Sarwat N. Hanna

Approximate solution of a flow over a ramp for large Froude number

Abstract An approximate method is presented to solve the problem of steady free-surface flow of an ideal fluid over a semi-infinite ramp in the bottom. Schwartz-Christoffel transformation is used to map the region of flow, in the complex potential-plane, onto the upper half-plane. The Hilbert transformation as well as the perturbation technique are used as a basis for the approximate solution of the problem for large Froude number and small inclination angle of the ramp. General equations, in integral form, for any order of approximation are obtained. Solution up to first-order approximation is discussed and illustrated. Elevation of the free-surface for different ramp heights, different inclination angles of the ramp and different Froude numbers are plotted. An approximate formula of maximum elevation of the free-surface in terms of the ramp heights and its inclination angle is found.

Super-critical free-surface flow over a trapezoidal obstacle

A numerical method based on series truncation is presented to solve the problem of an irrotational, inviscid, incompressible and steady flow over a two-dimensional trapezoidal obstacle, with obstacle height W, lying on the bottom of the running stream. The suggested numerical method for the solution of the fully nonlinear problem is presented for which the flow is super-critical both upstream and downstream. It is found that solutions exist for symmetric trapezoidal for arbitrary size. The results are plotted for different trapezoidal shapes and different values of Froude number F > 1. The effect of the Froude number, the bottom height and the shape of the bottom are discussed.

Approximate solution of gravity flow from a uniform channel over triangular bottom for large Froude number

Abstract An approximate method is applied to solve the problem of steady free-surface flow of an ideal fluid over a semi-infinite triangle in the bottom of an open channel. The solution is based on the combined use of the conformal mapping and the Hilbert solution of a mixed boundary value problem in the upper half-plane. The obtained integral equations have been approximated for large Froude number. The perturbation technique is used as a basis for the approximate solution of the problem for small inclination interior angles of the triangle. Application of such approximations results in equations in integral form for any order of approximation. Solution up to first-order approximation is obtained and is dependent on the triangle height and the bottom shape. The distribution of the pressure coefficient along the bottom boundaries has been studied, and the results are plotted for different Froude number values. Favorable agreement with the results of different methods suggests that this method is effective in dealing with flow problems at large Froude number.

Approximate solution for gravity flow under a Tainter gate

Abstract An approximate shape of the free surface of an inviscid flow under a radial or Tainter gate as well as speed and direction of the flow along that free surface, in a sufficiently small neighbourhood of a common end point between the fixed and the free boundaries, has been presented. Conformal mapping, by Schwartz—Christoffel, has been applied to map the region of flow in the normalized complex potential plane onto the upper half-plane, and following Carters method we are able to find the approximate solution. The effect of the Froude number as well as the shape of the radial gate on the free surface has been studied and the curves are plotted. The accuracy of the results is more than sufficient for practical purposes.

Cartesian Parallel Manipulator Modeling, Control and Simulation

Parallel manipulators are robotic devices that differ from the more traditional serial robotic manipulators by their kinematic structure. Parallel manipulators are composed of multiple closed kinematic loops. Typically, these kinematic loops are formed by two or more kinematic chains that connect a moving platform to a base, where one joint in the chain is actuated and the other joints are passive. This kinematic structure allows parallel manipulators to be driven by actuators positioned on or near the base of the manipulator. In contrast, serial manipulators do not have closed kinematic loops and are usually actuated at each joint along the serial linkage. Accordingly, the actuators that are located at each joint along the serial linkage can account for a significant portion of the loading experienced by the manipulator, whereas the links of a parallel manipulator generally need not carry the load of the actuators. This allows the parallel manipulator links to be made lighter than the links of an analogous serial manipulator. The most noticeable interesting features of parallel mechanisms being: • High payload capacity. • High throughput movements (high accelerations). • High mechanical rigidity. • Low moving mass. • Simple mechanical construction. • Actuators can be located on the base. However, the most noticeable disadvantages being: • They have smaller workspaces than serial manipulators of similar size. • Singularities within working volume. • High coupling between the moving kinematic chains.

Kinematic analysis of a single link flexible manipulator

The present work investigates the dynamic analysis of a single link flexible manipulator with a tip mass using Tangential Coordinate System (TCS) and the Virtual Link Coordinate System (VLCS). The equations of motion are derived using the extended Hamiltons Principle. A third order polynomial trajectory is designed in the joint space. Numerical analysis is carried out for both types of coordinate systems and the total deflection is compared for both types of the coordinate.

Optimal Trajectory of Flexible Manipulators Using Genetic Algorithms

The applications of flexible manipulators are increasing and due to the high demand on fuel consumption there is a need to optimize the energy consumption for stable and durable operation of the flexible manipulators. In the present work the Genetic Algorithm (GA) is employed to optimize the total torque and the torque of the first link of a two-link flexible manipulator with a fourth order polynomial trajectory. The mathematical model of the manipulator is obtained using the extended Hamiltons Principle where the flexible links are treated as Euler- Bernoullis beam theory. A fifth order polynomial trajectory undergoes a rest-to rest maneuvering is proposed as a bench mark for validation.

Stability of periodic plane wave solutions of wave equations

Abstract Nonlinear wave equations with explicit periodic plane wave solutions are considered. The variational equations governing linear stability are derived and solved. The analysis is applied to the special cases of λφ4- and Sine-Gordon wave equations.

On the modeling and control of the Cartesian Parallel Manipulator

The Cartesian Parallel Manipulator (CPM) which proposed by Han Sung Kim, and Lung-Wen Tsai [1] consists of a moving platform that is connected to a fixed base by three limbs. Each limb is made up of one prismatic and three revolute joints and all joint axes are parallel to one another. In this way, each limb provides two rotational constraints to the moving platform and the combined effects of the three limbs lead to an over-constrained mechanism with three translational degrees of freedom. The manipulator behaves like a conventional X-Y-Z Cartesian machine due to the orthogonal arrangement of the three limbs.

Influence of surface tension on free-surface flow over a polygonal and curved obstruction

Abstract In a previous study by the author (1993), the two-dimensional steady flow of a fluid over a polygonal and curved obstruction on the bottom of a stream is discussed, and a linearized solution for the free-surface profile is obtained. This study is generalized to include the effects of surface tension. A linearized theory based upon small elevations or depressions in the bottom is presented, in which the existence of three different branches of solutions is predicted, depending on the Froude number and the surface tension. The results are plotted for two special shapes of the bottom, in the different domains of solution.