Marc J. Richard

Many of 2D mechanical models have been developed to simulate liquid sloshing of a partially filled tank with different shapes. However, those models didn't represent properly the complex liquid motion, especially in the case of portable tanks. Indeed, forces exerted on the liquid can be lateral, longitudinal and vertical. Then, liquid displacement and pressure forces applied to the tank walls are undervalued and may cause design flaws. In this case, 2D mechanical models are ineffective for liquid motion simulation. In previous studies, a 3D equivalent mechanical model has been developed. This dynamical model is used to simulate different liquid motion in a partially filled tank that consider any sort of excitement forces and get more accurate results in terms of displacements and pressure forces. In this study, a brief description of the new dynamical model is given, including the liquid discretization process, stiffness and damping coefficients computing method and equations of motion. Afterward, the model is applied to an elliptical cross section tank to obtain displacement and pressure forces of the liquid. Finally, the results are compared to the literature.

The determination of the 6D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables (x,y,z,ϕ,θ,ψ), using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.

The determination of the 6-D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables (x, y, z, φ, θ, ψ), using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue.