Analytical Method for Determination of Internal Forces of Mechanisms and Manipulators

This paper presents a theory for the analytical determination of internal forces in the links of planar linkage mechanisms and manipulators with statically determinate structures, considering the distributed dynamic loads. Linkage mechanisms and manipulators were divided into elements and joints. Discrete models were created for both the elements and the entire mechanism. The dynamic equations of equilibrium for the discrete model of the elements and the hinged and rigid joints, under the action of longitudinal and transverse distributed dynamic trapezoidal loads, were derived. In the dynamic equations of the equilibrium of the discrete model of the elements and joints, the connections between the components of the force vector in the calculated cross-sections and the geometric, physical, and kinematic characteristics of the element were established for its plane-parallel motion. According to the developed technique, programs were created in the Maple system, and animations of the motion of the mechanisms were produced. The links were constructed with the intensity of transverse- and longitudinal-distributed dynamic loads, bending moments, and shearing and normal forces, depending on the kinematic characteristics of the links