Dynamic modal analysis and synthesis of RSCR spatial mechanism

Abstract EN

In this work, analysis and synthesis of RSCR (Revolute -Spherical-Cylindrical -Revolute) spatial mechanism is presented.

This work is based on the Hartenberg-Denavit 4x4 matrix method for the geometric characteristics of the mechanism involving the following three cases : the cylindrical ,the conical and the one-sheet hyperboioid .These cases derive their names .from the nature of the locus of the slider of the linkage as viewed from the output side .Each case is then treated separately by analyzing displacement, velocity acceleration ,dynamic force and dynamic torque in each joint.

Also, method based on a Lagrangian formulation is presented to modelize the RSCR mechanism.

A finite element model is used to study the structural behavior of the links, using the displacements referenced in the rigid body motion configuration as degrees of freedom.

The finite element model is combined with the 4x4 matrix dynamics formulation and the equations of motion are derived from the lagrangian of the system.

Existing Visual Nastran 2002 -type finite element structural analysis program are combined with 4x4 matrix dynamic analysis techniques to yield a procedure capable of computing Free (Modal) Vibration for each case.

Several numerical examples are included in this work, and it was found that the best situation of the mechanism to be in a certain input angle range for cylindrical case.

While for one-sheet hyperboioid, the mechanism works in a limited input angle range similar to the cone case, and as a result, the mechanism is considered as a rocker - rocker type.