The Numerical Study of Efforts from the 4r Symmetrical Spherical Quadrilateral Mechanism

Abstract

The 4r spherical quadrilateral mechanism is made of three mobile elements and one fixed (the basis) connected through the four revolute kinematic pairs, whose axes intersect at the same point. It is multiple statically indeterminate and for calculating the efforts from kinematic pairs it is using the elastic linear calculation, in which the mechanism elements are considered deformabile rigid. The displacements in the local systems of reference, produced by external requests are small and defined by the vectors of small rotations, which act similarly to the angular velocity and small displacements, defined by displacement vectors. The use of the relative displacements method, with the expression of displacements under the form of a column matrix in plukeriane coordinates, makes possible the calculation of efforts and reactions in the kinematic pairs of this mechanism. The results of the numerical solving of this problem will be presented under the form of a diagrams and will be commented.