Development and application of planar computational general-purpose constrained multibody simulations in Matlab with simple graphical/visualization capability

Abstract

This study demonstrates the implementation and advantages in utilizing the Matlab programming environment for general-purpose simulations of constrained planar dynamic and kinematic multibody mechanical systems. Many currently available tools have a focus and can have limited flexibility through difficulty in data entry, limited access to source code, analysis of data or use of programming languages not readily taught. A Matlab source code is created, which includes the use of Microsoft Excel and GUI's created in GUIDE that allow a user to construct, simulate and analyze multibody systems in Matlab. This technique allows the user to utilize any of Matlab toolboxes for unique problems or integrate the base program into a Simulink environment. An overview of the general code structure and multibody kinematics and dynamics equations used are shown in this paper. For kinematic simulations, the system's Cartesian coordinates are found by finding the roots of the constraints vector at each time step. For the dynamic systems, the solver uses a numerical integration scheme with augmented form of the constrained equations of motion to solve for the system's accelerations. Examples are presented demonstrating the benefits of using the Matlab environment and the flexibility to easily expand the code to simulate unique problems. These examples include an Ackermann steering for automotive applications and a double pendulum at the influence of gravity. The last example shows how a custom function can be created to inject forces into the dynamic solver in order to simulate a structural beam at the influence of a heavy pendulum.