The Gough Stewart Robotic manipulator is a parallel manipulator with six-degree of freedom, which has six equations of Kinematics (Inverse and forward), with six variables (Lengths, Position, and Orientation). In this work derived the inverse equations, which used to compute the lengths of the linkages and its changes depended on the position and orientation of the platform's center, then derived the forward equations to calculate the position and orientation of the moving platform in terms of the lengths. This theoretical model of the kinematics analysis of the Gough Stewart has been built into the Simulink package in Matlab to obtain the lengths, position, and orientation for the manipulator at any time of motion. The input parameters (Position and Orientation) in inverse blocks compared with the output parameters (Position and Orientation) in the forward blocks, which show good results.

This work deals with Gough-Stewart robot manipulator, which has six degrees of freedom, six actuators, fixed base, and moving platforms. Here, the Jacobian matrix derived to detect the singular point in the workspace for manipulator at determinant of Jacobian matrix equal to zero, then derived the equation of motion from the dynamic analysis by Lagrange method to verify the singular points with Jacobian where the forces increase rapidly at this point. Finally, design blocks in Simulink include the Jacobian matrix and the equations of motion to detection the singularities at any time for current input parameters (X, Y, Z, α, β, γ), where the determinant of the Jacobian equal to zero at maximum forces.

The study of cracks behaviour in a composite plate is of significant importance in the dynamics of the Mechanical parts in order to avoid design failures due to resonance or high amplitude vibrations. In this paper, a square glass-epoxy composite plate is adopted. The plate has four layers with symmetric and asymmetric lamination. Assuming the cracks are profound as defects. The results were obtained by using a numerical solution of mechanical APDL from ANSYS. It has been found for different boundary conditions that the rank of natural frequencies is decreased by increasing the crack ratio due to the reduction of the plate’s stiffness, whereas the crack direction has no mentioned effect for a small angle of rotation. The accuracy of results is verified by comparing a single case of the current work with other previous investigations. Evaluate the influence of the crack length ratio, angle of the crack rotation, boundary conditions and lamination angles on the natural frequencies of the square composite plate with glass-epoxy materials.