This paper aims at experimentally investigating the dynamical behaviors when a system of rigid bodies undergoes so-called paradoxical situations. An experimental setup corresponding to the analytical model presented in our prior work [28] is developed, in which a two-link robotic system comes into contact with a moving rail. The experimental results clearly show that a tangential impact does exist at the contact point and takes a peculiar property well coinciding with the maximum dissipation principle stated in [11] by Moreau; the relative tangential velocity of the contact point must immediately approach zero once a Painlevé paradox occurs. After the tangential impact, a bouncing motion may be excited and is influenced by the speed of the moving rail. We adopt the tangential impact rule presented in [28] to determine the post-impact velocities of the system, and use an event-driven algorithm to perform numerical simulations. The qualitative comparisons between the numerical and experimental results are carried out and show good agreements. This study not only presents an experimental support for the shock assumption related to the problem of the Painlevé paradox, but can also find its applications in better understanding the instability phenomena appearing in robotic systems.

The hopping or bouncing motion can be observed when robotic manipulators are sliding on a rough surface. Making clear the reason of generating such phenomenon is important for the control and dynamical analysis for mechanical systems. In particular, such phenomenon may be related to the problem of Painlevé paradox. By using LCP theory, a general criterion for identifying the bouncing motion appearing in a planar multibody system subject to single unilateral constraint is established, and found its application to a two-link robotic manipulator that comes in contact with a rough constantly moving belt. The admissible set in state space that can assure the manipulator keeping contact with the rough surface is investigated, and found which is influenced by the value of the friction coefficient and the configuration of the system. Painlevé paradox can cause either multiple solutions or non-existence of solutions in calculating contact force. Developing some methods to fill in the flaw is also important for perfecting the theory of rigid-body dynamics. The properties of the tangential impact relating to the inconsistent case of Painlevé paradox have been discovered in this paper, and a jump rule for determining the post-states after the tangential impact finishes is developed. Finally, the comprehensively numerical simulation for the two-link robotic manipulator is

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Volute is an important hydraulic part of centrifugal pump, hydraulic loss within pump volute takes up a large part of total hydraulic loss within pump, thus appropriate design of pump volute has significant meaning to centrifugal pump performance. In this paper, numerical method was adopted to investigate volute main geometric parameters, including volute throat area, volute cross-section shape, design rule of spiral development area, and radial gap between impeller and volute tongue to pump performance. A design method of high-efficiency pump volute is developed through the influence of volute main geometric parameters to pump performance. This paper could provide theoretical guidance to high-efficiency pump volute design.

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The flow problem resulting from the stretching of a surface with convective conditions in a magnetohydrodynamic nanofluid with solar radiation is examined. Both heat and nanoparticle mass transfer convective conditions are employed. An incompressible third grade fluid which exhibits shear thinning and shear thickening characteristics is used as a base fluid. Concept of convective nanoparticle mass condition is introduced. Effects of Brownian motion and thermophoresis on magnetohydrodynamic flow of nanofluid are accounted in the presence of thermal radiation. Energy equation incorporates the features of Joule heating. The impact of physical parameters on the temperature and nanoparticle concentration has been pointed out. Numerical values of skin-friction coefficient are presented and analysed. It is hoped that this present investigation serves as a stimulus for the next generation of solar film collectors, heat exchangers technology, material processing, geothermal energy storage, and all those processes which are highly affected by the heat enhancement concept.