Computations analysis of a four-link spherical mechanism for a spatial simulator

Machine-building Engineering and Machine Science

Machine science, drive systems and machinery


Faizov M. R.*, Khabibullin F. F.**

Kazan National Research Technical University named after A.N. Tupolev, KNRTU-KAI, 10, Karl Marks str., Kazan, 420111, Russia



This work presents a spherical mechanism with four links, interconnected by rotational kinematic pairs. Based on the spherical mechanism by the type of a crank-and-rocker mechanism, a simulator, shown on the figures of the article, is being developed. While the mechanism kinematics analysis we create the structural scheme with notations of its sides and links. For the convenience, and simplified and advantageous computation it was determined that the opposite situated links would have equal angles of crossing. Two techniques are employed while spherical mechanism computing. The first technique consists in developing a mechanism mathematical model. Additional angles and hinges points of a mechanism, which will be employed in subsequent computations, are accounted for while the mathematical model developing. Since we use two techniques of comparison, we equate both techniques through the same speed and rotation time. Having performed kinematic computation, we specify the complete revolution of rotation of the mechanism. During equations analysis we make to the conclusion that with complete revolution of the leading link the driven links manage performing one-half revolution. While graphs plotting of angular speeds and accelerations maximum and minimum points can be observed. Likewise, the angular acceleration increases three-fold from the angular acceleration. For the complete pattern of computations, we perform analysis of moment of inertia of the mechanism connecting rod, which will be the capsule of the simulator. The centrifugal moment of inertia through the point, located at the center of the connecting rod lengthwise the direction cosines, was obtained for the mathematical model. The moment of inertia of leading and driven links is determined by the simpler technique. For precise computations, the displacement angle of the connecting rod relative to the driven crank in hinges are obtained. The angle of rotation of both connecting rod and its center point on each axis separately is being determined. For convenience, the values of mass and radius are set as constants. In the future, we shall set these values from the definite task of the mechanism. Having plotted the graph of the connecting rod moment of inertia by the two techniques, we obtain several maximum points of loads.


four-link spherical mechanism, spherical crank-and-rocker mechanism, moment of instant rotation, connecting rod moment of inertia


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