Numerical Solutions for Kinematics of Multi-bar Mechanisms Using Graph Theory and Computer Simulations

A method is presented to demonstrate the application of computer simulations in the kinematic analysis of planar mechanisms, emphasizing its use in teaching the latter topic in a corresponding undergraduate course. Concepts of rigid-body dynamics are utilized in the kinematics of machines to analyze the motions (and forces in dynamics) transmitted within multiple interconnected links that make a mechanism, such as a car engine, airplane landing gear, press machine, door closer, and so on. Due to the tediousness of the analytical solutions, most textbooks limit the derivation of the equations to four-bar linkages like crank-rocker and crank-slider mechanisms. Benefiting from the advancements in computer programs, such as MATLAB, and their efficiency in solving large systems of linear and nonlinear equations, a method is proposed to facilitate teaching kinematic analysis of multi-bar linkages to undergraduate students while fostering the application of computational engineering via real-life examples. The results obtained from this method are shown to be in excellent agreement with the algebraic solution of the relative motion equations for each element in the mechanism.