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. KEYWORDS: Kinematics of Machines; Linkage; Numerical Solutions; Graph Theory; Machine Dynamics; Computer Simulation; Mechanism; Linkage Kinematics