Static force analysis of mechanisms with four-bar linkages based on flexibility conditions

The four-bar linkages are widely used in both planar and spatial mechanisms and robotic manipulators. Static force analysis of the four-bar mechanisms subjected to spatial external loading working under gravitational forces is formulated in this article. The formulation is based on structural matrix force and stiffness methods with the free-body diagrams for each of the links considered. The four-bar mechanism considered is over-determined as there are additional constraints compared to a statically determined four-bar mechanism. A method of solution, based on the matrix force analysis, incorporating the flexibility of the mechanism is given. The methodology is simulated for a mechanism with a planar four-bar linkage where the plane of motion could be varied by rotating about a revolute joint that connects the four-bar linkage to the base.