In the paper, it is introduced a method to det ermine joint reaction forces, constraint forces and internal forces at the cross section of linkages. Based on the principle of compatibility and the ideality of constraints, the methodology is presented to analyze and determine reaction forces in planar mechanisms. | Vietnam Journal of Mechanics, VAST, , No. l (2009), pp. 57 - 64 DETERMINING REACTION FORCES IN PLANAR MECHANISMS Do Sanh1, Dinh Van Phong1, Do Dang Khoa 1 , Phan Dang Phong 2 1 Hanoi University of Technology, . 2 National R esearch Institute of Mechanical Engineering, Hanoi Abstract. In the paper, it is introduced a method to det ermine joint reaction forces, constraint forces and internal forces at the cross section of linkages. Based on the principle of compatibility and the ideality of constraints, the methodology is presented to analyze and determine reaction forces in planar mechanisms. 1. INTRODUCTION There are two main objectives in Dynamics. One is to determine the motion of dynamic systems, and the other is to specify forces exerted on that system. Determining reaction forces is part of the latter. It is important not only to the dynamics analysis of systems and its endurance but also to its control problems, especially the program motion one. In the program motion problem, reaction forces are considered as control inputs whereas constraints can be understood as the program to be realized. Generally, reaction forces are determined based on d'Alembert principle by solving the equations of dynamic equilibrium. The principle reduces the problem of dynamics to a problem in statics by adding the forces of inertia. The forces of inertia combine with the externally applied forces to produce dynamic equilibrium. However, this approach is not always easy to apply for complicated systems, especially for mechanisms. In the paper, another approach to determine reaction forces is presented based on the principle of compatibility and the ideality of constraints. It is a matrix-based approach so that one can easily use common sctftware such as Mathlab, Maple, and MathCad to assist the calculation process. 2. BACKGROUND Let's consider a dynamic system whose positions are located by t he generalized coordinates Qi ( i = 1, m). It assumes that all the constraints
