Abstract:

The rigid body represents an important concept in theoretical and technical mechanics, both due to its simplicity and its applicability for the modeling in first¬ order approximation of various mechanical systems, such as mechanisms, structures, components that transmit the motion of vibrating systems etc. In most technical applications, rigid bodies are connected by constrains, i.e. by systems that limit their relative motions. Various applications, as those in statics, that study the equilibrium conditions of systems, in dynamics, that study the motions of systems under the action of forces, or those of strength of materials, that calculate the capacity of systems to resist forces that act upon them, require the prior determination of reactions developed in the constraints between the bodies of the system. Such considerations represent the reason for which the curricula of the first years of engineering faculties in most universities of the world include chapters dedicated to the equilibrium of a rigid body subjected to constraints. The calculation methods presented in these chapters represent an indispensable instrument in engineering education. However, limiting the teaching process to theoretical presentation can prove inefficient and tedious. For this reason, the authors of the present paper have developed a computer program that determines the reactions developed in certain types of constraints of a rigid body, in equilibrium under a system of forces and couples of forces. The code allows defining three types of constraints (simple support, hinge and clamping), as well as forces (with their components and application points) and couples acting upon the body. The reactions are computed and displayed graphically together with the applied forces. The program can be used for the verification of the results obtained by the students by manual calculations, as well as for the visualization of the effects of the modifications made to the configuration of the system, such as changes of applied forces and couples, or modification of the constraints. The program adds up to a virtual laboratory dedicated to the study of mechanics and developed by the author in recent years.

Keywords:

Engineering mechanics, rigid body, in-class study, constraints.