt. eg Abstract This paper presents a systematic simulation algorithm for flexible manipulators with revolute joints. This algorithm takes into consideration the flexibility of links and joints, structural damping and joints' internal clearance. Flexible multi-body dynamics formulations are employed to obtain the equations of motion of such manipulators by considering their links as a lumped and as a consistent mass system.

0 m ] O02-- I . 02 11 e 0 0~ o, i o. 5 Fig. 10. E x a m p l e 1 Difference in Orientation from Rigid System at point A Fig. 11. E x a m p l e 2: T w o - L i n k M a n i p u l a t o r Current Advances in Mechanical Design and Production, MDP-7 i!!. I-T~ 35 J -3 (Sec) T'~ne (See) (a) Actuator 1 Torque (b) Actuator 2 Torque Fig. 12. Example 2 Actuator Torques 'Fi ,i /// :L , |~ ~,~ t~,-,,: Ii l++',',=_.. , 1/ o [ "~ os I i s l~,ne (-) 2 2'S ' I . i 3 3s (a) Orientation of Linkl at Point A o os t t l ' * .

Fourth order Runge-Kutta [13] is used for time step integration. 4. Example 1: One-Link Manipulator A single link (Fig. m, (Fig. 8), no damping is considered and the revolute joint is assumed to be perfect. 0 rad/s with no initial strain. Simulation is performed for 4 cases: a rigid body system, 4 and 8 element per link lumped mass, and 4-element per link consistent mass. The expected motion of the link is to be vibrating but its gross motion should be following the motion of the rigid body system.

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