Kinetostatic analysis of assur dyads

The core of computer-aided design systems for design and calculation of plane mechanisms is the modular mathematical methods of studying the dynamics of the mechanisms. The most common approach is Multibody Dynamics, where a mechanism is divided into links that are assumed to be rigid bodies. The number of links is equal to the number of analysis modules. Another approach takes into consideration the structure of a mechanism, which can allow a reduction in the number of modules that need analysis. This approach necessitates the development of a plane mechanism classification and a comprehensive set of mathematical methods for analyzing the kinematics, kinetostatics, and dynamics of all possible structural elements. Of all the classification systems, Artobolevsky's one is the most aligned with the stated needs. Class II plane mechanisms according to the pointed classification have been fully covered by modular kinematic analysis algorithms, but kinetostatic analysis remains limited to a graph-analytical approach. The paper presents a unified analytical method of kinetostatic analysis of Assur dyads, which, along with class I mechanisms, constitute the structural elements of the class II mechanisms. The method is based on the vector equations of kinetostatics, solved using vector algebra tools. A full kinematic analysis must be performed beforehand. Active forces, inertial forces and reactions in kinematic pairs are represented as vectors, decomposed in the local bases rigidly attached to the dyad's links. The bases must be determined during the position analysis. The presented method is appropriate to use in combination with kinematic analysis, which also relies on vector algebra methods. It can be algorithmized and integrated into computer-aided design systems for class II plane mechanisms.