Solving and Analyzing Nonlinear Multibody Dynamic Engineering Systems with a Piecewise Linearization Approach

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Almost all dynamic systems used in engineering fields are multibody dynamic (MBD) systems, such as those in robotics, aircrafts, artificial limbs, etc. Solving for such systems can be challenging as the systems are typically multidimensional and can be nonlinear and complex with a high degree of coupling between variables. In practice, therefore, one may have to rely on numerical or approximate approaches for solving the systems as analytical solutions of the MBD systems is difficult to achieve, if not impossible. Moreover, in solving such systems with existing methods, linearization and simplifications are usually unavoidable, which negatively affect the accuracy and reliability and may even lead to erroneous solutions. An innovative methodology with higher degree of accuracy and reliability is therefore desired for solving and analyzing MBD systems in general. Significant research progresses have been achieved by the applicant and his research team in developing new analytical and numerical methods for solving nonlinear complex dynamic systems. Highly accurate and reliable results have been obtained with less computational time, when compared against other numerical methods such as the most popular Runge-Kutta method. The methods and techniques developed by the applicant provide a solid foundation and tools for advancing the proposed research program. The aim of the proposed research program is to develop a piecewise linearization approach suitable for accurately and reliably solving and analyzing nonlinear MBD systems which are difficult to solve with desired accuracy and reliability using existing methods. To achieve the aim, the P-T method previously developed by the applicant and other methods will be modified and extended. The proposed research will combine the modified P-T method, Taylor expansion, Laplacian transformation, and residue theorem to theoretically and numerically solve for MBD systems. Analytical solutions for linear MBD systems are expected to be achieved and continuous semi-analytical solutions, along with numerical solutions, are expected to be derived for nonlinear MBD systems. An engineering application oriented algorithm for solving nonlinear MBD systems is also expected to be developed using the aforementioned piecewise linearization approach. The approach to be developed, along with the computational algorithm and their orientation towards industrial applications, will significantly advance current approaches for solving, analyzing and optimizing linear and nonlinear MBD systems. The results of the proposed research program will therefore tangibly improve the design as well as operation and control quality of MBD systems. This is particularly significant for complex, precise, highspeed and AI controlled equipment and machines that are in increasing demand in industry.